%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP045^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:06 AM UTC 2026
% Result : Theorem 28.24s 5.60s
% Output : Refutation 28.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP045^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n013.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:23 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : ITP045^2 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.47 % Domain : Interactive Theorem Proving
% 0.31/0.47 % Problem : Sledgehammer Determinacy problem prob_286__3350038_1
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Des21]
% 0.31/0.47 % Names : Determinacy/prob_286__3350038_1 [Des21]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.67 v8.1.0, 0.75 v7.5.0
% 0.31/0.47 % Syntax : Number of formulae : 333 ( 96 unt; 71 typ; 0 def)
% 0.31/0.47 % Number of atoms : 837 ( 375 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 13 ( 3 avg)
% 0.31/0.47 % Number of connectives : 23496 ( 118 ~; 33 |; 56 &;22909 @)
% 0.31/0.47 % ( 0 <=>; 380 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 44 ( 13 avg)
% 0.31/0.47 % Number of types : 5 ( 4 usr)
% 0.31/0.47 % Number of type conns : 2601 (2601 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 70 ( 67 usr; 11 con; 0-7 aty)
% 0.31/0.47 % Number of variables : 1699 ( 57 ^;1480 !; 52 ?;1699 :)
% 0.31/0.47 % ( 110 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.47 % SPC : TH1_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:58.659
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % Could-be-implicit typings (10)
% 0.31/0.47 thf(ty_t_Product__Type_Oprod,type,
% 0.31/0.47 product_prod: $tType > $tType > $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Option_Ooption,type,
% 0.31/0.47 option: $tType > $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Data_Oconst,type,
% 0.31/0.47 const: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Data_Ocntxt,type,
% 0.31/0.47 cntxt: $tType > $tType > $tType > $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Data_Oexpr,type,
% 0.31/0.47 expr: $tType > $tType > $tType > $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Data_Oval,type,
% 0.31/0.47 val: $tType > $tType > $tType > $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Set_Oset,type,
% 0.31/0.47 set: $tType > $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_tf_v,type,
% 0.31/0.47 v: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_tf_r,type,
% 0.31/0.47 r: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_tf_l,type,
% 0.31/0.47 l: $tType ).
% 0.31/0.47
% 0.31/0.47 % Explicit typings (61)
% 0.31/0.47 thf(sy_cl_HOL_Otype,type,
% 0.31/0.47 type:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.31/0.47 order:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Ocombine,type,
% 0.31/0.47 combine:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( A > ( option @ B ) ) > A > ( option @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oconst_OF,type,
% 0.31/0.47 f: const ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oconst_OT,type,
% 0.31/0.47 t: const ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oconst_OUnit,type,
% 0.31/0.47 unit: const ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Odoms,type,
% 0.31/0.47 doms:
% 0.31/0.47 !>[L: $tType,R: $tType,V: $tType] : ( ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > ( set @ L ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oexpr_OAssign,type,
% 0.31/0.47 assign:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oexpr_OIte,type,
% 0.31/0.47 ite:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oexpr_ORead,type,
% 0.31/0.47 read:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oexpr_ORef,type,
% 0.31/0.47 ref:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oexpr_ORfork,type,
% 0.31/0.47 rfork:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oexpr_ORjoin,type,
% 0.31/0.47 rjoin:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oexpr_OVE,type,
% 0.31/0.47 ve:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( val @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oplug,type,
% 0.31/0.47 plug:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( cntxt @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oval_OCV,type,
% 0.31/0.47 cv:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( const > ( val @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oval_OLoc,type,
% 0.31/0.47 loc:
% 0.31/0.47 !>[L: $tType,R: $tType,V: $tType] : ( L > ( val @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Data_Oval_ORid,type,
% 0.31/0.47 rid:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( R > ( val @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Executions_Osubstitution_Oexecution,type,
% 0.31/0.47 execution:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( expr @ R @ L @ V ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Executions_Osubstitution_Oinductive__invariant,type,
% 0.31/0.47 inductive_invariant:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Executions_Osubstitution_Omaximal__execution,type,
% 0.31/0.47 maximal_execution:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( expr @ R @ L @ V ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Executions_Osubstitution_Oreachable,type,
% 0.31/0.47 reachable:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Executions_Osubstitution_Osteps,type,
% 0.31/0.47 steps:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( set @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Executions_Osubstitution_Oterminates__in,type,
% 0.31/0.47 terminates_in:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( expr @ R @ L @ V ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Finite__Set_Ofinite,type,
% 0.31/0.47 finite_finite:
% 0.31/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Fun_Ofun__upd,type,
% 0.31/0.47 fun_upd:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_If,type,
% 0.31/0.47 if:
% 0.31/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Map_Odom,type,
% 0.31/0.47 dom:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Occurrences_OLID_092_060_094sub_062G,type,
% 0.31/0.47 lID_G:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( set @ L ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Occurrences_OLID_092_060_094sub_062L,type,
% 0.31/0.47 lID_L:
% 0.31/0.47 !>[L: $tType,R: $tType,V: $tType] : ( ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > ( set @ L ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Occurrences_ORID_092_060_094sub_062G,type,
% 0.31/0.47 rID_G:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( set @ R ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Occurrences_ORID_092_060_094sub_062L,type,
% 0.31/0.47 rID_L:
% 0.31/0.47 !>[L: $tType,R: $tType,V: $tType] : ( ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > ( set @ R ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume,type,
% 0.31/0.47 domains_subsume:
% 0.31/0.47 !>[L: $tType,R: $tType,V: $tType] : ( ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally,type,
% 0.31/0.47 domain398919503obally:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step,type,
% 0.31/0.47 revision_step:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > R > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed,type,
% 0.31/0.47 revisi1433015572elaxed:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > R > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible,type,
% 0.31/0.47 subsumes_accessible:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( R > R > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally,type,
% 0.31/0.47 subsum380726323obally:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_ONone,type,
% 0.31/0.47 none:
% 0.31/0.47 !>[A: $tType] : ( option @ A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_OSome,type,
% 0.31/0.47 some:
% 0.31/0.47 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Othe,type,
% 0.31/0.47 the:
% 0.31/0.47 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/0.47 ord_less_eq:
% 0.31/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.31/0.47 top_top:
% 0.31/0.47 !>[A: $tType] : A ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair,type,
% 0.31/0.47 product_Pair:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Renaming_Oeq__states,type,
% 0.31/0.47 eq_states:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect,type,
% 0.31/0.47 collect:
% 0.31/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Substitution_Osubstitution,type,
% 0.31/0.47 substitution:
% 0.31/0.47 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Transitive__Closure_Ortrancl,type,
% 0.31/0.47 transitive_rtrancl:
% 0.31/0.47 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member,type,
% 0.31/0.47 member:
% 0.31/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v__092_060E_062,type,
% 0.31/0.47 e: cntxt @ r @ l @ v ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v__092_060sigma_062,type,
% 0.31/0.47 sigma: l > ( option @ ( val @ r @ l @ v ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v__092_060tau_062,type,
% 0.31/0.47 tau: l > ( option @ ( val @ r @ l @ v ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_e,type,
% 0.31/0.47 e2: expr @ r @ l @ v ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_r,type,
% 0.31/0.47 r2: r ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_r_H,type,
% 0.31/0.47 r3: r ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_r_H_H,type,
% 0.31/0.47 r4: r ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_s_092_060_094sub_0621,type,
% 0.31/0.47 s_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_s_092_060_094sub_0622,type,
% 0.31/0.47 s_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_s_092_060_094sub_0622_H,type,
% 0.31/0.47 s_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_subst,type,
% 0.31/0.47 subst: ( expr @ r @ l @ v ) > v > ( expr @ r @ l @ v ) > ( expr @ r @ l @ v ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_x,type,
% 0.31/0.47 x: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ).
% 0.31/0.47
% 0.31/0.47 % Relevant facts (255)
% 0.31/0.47 thf(fact_0_assms_I4_J,axiom,
% 0.31/0.47 ~ ( member @ r @ r4 @ ( rID_G @ r @ l @ v @ s_2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % assms(4)
% 0.31/0.47 thf(fact_1_assms_I7_J,axiom,
% 0.31/0.47 r2 != r4 ).
% 0.31/0.47
% 0.31/0.47 % assms(7)
% 0.31/0.47 thf(fact_2_assms_I6_J,axiom,
% 0.31/0.47 r2 != r3 ).
% 0.31/0.47
% 0.31/0.47 % assms(6)
% 0.31/0.47 thf(fact_3_assms_I1_J,axiom,
% 0.31/0.47 ( s_2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ x ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % assms(1)
% 0.31/0.47 thf(fact_4_assms_I3_J,axiom,
% 0.31/0.47 ( ( s_2 @ r3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( rfork @ r @ l @ v @ e2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % assms(3)
% 0.31/0.47 thf(fact_5_assms_I2_J,axiom,
% 0.31/0.47 ( s_22
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ r4 ) ) ) ) ) ) ) @ r4
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ sigma @ tau )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.31/0.47 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.31/0.47 @ e2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % assms(2)
% 0.31/0.47 thf(fact_6_revision__step_Ofork,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v,R3: r] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rfork @ r @ l @ v @ E2 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 0.31/0.47 => ( revision_step @ r @ l @ v @ subst @ R2 @ S
% 0.31/0.47 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) @ R3
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.31/0.47 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.fork
% 0.31/0.47 thf(fact_7_assms_I5_J,axiom,
% 0.31/0.47 ( revision_step @ r @ l @ v @ subst @ r2 @ s_22
% 0.31/0.47 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )
% 0.31/0.47 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ r4 ) ) ) ) ) ) ) @ r4
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ sigma @ tau )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.31/0.47 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.31/0.47 @ e2 ) ) ) )
% 0.31/0.47 @ r2
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ x ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % assms(5)
% 0.31/0.47 thf(fact_8_restrictions__inwards,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X2: A,X3: A,F: A > ( option @ B ),Y: B] :
% 0.31/0.47 ( ( X2 != X3 )
% 0.31/0.47 => ( ( fun_upd @ A @ ( option @ B ) @ ( fun_upd @ A @ ( option @ B ) @ F @ X2 @ ( some @ B @ Y ) ) @ X3 @ ( none @ B ) )
% 0.31/0.47 = ( fun_upd @ A @ ( option @ B ) @ ( fun_upd @ A @ ( option @ B ) @ F @ X3 @ ( none @ B ) ) @ X2 @ ( some @ B @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % restrictions_inwards
% 0.31/0.47 thf(fact_9_empty__upd__none,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,X2: A] :
% 0.31/0.47 ( ( fun_upd @ A @ ( option @ B )
% 0.31/0.47 @ ^ [X: A] : ( none @ B )
% 0.31/0.47 @ X2
% 0.31/0.47 @ ( none @ B ) )
% 0.31/0.47 = ( ^ [X: A] : ( none @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_upd_none
% 0.31/0.47 thf(fact_10_not__None__eq,axiom,
% 0.31/0.47 ! [A: $tType,X2: option @ A] :
% 0.31/0.47 ( ( X2
% 0.31/0.47 != ( none @ A ) )
% 0.31/0.47 = ( ? [Y2: A] :
% 0.31/0.47 ( X2
% 0.31/0.47 = ( some @ A @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_None_eq
% 0.31/0.47 thf(fact_11_not__Some__eq,axiom,
% 0.31/0.47 ! [A: $tType,X2: option @ A] :
% 0.31/0.47 ( ( ! [Y2: A] :
% 0.31/0.47 ( X2
% 0.31/0.47 != ( some @ A @ Y2 ) ) )
% 0.31/0.47 = ( X2
% 0.31/0.47 = ( none @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_Some_eq
% 0.31/0.47 thf(fact_12_map__upd__nonempty,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,T: A > ( option @ B ),K: A,X2: B] :
% 0.31/0.47 ( ( fun_upd @ A @ ( option @ B ) @ T @ K @ ( some @ B @ X2 ) )
% 0.31/0.47 != ( ^ [X: A] : ( none @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_nonempty
% 0.31/0.47 thf(fact_13_fork__pseudodeterministic,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rfork @ r @ l @ v @ E2 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( ? [R4: r] :
% 0.31/0.47 ( ~ ( member @ r @ R4 @ ( rID_G @ r @ l @ v @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rfork @ r @ l @ v @ E2 ) ) ) ) ) ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R4 ) ) ) ) ) ) ) @ R4
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.31/0.47 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fork_pseudodeterministic
% 0.31/0.47 thf(fact_14_revision__step__relaxed_Ofork,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v,R3: r] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rfork @ r @ l @ v @ E2 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S
% 0.31/0.47 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) @ R3
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.31/0.47 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.fork
% 0.31/0.47 thf(fact_15_val_Oinject_I4_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X4: R,Y4: R] :
% 0.31/0.47 ( ( ( rid @ R @ L @ V @ X4 )
% 0.31/0.47 = ( rid @ R @ L @ V @ Y4 ) )
% 0.31/0.47 = ( X4 = Y4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.inject(4)
% 0.31/0.47 thf(fact_16_injective__cntxt,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,E: cntxt @ A @ B @ C,E1: expr @ A @ B @ C,E22: expr @ A @ B @ C] :
% 0.31/0.47 ( ( ( plug @ A @ B @ C @ E @ E1 )
% 0.31/0.47 = ( plug @ A @ B @ C @ E @ E22 ) )
% 0.31/0.47 = ( E1 = E22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % injective_cntxt
% 0.31/0.47 thf(fact_17_expr_Oinject_I1_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,Y1: val @ R @ L @ V] :
% 0.31/0.47 ( ( ( ve @ R @ L @ V @ X1 )
% 0.31/0.47 = ( ve @ R @ L @ V @ Y1 ) )
% 0.31/0.47 = ( X1 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(1)
% 0.31/0.47 thf(fact_18_fun__upd__upd,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B,Z: B] :
% 0.31/0.47 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X2 @ Y ) @ X2 @ Z )
% 0.31/0.47 = ( fun_upd @ A @ B @ F @ X2 @ Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_upd
% 0.31/0.47 thf(fact_19_fun__upd__triv,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,X2: A] :
% 0.31/0.47 ( ( fun_upd @ A @ B @ F @ X2 @ ( F @ X2 ) )
% 0.31/0.47 = F ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_triv
% 0.31/0.47 thf(fact_20_option_Oinject,axiom,
% 0.31/0.47 ! [A: $tType,X22: A,Y22: A] :
% 0.31/0.47 ( ( ( some @ A @ X22 )
% 0.31/0.47 = ( some @ A @ Y22 ) )
% 0.31/0.47 = ( X22 = Y22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inject
% 0.31/0.47 thf(fact_21_fun__upd__apply,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( fun_upd @ B @ A )
% 0.31/0.47 = ( ^ [F2: B > A,X: B,Y2: A,Z2: B] : ( if @ A @ ( Z2 = X ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_apply
% 0.31/0.47 thf(fact_22_expr_Oinject_I7_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X7: expr @ R @ L @ V,Y7: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ( rfork @ R @ L @ V @ X7 )
% 0.31/0.47 = ( rfork @ R @ L @ V @ Y7 ) )
% 0.31/0.47 = ( X7 = Y7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(7)
% 0.31/0.47 thf(fact_23_RID_092_060_094sub_062GI_I1_J,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R2: B,V2: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ V2 ) )
% 0.31/0.47 => ( member @ B @ R2 @ ( rID_G @ B @ A @ C @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>GI(1)
% 0.31/0.47 thf(fact_24_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,R3: A,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 0.31/0.47 ( ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) )
% 0.31/0.47 => ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_restricted_global_in_unrestricted_global(1)
% 0.31/0.47 thf(fact_25_only__fork__introduces__rids_H,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: expr @ r @ l @ v] :
% 0.31/0.47 ( ( S @ R2 )
% 0.31/0.47 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( rfork @ r @ l @ v @ E4 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 0.31/0.47 => ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % only_fork_introduces_rids'
% 0.31/0.47 thf(fact_26_in__restricted__global__in__updated__global_I1_J,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,R3: A,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A,Ls: product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) )] :
% 0.31/0.47 ( ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) )
% 0.31/0.47 => ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_restricted_global_in_updated_global(1)
% 0.31/0.47 thf(fact_27_substitution__axioms,axiom,
% 0.31/0.47 substitution @ r @ l @ v @ subst ).
% 0.31/0.47
% 0.31/0.47 % substitution_axioms
% 0.31/0.47 thf(fact_28_expr_Odistinct_I11_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X7: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ve @ R @ L @ V @ X1 )
% 0.31/0.47 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(11)
% 0.31/0.47 thf(fact_29_fun__upd__idem__iff,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B] :
% 0.31/0.47 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y )
% 0.31/0.47 = F )
% 0.31/0.47 = ( ( F @ X2 )
% 0.31/0.47 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_idem_iff
% 0.31/0.47 thf(fact_30_fun__upd__twist,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,A2: A,C2: A,M: A > B,B2: B,D: B] :
% 0.31/0.47 ( ( A2 != C2 )
% 0.31/0.47 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ A2 @ B2 ) @ C2 @ D )
% 0.31/0.47 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ C2 @ D ) @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_twist
% 0.31/0.47 thf(fact_31_fun__upd__other,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,Z: A,X2: A,F: A > B,Y: B] :
% 0.31/0.47 ( ( Z != X2 )
% 0.31/0.47 => ( ( fun_upd @ A @ B @ F @ X2 @ Y @ Z )
% 0.31/0.47 = ( F @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_other
% 0.31/0.47 thf(fact_32_fun__upd__same,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: B > A,X2: B,Y: A] :
% 0.31/0.47 ( ( fun_upd @ B @ A @ F @ X2 @ Y @ X2 )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_same
% 0.31/0.47 thf(fact_33_fun__upd__idem,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F: B > A,X2: B,Y: A] :
% 0.31/0.47 ( ( ( F @ X2 )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( fun_upd @ B @ A @ F @ X2 @ Y )
% 0.31/0.47 = F ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_idem
% 0.31/0.47 thf(fact_34_fun__upd__eqD,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B,G: A > B,Z: B] :
% 0.31/0.47 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y )
% 0.31/0.47 = ( fun_upd @ A @ B @ G @ X2 @ Z ) )
% 0.31/0.47 => ( Y = Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_eqD
% 0.31/0.47 thf(fact_35_fun__upd__def,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( fun_upd @ A @ B )
% 0.31/0.47 = ( ^ [F2: A > B,A3: A,B3: B,X: A] : ( if @ B @ ( X = A3 ) @ B3 @ ( F2 @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_def
% 0.31/0.47 thf(fact_36_combine__options__cases,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X2: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 0.31/0.47 ( ( ( X2
% 0.31/0.47 = ( none @ A ) )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ( ( Y
% 0.31/0.47 = ( none @ B ) )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ! [A4: A,B4: B] :
% 0.31/0.47 ( ( X2
% 0.31/0.47 = ( some @ A @ A4 ) )
% 0.31/0.47 => ( ( Y
% 0.31/0.47 = ( some @ B @ B4 ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_37_split__option__all,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.31/0.47 ! [X5: option @ A] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: ( option @ A ) > $o] :
% 0.31/0.47 ( ( P3 @ ( none @ A ) )
% 0.31/0.47 & ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_all
% 0.31/0.47 thf(fact_38_split__option__ex,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.31/0.47 ? [X5: option @ A] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: ( option @ A ) > $o] :
% 0.31/0.47 ( ( P3 @ ( none @ A ) )
% 0.31/0.47 | ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_ex
% 0.31/0.47 thf(fact_39_option_Oinducts,axiom,
% 0.31/0.47 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.31/0.47 ( ( P @ ( none @ A ) )
% 0.31/0.47 => ( ! [X6: A] : ( P @ ( some @ A @ X6 ) )
% 0.31/0.47 => ( P @ Option ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inducts
% 0.31/0.47 thf(fact_40_option_Oexhaust,axiom,
% 0.31/0.47 ! [A: $tType,Y: option @ A] :
% 0.31/0.47 ( ( Y
% 0.31/0.47 != ( none @ A ) )
% 0.31/0.47 => ~ ! [X23: A] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( some @ A @ X23 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust
% 0.31/0.47 thf(fact_41_option_OdiscI,axiom,
% 0.31/0.47 ! [A: $tType,Option: option @ A,X22: A] :
% 0.31/0.47 ( ( Option
% 0.31/0.47 = ( some @ A @ X22 ) )
% 0.31/0.47 => ( Option
% 0.31/0.47 != ( none @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.discI
% 0.31/0.47 thf(fact_42_option_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,X22: A] :
% 0.31/0.47 ( ( none @ A )
% 0.31/0.47 != ( some @ A @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.distinct(1)
% 0.31/0.47 thf(fact_43_combine_Ocases,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,X2: product_prod @ ( A > ( option @ B ) ) @ ( product_prod @ ( A > ( option @ B ) ) @ A )] :
% 0.31/0.47 ~ ! [F3: A > ( option @ B ),G2: A > ( option @ B ),X6: A] :
% 0.31/0.47 ( X2
% 0.31/0.47 != ( product_Pair @ ( A > ( option @ B ) ) @ ( product_prod @ ( A > ( option @ B ) ) @ A ) @ F3 @ ( product_Pair @ ( A > ( option @ B ) ) @ A @ G2 @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine.cases
% 0.31/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.31/0.47 = ( P @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A: $tType,A5: set @ A] :
% 0.31/0.47 ( ( collect @ A
% 0.31/0.47 @ ^ [X: A] : ( member @ A @ X @ A5 ) )
% 0.31/0.47 = A5 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_46_Collect__cong,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.47 ( ! [X6: A] :
% 0.31/0.47 ( ( P @ X6 )
% 0.31/0.47 = ( Q @ X6 ) )
% 0.31/0.47 => ( ( collect @ A @ P )
% 0.31/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_47_ext,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/0.47 ( ! [X6: A] :
% 0.31/0.47 ( ( F @ X6 )
% 0.31/0.47 = ( G @ X6 ) )
% 0.31/0.47 => ( F = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % ext
% 0.31/0.47 thf(fact_48_map__upd__Some__unfold,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,M: B > ( option @ A ),A2: B,B2: A,X2: B,Y: A] :
% 0.31/0.47 ( ( ( fun_upd @ B @ ( option @ A ) @ M @ A2 @ ( some @ A @ B2 ) @ X2 )
% 0.31/0.47 = ( some @ A @ Y ) )
% 0.31/0.47 = ( ( ( X2 = A2 )
% 0.31/0.47 & ( B2 = Y ) )
% 0.31/0.47 | ( ( X2 != A2 )
% 0.31/0.47 & ( ( M @ X2 )
% 0.31/0.47 = ( some @ A @ Y ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_Some_unfold
% 0.31/0.47 thf(fact_49_map__upd__triv,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,T: B > ( option @ A ),K: B,X2: A] :
% 0.31/0.47 ( ( ( T @ K )
% 0.31/0.47 = ( some @ A @ X2 ) )
% 0.31/0.47 => ( ( fun_upd @ B @ ( option @ A ) @ T @ K @ ( some @ A @ X2 ) )
% 0.31/0.47 = T ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_triv
% 0.31/0.47 thf(fact_50_map__upd__eqD1,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,M: A > ( option @ B ),A2: A,X2: B,N: A > ( option @ B ),Y: B] :
% 0.31/0.47 ( ( ( fun_upd @ A @ ( option @ B ) @ M @ A2 @ ( some @ B @ X2 ) )
% 0.31/0.47 = ( fun_upd @ A @ ( option @ B ) @ N @ A2 @ ( some @ B @ Y ) ) )
% 0.31/0.47 => ( X2 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_eqD1
% 0.31/0.47 thf(fact_51_LID__local__store_Oinduct,axiom,
% 0.31/0.47 ! [V: $tType,R: $tType,L: $tType,P: ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > $o,A0: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 0.31/0.47 ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E4: expr @ R @ L @ V] : ( P @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ E4 ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ).
% 0.31/0.47
% 0.31/0.47 % LID_local_store.induct
% 0.31/0.47 thf(fact_52_LID__local__store_Ocases,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X2: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 0.31/0.47 ~ ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E4: expr @ R @ L @ V] :
% 0.31/0.47 ( X2
% 0.31/0.47 != ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ E4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LID_local_store.cases
% 0.31/0.47 thf(fact_53_combine_Osimps,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( combine @ A @ B )
% 0.31/0.47 = ( ^ [F2: A > ( option @ B ),G3: A > ( option @ B ),X: A] :
% 0.31/0.47 ( if @ ( option @ B )
% 0.31/0.47 @ ( ( G3 @ X )
% 0.31/0.47 = ( none @ B ) )
% 0.31/0.47 @ ( F2 @ X )
% 0.31/0.47 @ ( G3 @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine.simps
% 0.31/0.47 thf(fact_54_combine_Oelims,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,X2: A > ( option @ B ),Xa: A > ( option @ B ),Xb: A,Y: option @ B] :
% 0.31/0.47 ( ( ( combine @ A @ B @ X2 @ Xa @ Xb )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( ( Xa @ Xb )
% 0.31/0.47 = ( none @ B ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 = ( X2 @ Xb ) ) )
% 0.31/0.47 & ( ( ( Xa @ Xb )
% 0.31/0.47 != ( none @ B ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 = ( Xa @ Xb ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine.elims
% 0.31/0.47 thf(fact_55_local__steps__commute,axiom,
% 0.31/0.47 ! [S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,X2: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ),S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r,Y: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) )] :
% 0.31/0.47 ( ( S_2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) )
% 0.31/0.47 => ( ( S_22
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Y ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Y ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Y ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Y ) ) @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) )
% 0.31/0.47 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local_steps_commute
% 0.31/0.47 thf(fact_56_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S
% 0.31/0.47 @ ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_57_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 0.31/0.47 => ( revision_step @ r @ l @ v @ subst @ R2 @ S
% 0.31/0.47 @ ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_58_transition__relations__equivalent,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transition_relations_equivalent
% 0.31/0.47 thf(fact_59_SLC__commute,axiom,
% 0.31/0.47 ! [S_33: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_34: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r,S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( S_33 = S_34 )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_33 )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_34 )
% 0.31/0.47 => ( ( eq_states @ r @ l @ v @ S_33 @ S_34 )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_33 )
% 0.31/0.47 | ( S_2 = S_33 ) )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_34 )
% 0.31/0.47 | ( S_22 = S_34 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SLC_commute
% 0.31/0.47 thf(fact_60_SLC__sym,axiom,
% 0.31/0.47 ! [R3: r,S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ? [S_35: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_36: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ r @ l @ v @ S_35 @ S_36 )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_35 )
% 0.31/0.47 | ( S_2 = S_35 ) )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_36 )
% 0.31/0.47 | ( S_22 = S_36 ) ) )
% 0.31/0.47 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_3 )
% 0.31/0.47 | ( S_22 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_32 )
% 0.31/0.47 | ( S_2 = S_32 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SLC_sym
% 0.31/0.47 thf(fact_61_local__determinism,axiom,
% 0.31/0.47 ! [R2: r,S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_1 @ S_2 )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_1 @ S_22 )
% 0.31/0.47 => ( eq_states @ r @ l @ v @ S_2 @ S_22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local_determinism
% 0.31/0.47 thf(fact_62_reachability__closed__under__execution__step,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( reachable @ r @ l @ v @ subst @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachability_closed_under_execution_step
% 0.31/0.47 thf(fact_63_only__fork__introduces__rids,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: expr @ r @ l @ v] :
% 0.31/0.47 ( ( S @ R2 )
% 0.31/0.47 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( rfork @ r @ l @ v @ E4 ) ) ) ) ) )
% 0.31/0.47 => ( ord_less_eq @ ( set @ r ) @ ( rID_G @ r @ l @ v @ S2 ) @ ( rID_G @ r @ l @ v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % only_fork_introduces_rids
% 0.31/0.47 thf(fact_64_substitution_Ofork__pseudodeterministic,axiom,
% 0.31/0.47 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rfork @ R @ L @ V @ E2 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( ? [R4: R] :
% 0.31/0.47 ( ~ ( member @ R @ R4 @ ( rID_G @ R @ L @ V @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rfork @ R @ L @ V @ E2 ) ) ) ) ) ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R4 ) ) ) ) ) ) ) @ R4
% 0.31/0.47 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 0.31/0.47 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau )
% 0.31/0.47 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 0.31/0.47 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.fork_pseudodeterministic
% 0.31/0.47 thf(fact_65_expr_Oinject_I8_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X8: expr @ R @ L @ V,Y8: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ( rjoin @ R @ L @ V @ X8 )
% 0.31/0.47 = ( rjoin @ R @ L @ V @ Y8 ) )
% 0.31/0.47 = ( X8 = Y8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(8)
% 0.31/0.47 thf(fact_66_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R5: r,S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S_1 @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S_1 @ R5 )
% 0.31/0.47 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SLC_join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_67_reachable__def,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 = ( ? [E5: expr @ r @ l @ v,S3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] : ( execution @ r @ l @ v @ subst @ E5 @ S3 @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_def
% 0.31/0.47 thf(fact_68_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rjoin\<^sub>\<epsilon>_deterministic
% 0.31/0.47 thf(fact_69_substitution_Olocal__determinism,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_1 @ S_2 )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_1 @ S_22 )
% 0.31/0.47 => ( eq_states @ R @ L @ V @ S_2 @ S_22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.local_determinism
% 0.31/0.47 thf(fact_70_substitution_OSLC__commute,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_33: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_34: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R,S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( S_33 = S_34 )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_33 )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_34 )
% 0.31/0.47 => ( ( eq_states @ R @ L @ V @ S_33 @ S_34 )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_33 )
% 0.31/0.47 | ( S_2 = S_33 ) )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_34 )
% 0.31/0.47 | ( S_22 = S_34 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.SLC_commute
% 0.31/0.47 thf(fact_71_substitution_OSLC__sym,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R3: R,S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ? [S_35: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_36: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ R @ L @ V @ S_35 @ S_36 )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_35 )
% 0.31/0.47 | ( S_2 = S_35 ) )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_36 )
% 0.31/0.47 | ( S_22 = S_36 ) ) )
% 0.31/0.47 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_3 )
% 0.31/0.47 | ( S_22 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_32 )
% 0.31/0.47 | ( S_2 = S_32 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.SLC_sym
% 0.31/0.47 thf(fact_72_expr_Odistinct_I13_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ve @ R @ L @ V @ X1 )
% 0.31/0.47 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(13)
% 0.31/0.47 thf(fact_73_expr_Odistinct_I55_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X7: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.31/0.47 ( ( rfork @ R @ L @ V @ X7 )
% 0.31/0.47 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(55)
% 0.31/0.47 thf(fact_74_substitution_Olocal__steps__commute,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,X2: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ),S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R,Y: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) )
% 0.31/0.47 => ( ( S_22
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Y ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Y ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Y ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Y ) ) @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) )
% 0.31/0.47 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.local_steps_commute
% 0.31/0.47 thf(fact_75_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R2: B] : ( ord_less_eq @ ( set @ B ) @ ( rID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) @ ( rID_G @ B @ A @ C @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % ID_restricted_global_subset_unrestricted(2)
% 0.31/0.47 thf(fact_76_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R5: R,S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S_1 @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S_1 @ R5 )
% 0.31/0.47 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.SLC_join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_77_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.31/0.47 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.rjoin\<^sub>\<epsilon>_deterministic
% 0.31/0.47 thf(fact_78_inductive__invariant__is__execution__invariant,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),P: ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) > $o] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( ( inductive_invariant @ r @ l @ v @ subst @ P )
% 0.31/0.47 => ( P @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inductive_invariant_is_execution_invariant
% 0.31/0.47 thf(fact_79_substitution_Orevision__step__relaxed_Ofork,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V,R3: R] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rfork @ R @ L @ V @ E2 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S
% 0.31/0.47 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) @ R3
% 0.31/0.47 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 0.31/0.47 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau )
% 0.31/0.47 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 0.31/0.47 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.fork
% 0.31/0.47 thf(fact_80_substitution_Orevision__step_Ofork,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V,R3: R] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rfork @ R @ L @ V @ E2 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 0.31/0.47 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S
% 0.31/0.47 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) @ R3
% 0.31/0.47 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 0.31/0.47 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau )
% 0.31/0.47 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 0.31/0.47 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.fork
% 0.31/0.47 thf(fact_81_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S
% 0.31/0.47 @ ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_82_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 0.31/0.47 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S
% 0.31/0.47 @ ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_83_substitution_Oonly__fork__introduces__rids,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: expr @ R @ L @ V] :
% 0.31/0.47 ( ( S @ R2 )
% 0.31/0.47 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( rfork @ R @ L @ V @ E4 ) ) ) ) ) )
% 0.31/0.47 => ( ord_less_eq @ ( set @ R ) @ ( rID_G @ R @ L @ V @ S2 ) @ ( rID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.only_fork_introduces_rids
% 0.31/0.47 thf(fact_84_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( domain398919503obally @ r @ l @ v @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_\<S>\<^sub>G
% 0.31/0.47 thf(fact_85_domains__subsume__globally__def,axiom,
% 0.31/0.47 ( ( domain398919503obally @ r @ l @ v )
% 0.31/0.47 = ( ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ! [R6: r,Ls2: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) )] :
% 0.31/0.47 ( ( ( S4 @ R6 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Ls2 ) )
% 0.31/0.47 => ( domains_subsume @ l @ r @ v @ Ls2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domains_subsume_globally_def
% 0.31/0.47 thf(fact_86_substitution_Orevision__step_Ocong,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType] :
% 0.31/0.47 ( ( revision_step @ R @ L @ V )
% 0.31/0.47 = ( revision_step @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.cong
% 0.31/0.47 thf(fact_87_substitution_Orevision__step__relaxed_Ocong,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType] :
% 0.31/0.47 ( ( revisi1433015572elaxed @ R @ L @ V )
% 0.31/0.47 = ( revisi1433015572elaxed @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.cong
% 0.31/0.47 thf(fact_88_substitution_Oonly__fork__introduces__rids_H,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: expr @ R @ L @ V] :
% 0.31/0.47 ( ( S @ R2 )
% 0.31/0.47 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( rfork @ R @ L @ V @ E4 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 0.31/0.47 => ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.only_fork_introduces_rids'
% 0.31/0.47 thf(fact_89_nice__ind__inv__is__inductive__invariant,axiom,
% 0.31/0.47 ( inductive_invariant @ r @ l @ v @ subst
% 0.31/0.47 @ ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( domain398919503obally @ r @ l @ v @ S4 )
% 0.31/0.47 & ( subsum380726323obally @ r @ l @ v @ S4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nice_ind_inv_is_inductive_invariant
% 0.31/0.47 thf(fact_90_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ( domain398919503obally @ r @ l @ v @ S )
% 0.31/0.47 => ( ( subsum380726323obally @ r @ l @ v @ S )
% 0.31/0.47 => ( subsum380726323obally @ r @ l @ v @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.31/0.47 thf(fact_91_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ( domain398919503obally @ r @ l @ v @ S )
% 0.31/0.47 => ( ( subsum380726323obally @ r @ l @ v @ S )
% 0.31/0.47 => ( domain398919503obally @ r @ l @ v @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.31/0.47 thf(fact_92_valid__stepE,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( member @ ( product_prod @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) @ ( product_Pair @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ S @ S2 ) @ ( steps @ r @ l @ v @ subst ) )
% 0.31/0.47 => ? [R7: r] : ( revision_step @ r @ l @ v @ subst @ R7 @ S @ S2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % valid_stepE
% 0.31/0.47 thf(fact_93_substitution_Odomains__subsume__globallyI,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ! [R7: R,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E4: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ( S @ R7 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ E4 ) ) ) )
% 0.31/0.47 => ( domains_subsume @ L @ R @ V @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ E4 ) ) ) )
% 0.31/0.47 => ( domain398919503obally @ R @ L @ V @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.domains_subsume_globallyI
% 0.31/0.47 thf(fact_94_substitution_Otransition__relations__equivalent,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.transition_relations_equivalent
% 0.31/0.47 thf(fact_95_valid__stepI,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( member @ ( product_prod @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) @ ( product_Pair @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ S @ S2 ) @ ( steps @ r @ l @ v @ subst ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % valid_stepI
% 0.31/0.47 thf(fact_96_domains__subsume__globallyI,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ! [R7: r,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E4: expr @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R7 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ E4 ) ) ) )
% 0.31/0.47 => ( domains_subsume @ l @ r @ v @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ E4 ) ) ) )
% 0.31/0.47 => ( domain398919503obally @ r @ l @ v @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % domains_subsume_globallyI
% 0.31/0.47 thf(fact_97_maximal__execution__def,axiom,
% 0.31/0.47 ! [E2: expr @ r @ l @ v,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( maximal_execution @ r @ l @ v @ subst @ E2 @ S @ S2 )
% 0.31/0.47 = ( ( execution @ r @ l @ v @ subst @ E2 @ S @ S2 )
% 0.31/0.47 & ~ ? [S5: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] : ( member @ ( product_prod @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) @ ( product_Pair @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ S2 @ S5 ) @ ( steps @ r @ l @ v @ subst ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % maximal_execution_def
% 0.31/0.47 thf(fact_98_substitution_Osteps_Ocong,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType] :
% 0.31/0.47 ( ( steps @ R @ L @ V )
% 0.31/0.47 = ( steps @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.steps.cong
% 0.31/0.47 thf(fact_99_substitution_Ovalid__stepE,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( member @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) @ ( product_Pair @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ S @ S2 ) @ ( steps @ R @ L @ V @ Subst ) )
% 0.31/0.47 => ? [R7: R] : ( revision_step @ R @ L @ V @ Subst @ R7 @ S @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.valid_stepE
% 0.31/0.47 thf(fact_100_substitution_Ovalid__stepI,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( member @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) @ ( product_Pair @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ S @ S2 ) @ ( steps @ R @ L @ V @ Subst ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.valid_stepI
% 0.31/0.47 thf(fact_101_substitution_Oreachable_Ocong,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType] :
% 0.31/0.47 ( ( reachable @ R @ L @ V )
% 0.31/0.47 = ( reachable @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable.cong
% 0.31/0.47 thf(fact_102_substitution_Oinductive__invariant_Ocong,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType] :
% 0.31/0.47 ( ( inductive_invariant @ R @ L @ V )
% 0.31/0.47 = ( inductive_invariant @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.inductive_invariant.cong
% 0.31/0.47 thf(fact_103_substitution_Oexecution_Ocong,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType] :
% 0.31/0.47 ( ( execution @ R @ L @ V )
% 0.31/0.47 = ( execution @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.execution.cong
% 0.31/0.47 thf(fact_104_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( inductive_invariant @ R @ L @ V @ Subst
% 0.31/0.47 @ ^ [S4: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( domain398919503obally @ R @ L @ V @ S4 )
% 0.31/0.47 & ( subsum380726323obally @ R @ L @ V @ S4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.nice_ind_inv_is_inductive_invariant
% 0.31/0.47 thf(fact_105_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ( domain398919503obally @ R @ L @ V @ S )
% 0.31/0.47 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 0.31/0.47 => ( subsum380726323obally @ R @ L @ V @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.31/0.47 thf(fact_106_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ( domain398919503obally @ R @ L @ V @ S )
% 0.31/0.47 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 0.31/0.47 => ( domain398919503obally @ R @ L @ V @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.31/0.47 thf(fact_107_substitution_Odomains__subsume__globally__def,axiom,
% 0.31/0.47 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( domain398919503obally @ R @ L @ V @ S )
% 0.31/0.47 = ( ! [R6: R,Ls2: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 0.31/0.47 ( ( ( S @ R6 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Ls2 ) )
% 0.31/0.47 => ( domains_subsume @ L @ R @ V @ Ls2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.domains_subsume_globally_def
% 0.31/0.47 thf(fact_108_substitution_Oreachability__closed__under__execution__step,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( reachable @ R @ L @ V @ Subst @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachability_closed_under_execution_step
% 0.31/0.47 thf(fact_109_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( domain398919503obally @ R @ L @ V @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_\<S>\<^sub>G
% 0.31/0.47 thf(fact_110_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),P: ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( ( inductive_invariant @ R @ L @ V @ Subst @ P )
% 0.31/0.47 => ( P @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.inductive_invariant_is_execution_invariant
% 0.31/0.47 thf(fact_111_substitution_Oreachable__def,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 = ( ? [E5: expr @ R @ L @ V,S3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] : ( execution @ R @ L @ V @ Subst @ E5 @ S3 @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_def
% 0.31/0.47 thf(fact_112_SLC__join,axiom,
% 0.31/0.47 ! [S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R5: r,S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),Sigma3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v,R3: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S_1 @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S_1 @ R5 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SLC_join
% 0.31/0.47 thf(fact_113_join__and__local__commute,axiom,
% 0.31/0.47 ! [S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R5: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r,Ls: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ),Sigma3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v] :
% 0.31/0.47 ( ( S_2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) )
% 0.31/0.47 => ( ( S_22
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Ls ) ) )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ( ( R3 != R5 )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Ls ) ) )
% 0.31/0.47 => ( ( ( S_22 @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S_22 @ R5 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 0.31/0.47 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % join_and_local_commute
% 0.31/0.47 thf(fact_114_substitution_Omaximal__execution__def,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),E2: expr @ R @ L @ V,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( maximal_execution @ R @ L @ V @ Subst @ E2 @ S @ S2 )
% 0.31/0.47 = ( ( execution @ R @ L @ V @ Subst @ E2 @ S @ S2 )
% 0.31/0.47 & ~ ? [S5: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] : ( member @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) @ ( product_Pair @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ S2 @ S5 ) @ ( steps @ R @ L @ V @ Subst ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.maximal_execution_def
% 0.31/0.47 thf(fact_115_substitution_Osubsumes__accessible__globallyI,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ! [R_1: R,Sigma_1: L > ( option @ ( val @ R @ L @ V ) ),Tau_1: L > ( option @ ( val @ R @ L @ V ) ),E_1: expr @ R @ L @ V,R_2: R,Sigma_2: L > ( option @ ( val @ R @ L @ V ) ),Tau_2: L > ( option @ ( val @ R @ L @ V ) ),E_2: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ( S @ R_1 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma_1 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau_1 @ E_1 ) ) ) )
% 0.31/0.47 => ( ( ( S @ R_2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma_2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau_2 @ E_2 ) ) ) )
% 0.31/0.47 => ( subsumes_accessible @ R @ L @ V @ R_1 @ R_2 @ S ) ) )
% 0.31/0.47 => ( subsum380726323obally @ R @ L @ V @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.subsumes_accessible_globallyI
% 0.31/0.47 thf(fact_116_revision__step__relaxed_Ojoin,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r,Sigma3: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.join
% 0.31/0.47 thf(fact_117_val_Oinject_I1_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X1: const,Y1: const] :
% 0.31/0.47 ( ( ( cv @ R @ L @ V @ X1 )
% 0.31/0.47 = ( cv @ R @ L @ V @ Y1 ) )
% 0.31/0.47 = ( X1 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.inject(1)
% 0.31/0.47 thf(fact_118_terminates__in__def,axiom,
% 0.31/0.47 ! [E2: expr @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( terminates_in @ r @ l @ v @ subst @ E2 @ S2 )
% 0.31/0.47 = ( ? [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] : ( maximal_execution @ r @ l @ v @ subst @ E2 @ S4 @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % terminates_in_def
% 0.31/0.47 thf(fact_119_revision__step_Ojoin,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r,Sigma3: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 0.31/0.47 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.join
% 0.31/0.47 thf(fact_120_subsumes__accessible__globallyI,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ! [R_1: r,Sigma_1: l > ( option @ ( val @ r @ l @ v ) ),Tau_1: l > ( option @ ( val @ r @ l @ v ) ),E_1: expr @ r @ l @ v,R_2: r,Sigma_2: l > ( option @ ( val @ r @ l @ v ) ),Tau_2: l > ( option @ ( val @ r @ l @ v ) ),E_2: expr @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R_1 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma_1 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau_1 @ E_1 ) ) ) )
% 0.31/0.47 => ( ( ( S @ R_2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma_2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau_2 @ E_2 ) ) ) )
% 0.31/0.47 => ( subsumes_accessible @ r @ l @ v @ R_1 @ R_2 @ S ) ) )
% 0.31/0.47 => ( subsum380726323obally @ r @ l @ v @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsumes_accessible_globallyI
% 0.31/0.47 thf(fact_121_rjoin__deterministic,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r,Sigma3: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rjoin_deterministic
% 0.31/0.47 thf(fact_122_substitution_Omaximal__execution_Ocong,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType] :
% 0.31/0.47 ( ( maximal_execution @ R @ L @ V )
% 0.31/0.47 = ( maximal_execution @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.maximal_execution.cong
% 0.31/0.47 thf(fact_123_val_Odistinct_I5_J,axiom,
% 0.31/0.47 ! [L: $tType,V: $tType,R: $tType,X1: const,X4: R] :
% 0.31/0.47 ( ( cv @ R @ L @ V @ X1 )
% 0.31/0.47 != ( rid @ R @ L @ V @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.distinct(5)
% 0.31/0.47 thf(fact_124_substitution_Orevision__step_Ojoin,axiom,
% 0.31/0.47 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R,Sigma3: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 0.31/0.47 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.join
% 0.31/0.47 thf(fact_125_substitution_Orjoin__deterministic,axiom,
% 0.31/0.47 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R,Sigma3: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.rjoin_deterministic
% 0.31/0.47 thf(fact_126_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 0.31/0.47 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R,Sigma3: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.join
% 0.31/0.47 thf(fact_127_substitution_Ojoin__and__local__commute,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R5: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R,Ls: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ),Sigma3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) )
% 0.31/0.47 => ( ( S_22
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Ls ) ) )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ( ( R3 != R5 )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Ls ) ) )
% 0.31/0.47 => ( ( ( S_22 @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S_22 @ R5 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 0.31/0.47 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.join_and_local_commute
% 0.31/0.47 thf(fact_128_substitution_OSLC__join,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R5: R,S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),Sigma3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V,R3: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S_1 @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S_1 @ R5 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.SLC_join
% 0.31/0.47 thf(fact_129_reachable__imp__identifiers__finite_I1_J,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( finite_finite @ r @ ( rID_G @ r @ l @ v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_identifiers_finite(1)
% 0.31/0.47 thf(fact_130_RID_092_060_094sub_062G__finite__invariant,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ( finite_finite @ r @ ( rID_G @ r @ l @ v @ S ) )
% 0.31/0.47 => ( finite_finite @ r @ ( rID_G @ r @ l @ v @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>G_finite_invariant
% 0.31/0.47 thf(fact_131_reachability__closed__under__execution,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( ( member @ ( product_prod @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) @ ( product_Pair @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ S @ S2 ) @ ( transitive_rtrancl @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( steps @ r @ l @ v @ subst ) ) )
% 0.31/0.47 => ( reachable @ r @ l @ v @ subst @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachability_closed_under_execution
% 0.31/0.47 thf(fact_132_revision__step__relaxed_OifTrue,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E1 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.ifTrue
% 0.31/0.47 thf(fact_133_empty__map__finite_I3_J,axiom,
% 0.31/0.47 ! [H: $tType,I: $tType,G4: $tType] :
% 0.31/0.47 ( finite_finite @ G4
% 0.31/0.47 @ ( rID_G @ G4 @ H @ I
% 0.31/0.47 @ ^ [X: G4] : ( none @ ( product_prod @ ( H > ( option @ ( val @ G4 @ H @ I ) ) ) @ ( product_prod @ ( H > ( option @ ( val @ G4 @ H @ I ) ) ) @ ( expr @ G4 @ H @ I ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_map_finite(3)
% 0.31/0.47 thf(fact_134_expr_Oinject_I3_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,Y31: expr @ R @ L @ V,Y32: expr @ R @ L @ V,Y33: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 0.31/0.47 = ( ite @ R @ L @ V @ Y31 @ Y32 @ Y33 ) )
% 0.31/0.47 = ( ( X31 = Y31 )
% 0.31/0.47 & ( X32 = Y32 )
% 0.31/0.47 & ( X33 = Y33 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(3)
% 0.31/0.47 thf(fact_135_revision__step_OifTrue,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E1 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.ifTrue
% 0.31/0.47 thf(fact_136_finite__state__imp__restriction__finite_I1_J,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 0.31/0.47 ( ( finite_finite @ A @ ( rID_G @ A @ B @ C @ S ) )
% 0.31/0.47 => ( finite_finite @ A @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_state_imp_restriction_finite(1)
% 0.31/0.47 thf(fact_137_ifTrue__deterministic,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E1 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ifTrue_deterministic
% 0.31/0.47 thf(fact_138_expr_Odistinct_I3_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ve @ R @ L @ V @ X1 )
% 0.31/0.47 != ( ite @ R @ L @ V @ X31 @ X32 @ X33 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(3)
% 0.31/0.47 thf(fact_139_expr_Odistinct_I35_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(35)
% 0.31/0.47 thf(fact_140_expr_Odistinct_I33_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(33)
% 0.31/0.47 thf(fact_141_substitution_Oterminates__in_Ocong,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType] :
% 0.31/0.47 ( ( terminates_in @ R @ L @ V )
% 0.31/0.47 = ( terminates_in @ R @ L @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.terminates_in.cong
% 0.31/0.47 thf(fact_142_const_Odistinct_I3_J,axiom,
% 0.31/0.47 unit != t ).
% 0.31/0.47
% 0.31/0.47 % const.distinct(3)
% 0.31/0.47 thf(fact_143_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ( finite_finite @ R @ ( rID_G @ R @ L @ V @ S ) )
% 0.31/0.47 => ( finite_finite @ R @ ( rID_G @ R @ L @ V @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.RID\<^sub>G_finite_invariant
% 0.31/0.47 thf(fact_144_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( finite_finite @ R @ ( rID_G @ R @ L @ V @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_identifiers_finite(1)
% 0.31/0.47 thf(fact_145_substitution_Oempty__map__finite_I3_J,axiom,
% 0.31/0.47 ! [R: $tType,L: $tType,V: $tType,H: $tType,I: $tType,G4: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( finite_finite @ G4
% 0.31/0.47 @ ( rID_G @ G4 @ H @ I
% 0.31/0.47 @ ^ [X: G4] : ( none @ ( product_prod @ ( H > ( option @ ( val @ G4 @ H @ I ) ) ) @ ( product_prod @ ( H > ( option @ ( val @ G4 @ H @ I ) ) ) @ ( expr @ G4 @ H @ I ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.empty_map_finite(3)
% 0.31/0.47 thf(fact_146_substitution_Oreachability__closed__under__execution,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( ( member @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) @ ( product_Pair @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ S @ S2 ) @ ( transitive_rtrancl @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( steps @ R @ L @ V @ Subst ) ) )
% 0.31/0.47 => ( reachable @ R @ L @ V @ Subst @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachability_closed_under_execution
% 0.31/0.47 thf(fact_147_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,C: $tType,A: $tType,B: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( finite_finite @ A @ ( rID_G @ A @ B @ C @ S ) )
% 0.31/0.47 => ( finite_finite @ A @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.finite_state_imp_restriction_finite(1)
% 0.31/0.47 thf(fact_148_substitution_OifTrue__deterministic,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E1 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.ifTrue_deterministic
% 0.31/0.47 thf(fact_149_substitution_Orevision__step_OifTrue,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E1 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.ifTrue
% 0.31/0.47 thf(fact_150_substitution_Orevision__step__relaxed_OifTrue,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E1 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.ifTrue
% 0.31/0.47 thf(fact_151_substitution_Oterminates__in__def,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),E2: expr @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( terminates_in @ R @ L @ V @ Subst @ E2 @ S2 )
% 0.31/0.47 = ( ? [S4: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] : ( maximal_execution @ R @ L @ V @ Subst @ E2 @ S4 @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.terminates_in_def
% 0.31/0.47 thf(fact_152_revision__step__relaxed_OifFalse,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E22 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.ifFalse
% 0.31/0.47 thf(fact_153_revision__step_OifFalse,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E22 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.ifFalse
% 0.31/0.47 thf(fact_154_ifFalse__deterministic,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E22 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ifFalse_deterministic
% 0.31/0.47 thf(fact_155_finite__Collect__subsets,axiom,
% 0.31/0.47 ! [A: $tType,A5: set @ A] :
% 0.31/0.47 ( ( finite_finite @ A @ A5 )
% 0.31/0.47 => ( finite_finite @ ( set @ A )
% 0.31/0.47 @ ( collect @ ( set @ A )
% 0.31/0.47 @ ^ [B5: set @ A] : ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_subsets
% 0.31/0.47 thf(fact_156_finite__Collect__disjI,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.47 ( ( finite_finite @ A
% 0.31/0.47 @ ( collect @ A
% 0.31/0.47 @ ^ [X: A] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 | ( Q @ X ) ) ) )
% 0.31/0.47 = ( ( finite_finite @ A @ ( collect @ A @ P ) )
% 0.31/0.47 & ( finite_finite @ A @ ( collect @ A @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_disjI
% 0.31/0.47 thf(fact_157_finite__Collect__conjI,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.47 ( ( ( finite_finite @ A @ ( collect @ A @ P ) )
% 0.31/0.47 | ( finite_finite @ A @ ( collect @ A @ Q ) ) )
% 0.31/0.47 => ( finite_finite @ A
% 0.31/0.47 @ ( collect @ A
% 0.31/0.47 @ ^ [X: A] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_conjI
% 0.31/0.47 thf(fact_158_const_Odistinct_I1_J,axiom,
% 0.31/0.47 unit != f ).
% 0.31/0.47
% 0.31/0.47 % const.distinct(1)
% 0.31/0.47 thf(fact_159_const_Odistinct_I5_J,axiom,
% 0.31/0.47 f != t ).
% 0.31/0.47
% 0.31/0.47 % const.distinct(5)
% 0.31/0.47 thf(fact_160_const_Oinduct,axiom,
% 0.31/0.47 ! [P: const > $o,Const: const] :
% 0.31/0.47 ( ( P @ unit )
% 0.31/0.47 => ( ( P @ f )
% 0.31/0.47 => ( ( P @ t )
% 0.31/0.47 => ( P @ Const ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % const.induct
% 0.31/0.47 thf(fact_161_const_Oexhaust,axiom,
% 0.31/0.47 ! [Y: const] :
% 0.31/0.47 ( ( Y != unit )
% 0.31/0.47 => ( ( Y != f )
% 0.31/0.47 => ( Y = t ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % const.exhaust
% 0.31/0.47 thf(fact_162_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,A5: set @ A,B6: set @ B,R8: A > B > $o] :
% 0.31/0.47 ( ~ ( finite_finite @ A @ A5 )
% 0.31/0.47 => ( ( finite_finite @ B @ B6 )
% 0.31/0.47 => ( ! [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ A5 )
% 0.31/0.47 => ? [Xa2: B] :
% 0.31/0.47 ( ( member @ B @ Xa2 @ B6 )
% 0.31/0.47 & ( R8 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: B] :
% 0.31/0.47 ( ( member @ B @ X6 @ B6 )
% 0.31/0.47 & ~ ( finite_finite @ A
% 0.31/0.47 @ ( collect @ A
% 0.31/0.47 @ ^ [A3: A] :
% 0.31/0.47 ( ( member @ A @ A3 @ A5 )
% 0.31/0.47 & ( R8 @ A3 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_163_not__finite__existsD,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o] :
% 0.31/0.47 ( ~ ( finite_finite @ A @ ( collect @ A @ P ) )
% 0.31/0.47 => ? [X_1: A] : ( P @ X_1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_finite_existsD
% 0.31/0.47 thf(fact_164_finite__has__maximal2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A5: set @ A,A2: A] :
% 0.31/0.47 ( ( finite_finite @ A @ A5 )
% 0.31/0.47 => ( ( member @ A @ A2 @ A5 )
% 0.31/0.47 => ? [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ A5 )
% 0.31/0.47 & ( ord_less_eq @ A @ A2 @ X6 )
% 0.31/0.47 & ! [Xa2: A] :
% 0.31/0.47 ( ( member @ A @ Xa2 @ A5 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ X6 @ Xa2 )
% 0.31/0.47 => ( X6 = Xa2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_has_maximal2
% 0.31/0.47 thf(fact_165_finite__has__minimal2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A5: set @ A,A2: A] :
% 0.31/0.47 ( ( finite_finite @ A @ A5 )
% 0.31/0.47 => ( ( member @ A @ A2 @ A5 )
% 0.31/0.47 => ? [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ A5 )
% 0.31/0.47 & ( ord_less_eq @ A @ X6 @ A2 )
% 0.31/0.47 & ! [Xa2: A] :
% 0.31/0.47 ( ( member @ A @ Xa2 @ A5 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ Xa2 @ X6 )
% 0.31/0.47 => ( X6 = Xa2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_has_minimal2
% 0.31/0.47 thf(fact_166_finite__subset,axiom,
% 0.31/0.47 ! [A: $tType,A5: set @ A,B6: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.31/0.47 => ( ( finite_finite @ A @ B6 )
% 0.31/0.47 => ( finite_finite @ A @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_subset
% 0.31/0.47 thf(fact_167_infinite__super,axiom,
% 0.31/0.47 ! [A: $tType,S6: set @ A,T2: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ S6 @ T2 )
% 0.31/0.47 => ( ~ ( finite_finite @ A @ S6 )
% 0.31/0.47 => ~ ( finite_finite @ A @ T2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infinite_super
% 0.31/0.47 thf(fact_168_rev__finite__subset,axiom,
% 0.31/0.47 ! [A: $tType,B6: set @ A,A5: set @ A] :
% 0.31/0.47 ( ( finite_finite @ A @ B6 )
% 0.31/0.47 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.31/0.47 => ( finite_finite @ A @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_finite_subset
% 0.31/0.47 thf(fact_169_finite__update__induct,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,C2: B,P: ( A > B ) > $o] :
% 0.31/0.47 ( ( finite_finite @ A
% 0.31/0.47 @ ( collect @ A
% 0.31/0.47 @ ^ [A3: A] :
% 0.31/0.47 ( ( F @ A3 )
% 0.31/0.47 != C2 ) ) )
% 0.31/0.47 => ( ( P
% 0.31/0.47 @ ^ [A3: A] : C2 )
% 0.31/0.47 => ( ! [A4: A,B4: B,F3: A > B] :
% 0.31/0.47 ( ( finite_finite @ A
% 0.31/0.47 @ ( collect @ A
% 0.31/0.47 @ ^ [C3: A] :
% 0.31/0.47 ( ( F3 @ C3 )
% 0.31/0.47 != C2 ) ) )
% 0.31/0.47 => ( ( ( F3 @ A4 )
% 0.31/0.47 = C2 )
% 0.31/0.47 => ( ( B4 != C2 )
% 0.31/0.47 => ( ( P @ F3 )
% 0.31/0.47 => ( P @ ( fun_upd @ A @ B @ F3 @ A4 @ B4 ) ) ) ) ) )
% 0.31/0.47 => ( P @ F ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_update_induct
% 0.31/0.47 thf(fact_170_substitution_Orevision__step_OifFalse,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E22 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.ifFalse
% 0.31/0.47 thf(fact_171_substitution_OifFalse__deterministic,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E22 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.ifFalse_deterministic
% 0.31/0.47 thf(fact_172_substitution_Orevision__step__relaxed_OifFalse,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E22 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.ifFalse
% 0.31/0.47 thf(fact_173_reachable__imp__identifiers__available_I1_J,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( ~ ( finite_finite @ r @ ( top_top @ ( set @ r ) ) )
% 0.31/0.47 => ? [R7: r] :
% 0.31/0.47 ~ ( member @ r @ R7 @ ( rID_G @ r @ l @ v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_identifiers_available(1)
% 0.31/0.47 thf(fact_174_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 0.31/0.47 ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.31/0.47 => ( ( finite_finite @ B @ ( rID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ( finite_finite @ B @ ( rID_L @ A @ B @ C @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local_state_of_finite_restricted_global_state_is_finite(1)
% 0.31/0.47 thf(fact_175_empty__map__finite_I4_J,axiom,
% 0.31/0.47 ! [J: $tType,M2: $tType,K2: $tType] :
% 0.31/0.47 ( finite_finite @ J
% 0.31/0.47 @ ( lID_G @ K2 @ J @ M2
% 0.31/0.47 @ ^ [X: K2] : ( none @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( expr @ K2 @ J @ M2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_map_finite(4)
% 0.31/0.47 thf(fact_176_RID_092_060_094sub_062L__finite__invariant,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ( finite_finite @ l @ ( lID_G @ r @ l @ v @ S ) )
% 0.31/0.47 => ( finite_finite @ l @ ( lID_G @ r @ l @ v @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>L_finite_invariant
% 0.31/0.47 thf(fact_177_reachable__imp__identifiers__finite_I2_J,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( finite_finite @ l @ ( lID_G @ r @ l @ v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_identifiers_finite(2)
% 0.31/0.47 thf(fact_178_finite__option__UNIV,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( finite_finite @ ( option @ A ) @ ( top_top @ ( set @ ( option @ A ) ) ) )
% 0.31/0.47 = ( finite_finite @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_option_UNIV
% 0.31/0.47 thf(fact_179_finite__Collect__not,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o] :
% 0.31/0.47 ( ( finite_finite @ A @ ( collect @ A @ P ) )
% 0.31/0.47 => ( ( finite_finite @ A
% 0.31/0.47 @ ( collect @ A
% 0.31/0.47 @ ^ [X: A] :
% 0.31/0.47 ~ ( P @ X ) ) )
% 0.31/0.47 = ( finite_finite @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_not
% 0.31/0.47 thf(fact_180_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,L2: B,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 0.31/0.47 ( ( member @ B @ L2 @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) )
% 0.31/0.47 => ( member @ B @ L2 @ ( lID_G @ A @ B @ C @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_restricted_global_in_unrestricted_global(2)
% 0.31/0.47 thf(fact_181_RID_092_060_094sub_062GI_I2_J,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 0.31/0.47 ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.31/0.47 => ( ( member @ B @ R2 @ ( rID_L @ A @ B @ C @ Ls ) )
% 0.31/0.47 => ( member @ B @ R2 @ ( rID_G @ B @ A @ C @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>GI(2)
% 0.31/0.47 thf(fact_182_finite__state__imp__restriction__finite_I2_J,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 0.31/0.47 ( ( finite_finite @ B @ ( lID_G @ A @ B @ C @ S ) )
% 0.31/0.47 => ( finite_finite @ B @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_state_imp_restriction_finite(2)
% 0.31/0.47 thf(fact_183_in__restricted__global__in__updated__global_I2_J,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,L2: B,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A,Ls: product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) )] :
% 0.31/0.47 ( ( member @ B @ L2 @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) )
% 0.31/0.47 => ( member @ B @ L2 @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_restricted_global_in_updated_global(2)
% 0.31/0.47 thf(fact_184_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( ~ ( finite_finite @ L @ ( top_top @ ( set @ L ) ) )
% 0.31/0.47 => ? [L3: L] :
% 0.31/0.47 ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_identifiers_available(2)
% 0.31/0.47 thf(fact_185_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ( finite_finite @ L @ ( lID_G @ R @ L @ V @ S ) )
% 0.31/0.47 => ( finite_finite @ L @ ( lID_G @ R @ L @ V @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.RID\<^sub>L_finite_invariant
% 0.31/0.47 thf(fact_186_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R2: B] : ( ord_less_eq @ ( set @ A ) @ ( lID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) @ ( lID_G @ B @ A @ C @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % ID_restricted_global_subset_unrestricted(1)
% 0.31/0.47 thf(fact_187_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( finite_finite @ L @ ( lID_G @ R @ L @ V @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_identifiers_finite(2)
% 0.31/0.47 thf(fact_188_substitution_Oempty__map__finite_I4_J,axiom,
% 0.31/0.47 ! [R: $tType,L: $tType,V: $tType,J: $tType,M2: $tType,K2: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( finite_finite @ J
% 0.31/0.47 @ ( lID_G @ K2 @ J @ M2
% 0.31/0.47 @ ^ [X: K2] : ( none @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( expr @ K2 @ J @ M2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.empty_map_finite(4)
% 0.31/0.47 thf(fact_189_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.31/0.47 => ( ~ ( finite_finite @ R @ ( top_top @ ( set @ R ) ) )
% 0.31/0.47 => ? [R7: R] :
% 0.31/0.47 ~ ( member @ R @ R7 @ ( rID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_identifiers_available(1)
% 0.31/0.47 thf(fact_190_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,C: $tType,A: $tType,B: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( finite_finite @ B @ ( lID_G @ A @ B @ C @ S ) )
% 0.31/0.47 => ( finite_finite @ B @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.finite_state_imp_restriction_finite(2)
% 0.31/0.47 thf(fact_191_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,C: $tType,B: $tType,A: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.31/0.47 => ( ( finite_finite @ B @ ( rID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ( finite_finite @ B @ ( rID_L @ A @ B @ C @ Ls ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.local_state_of_finite_restricted_global_state_is_finite(1)
% 0.31/0.47 thf(fact_192_only__new__introduces__lids_H,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),L2: l] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,V3: val @ r @ l @ v] :
% 0.31/0.47 ( ( S @ R2 )
% 0.31/0.47 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ref @ r @ l @ v @ ( ve @ r @ l @ v @ V3 ) ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ l @ L2 @ ( lID_G @ r @ l @ v @ S ) )
% 0.31/0.47 => ~ ( member @ l @ L2 @ ( lID_G @ r @ l @ v @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % only_new_introduces_lids'
% 0.31/0.47 thf(fact_193_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 0.31/0.47 ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.31/0.47 => ( ( finite_finite @ A @ ( lID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ( finite_finite @ A @ ( lID_L @ A @ B @ C @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local_state_of_finite_restricted_global_state_is_finite(2)
% 0.31/0.47 thf(fact_194_only__new__introduces__lids,axiom,
% 0.31/0.47 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,V3: val @ r @ l @ v] :
% 0.31/0.47 ( ( S @ R2 )
% 0.31/0.47 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ref @ r @ l @ v @ ( ve @ r @ l @ v @ V3 ) ) ) ) ) ) )
% 0.31/0.47 => ( ord_less_eq @ ( set @ l ) @ ( lID_G @ r @ l @ v @ S2 ) @ ( lID_G @ r @ l @ v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % only_new_introduces_lids
% 0.31/0.47 thf(fact_195_expr_Oinject_I4_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,Y4: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ( ref @ R @ L @ V @ X4 )
% 0.31/0.47 = ( ref @ R @ L @ V @ Y4 ) )
% 0.31/0.47 = ( X4 = Y4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(4)
% 0.31/0.47 thf(fact_196_reachable__imp__identifiers__available_I2_J,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.31/0.47 => ( ~ ( finite_finite @ l @ ( top_top @ ( set @ l ) ) )
% 0.31/0.47 => ? [L3: l] :
% 0.31/0.47 ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_identifiers_available(2)
% 0.31/0.47 thf(fact_197_LID_092_060_094sub_062GI,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R2: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),L2: A] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.31/0.47 => ( ( member @ A @ L2 @ ( lID_L @ A @ B @ C @ Ls ) )
% 0.31/0.47 => ( member @ A @ L2 @ ( lID_G @ B @ A @ C @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LID\<^sub>GI
% 0.31/0.47 thf(fact_198_expr_Odistinct_I41_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ref @ R @ L @ V @ X4 )
% 0.31/0.47 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(41)
% 0.31/0.47 thf(fact_199_expr_Odistinct_I43_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ref @ R @ L @ V @ X4 )
% 0.31/0.47 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(43)
% 0.31/0.47 thf(fact_200_expr_Odistinct_I5_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X4: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ve @ R @ L @ V @ X1 )
% 0.31/0.47 != ( ref @ R @ L @ V @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(5)
% 0.31/0.47 thf(fact_201_expr_Odistinct_I27_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X4: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( ref @ R @ L @ V @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(27)
% 0.31/0.47 thf(fact_202_LID_092_060_094sub_062GE,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,L2: A,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) )] :
% 0.31/0.47 ( ( member @ A @ L2 @ ( lID_G @ B @ A @ C @ S ) )
% 0.31/0.47 => ~ ! [R7: B,Ls3: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) )] :
% 0.31/0.47 ( ( ( S @ R7 )
% 0.31/0.47 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls3 ) )
% 0.31/0.47 => ~ ( member @ A @ L2 @ ( lID_L @ A @ B @ C @ Ls3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LID\<^sub>GE
% 0.31/0.47 thf(fact_203_substitution_Oonly__new__introduces__lids_H,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),L2: L] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,V3: val @ R @ L @ V] :
% 0.31/0.47 ( ( S @ R2 )
% 0.31/0.47 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ref @ R @ L @ V @ ( ve @ R @ L @ V @ V3 ) ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ L @ L2 @ ( lID_G @ R @ L @ V @ S ) )
% 0.31/0.47 => ~ ( member @ L @ L2 @ ( lID_G @ R @ L @ V @ S2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.only_new_introduces_lids'
% 0.31/0.47 thf(fact_204_substitution_Oonly__new__introduces__lids,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,V3: val @ R @ L @ V] :
% 0.31/0.47 ( ( S @ R2 )
% 0.31/0.47 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ref @ R @ L @ V @ ( ve @ R @ L @ V @ V3 ) ) ) ) ) ) )
% 0.31/0.47 => ( ord_less_eq @ ( set @ L ) @ ( lID_G @ R @ L @ V @ S2 ) @ ( lID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.only_new_introduces_lids
% 0.31/0.47 thf(fact_205_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,C: $tType,B: $tType,A: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R3 )
% 0.31/0.47 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.31/0.47 => ( ( finite_finite @ A @ ( lID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) )
% 0.31/0.47 => ( ( R2 != R3 )
% 0.31/0.47 => ( finite_finite @ A @ ( lID_L @ A @ B @ C @ Ls ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.local_state_of_finite_restricted_global_state_is_finite(2)
% 0.31/0.47 thf(fact_206_domains__subsume__def,axiom,
% 0.31/0.47 ( ( domains_subsume @ l @ r @ v )
% 0.31/0.47 = ( ^ [Ls2: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) )] : ( ord_less_eq @ ( set @ l ) @ ( lID_L @ l @ r @ v @ Ls2 ) @ ( doms @ l @ r @ v @ Ls2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domains_subsume_def
% 0.31/0.47 thf(fact_207_revision__step_Onew,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,V2: val @ r @ l @ v,L2: l] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ref @ r @ l @ v @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ l @ L2 @ ( lID_G @ r @ l @ v @ S ) )
% 0.31/0.47 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L2 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.new
% 0.31/0.47 thf(fact_208_val_Oinject_I3_J,axiom,
% 0.31/0.47 ! [V: $tType,R: $tType,L: $tType,X34: L,Y3: L] :
% 0.31/0.47 ( ( ( loc @ L @ R @ V @ X34 )
% 0.31/0.47 = ( loc @ L @ R @ V @ Y3 ) )
% 0.31/0.47 = ( X34 = Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.inject(3)
% 0.31/0.47 thf(fact_209_new__pseudodeterministic,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,V2: val @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ref @ r @ l @ v @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( ? [L4: l] :
% 0.31/0.47 ( ~ ( member @ l @ L4 @ ( lID_G @ r @ l @ v @ S ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L4 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % new_pseudodeterministic
% 0.31/0.47 thf(fact_210_val_Odistinct_I15_J,axiom,
% 0.31/0.47 ! [L: $tType,V: $tType,R: $tType,X34: L,X4: R] :
% 0.31/0.47 ( ( loc @ L @ R @ V @ X34 )
% 0.31/0.47 != ( rid @ R @ L @ V @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.distinct(15)
% 0.31/0.47 thf(fact_211_val_Odistinct_I3_J,axiom,
% 0.31/0.47 ! [R: $tType,V: $tType,L: $tType,X1: const,X34: L] :
% 0.31/0.47 ( ( cv @ R @ L @ V @ X1 )
% 0.31/0.47 != ( loc @ L @ R @ V @ X34 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.distinct(3)
% 0.31/0.47 thf(fact_212_substitution_Odomains__subsume__def,axiom,
% 0.31/0.47 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),Ls: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( domains_subsume @ L @ R @ V @ Ls )
% 0.31/0.47 = ( ord_less_eq @ ( set @ L ) @ ( lID_L @ L @ R @ V @ Ls ) @ ( doms @ L @ R @ V @ Ls ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.domains_subsume_def
% 0.31/0.47 thf(fact_213_substitution_Onew__pseudodeterministic,axiom,
% 0.31/0.47 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,V2: val @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ref @ R @ L @ V @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( ? [L4: L] :
% 0.31/0.47 ( ~ ( member @ L @ L4 @ ( lID_G @ R @ L @ V @ S ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L4 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L4 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.new_pseudodeterministic
% 0.31/0.47 thf(fact_214_substitution_Orevision__step_Onew,axiom,
% 0.31/0.47 ! [R: $tType,V: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,V2: val @ R @ L @ V,L2: L] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ref @ R @ L @ V @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member @ L @ L2 @ ( lID_G @ R @ L @ V @ S ) )
% 0.31/0.47 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L2 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.new
% 0.31/0.47 thf(fact_215_revision__step__relaxed_Oset,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l,V2: val @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L2 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.set
% 0.31/0.47 thf(fact_216_substitution_Orevision__step__relaxed_Oset,axiom,
% 0.31/0.47 ! [R: $tType,L: $tType,V: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L,V2: val @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L2 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.set
% 0.31/0.47 thf(fact_217_expr_Oinject_I6_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,Y61: expr @ R @ L @ V,Y62: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ( assign @ R @ L @ V @ X61 @ X62 )
% 0.31/0.47 = ( assign @ R @ L @ V @ Y61 @ Y62 ) )
% 0.31/0.47 = ( ( X61 = Y61 )
% 0.31/0.47 & ( X62 = Y62 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(6)
% 0.31/0.47 thf(fact_218_expr_Odistinct_I39_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ref @ R @ L @ V @ X4 )
% 0.31/0.47 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(39)
% 0.31/0.47 thf(fact_219_expr_Odistinct_I51_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 0.31/0.47 ( ( assign @ R @ L @ V @ X61 @ X62 )
% 0.31/0.47 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(51)
% 0.31/0.47 thf(fact_220_expr_Odistinct_I53_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.31/0.47 ( ( assign @ R @ L @ V @ X61 @ X62 )
% 0.31/0.47 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(53)
% 0.31/0.47 thf(fact_221_expr_Odistinct_I9_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ve @ R @ L @ V @ X1 )
% 0.31/0.47 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(9)
% 0.31/0.47 thf(fact_222_expr_Odistinct_I31_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(31)
% 0.31/0.47 thf(fact_223_revision__step_Oset,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l,V2: val @ r @ l @ v] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ( member @ l @ L2 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau ) ) )
% 0.31/0.47 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L2 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.set
% 0.31/0.47 thf(fact_224_set__deterministic,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l,V2: val @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( ( member @ l @ L2 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L2 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % set_deterministic
% 0.31/0.47 thf(fact_225_dom__const,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B] :
% 0.31/0.47 ( ( dom @ A @ B
% 0.31/0.47 @ ^ [X: A] : ( some @ B @ ( F @ X ) ) )
% 0.31/0.47 = ( top_top @ ( set @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dom_const
% 0.31/0.47 thf(fact_226_domI,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,M: B > ( option @ A ),A2: B,B2: A] :
% 0.31/0.47 ( ( ( M @ A2 )
% 0.31/0.47 = ( some @ A @ B2 ) )
% 0.31/0.47 => ( member @ B @ A2 @ ( dom @ B @ A @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domI
% 0.31/0.47 thf(fact_227_domD,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,A2: A,M: A > ( option @ B )] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( dom @ A @ B @ M ) )
% 0.31/0.47 => ? [B4: B] :
% 0.31/0.47 ( ( M @ A2 )
% 0.31/0.47 = ( some @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domD
% 0.31/0.47 thf(fact_228_dom__def,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( dom @ A @ B )
% 0.31/0.47 = ( ^ [M3: A > ( option @ B )] :
% 0.31/0.47 ( collect @ A
% 0.31/0.47 @ ^ [A3: A] :
% 0.31/0.47 ( ( M3 @ A3 )
% 0.31/0.47 != ( none @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dom_def
% 0.31/0.47 thf(fact_229_domIff,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,A2: A,M: A > ( option @ B )] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( dom @ A @ B @ M ) )
% 0.31/0.47 = ( ( M @ A2 )
% 0.31/0.47 != ( none @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domIff
% 0.31/0.47 thf(fact_230_finite__map__freshness,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F: A > ( option @ B )] :
% 0.31/0.47 ( ( finite_finite @ A @ ( dom @ A @ B @ F ) )
% 0.31/0.47 => ( ~ ( finite_finite @ A @ ( top_top @ ( set @ A ) ) )
% 0.31/0.47 => ? [X6: A] :
% 0.31/0.47 ( ( F @ X6 )
% 0.31/0.47 = ( none @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_map_freshness
% 0.31/0.47 thf(fact_231_substitution_Oset__deterministic,axiom,
% 0.31/0.47 ! [R: $tType,L: $tType,V: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L,V2: val @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( ( member @ L @ L2 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L2 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.set_deterministic
% 0.31/0.47 thf(fact_232_substitution_Orevision__step_Oset,axiom,
% 0.31/0.47 ! [R: $tType,L: $tType,V: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L,V2: val @ R @ L @ V] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ( member @ L @ L2 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau ) ) )
% 0.31/0.47 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L2 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.set
% 0.31/0.47 thf(fact_233_revision__step_Oget,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( read @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( member @ l @ L2 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau ) ) )
% 0.31/0.47 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( the @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.get
% 0.31/0.47 thf(fact_234_revision__step__relaxed_Oget,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( read @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( the @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.get
% 0.31/0.47 thf(fact_235__092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r] :
% 0.31/0.47 ( ( domain398919503obally @ r @ l @ v @ S )
% 0.31/0.47 => ( ( member @ r @ R2 @ ( dom @ r @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ S ) )
% 0.31/0.47 => ( subsumes_accessible @ r @ l @ v @ R2 @ R2 @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<S>\<^sub>G_imp_\<A>_refl
% 0.31/0.47 thf(fact_236_subsumes__accessible__globally__def,axiom,
% 0.31/0.47 ( ( subsum380726323obally @ r @ l @ v )
% 0.31/0.47 = ( ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ! [R_12: r,R_22: r] :
% 0.31/0.47 ( ( member @ r @ R_12 @ ( dom @ r @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ S4 ) )
% 0.31/0.47 => ( ( member @ r @ R_22 @ ( dom @ r @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ S4 ) )
% 0.31/0.47 => ( subsumes_accessible @ r @ l @ v @ R_12 @ R_22 @ S4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsumes_accessible_globally_def
% 0.31/0.47 thf(fact_237_expr_Oinject_I5_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X52: expr @ R @ L @ V,Y5: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ( read @ R @ L @ V @ X52 )
% 0.31/0.47 = ( read @ R @ L @ V @ Y5 ) )
% 0.31/0.47 = ( X52 = Y5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(5)
% 0.31/0.47 thf(fact_238_option_Ocollapse,axiom,
% 0.31/0.47 ! [A: $tType,Option: option @ A] :
% 0.31/0.47 ( ( Option
% 0.31/0.47 != ( none @ A ) )
% 0.31/0.47 => ( ( some @ A @ ( the @ A @ Option ) )
% 0.31/0.47 = Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.collapse
% 0.31/0.47 thf(fact_239_get__deterministic,axiom,
% 0.31/0.47 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( read @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( ( member @ l @ L2 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( the @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % get_deterministic
% 0.31/0.47 thf(fact_240_expr_Odistinct_I37_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,X52: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ref @ R @ L @ V @ X4 )
% 0.31/0.47 != ( read @ R @ L @ V @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(37)
% 0.31/0.47 thf(fact_241_option_Oexpand,axiom,
% 0.31/0.47 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 0.31/0.47 ( ( ( Option
% 0.31/0.47 = ( none @ A ) )
% 0.31/0.47 = ( Option2
% 0.31/0.47 = ( none @ A ) ) )
% 0.31/0.47 => ( ( ( Option
% 0.31/0.47 != ( none @ A ) )
% 0.31/0.47 => ( ( Option2
% 0.31/0.47 != ( none @ A ) )
% 0.31/0.47 => ( ( the @ A @ Option )
% 0.31/0.47 = ( the @ A @ Option2 ) ) ) )
% 0.31/0.47 => ( Option = Option2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.expand
% 0.31/0.47 thf(fact_242_expr_Odistinct_I47_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X52: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 0.31/0.47 ( ( read @ R @ L @ V @ X52 )
% 0.31/0.47 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(47)
% 0.31/0.47 thf(fact_243_expr_Odistinct_I49_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X52: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.31/0.47 ( ( read @ R @ L @ V @ X52 )
% 0.31/0.47 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(49)
% 0.31/0.47 thf(fact_244_expr_Odistinct_I7_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X52: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ve @ R @ L @ V @ X1 )
% 0.31/0.47 != ( read @ R @ L @ V @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(7)
% 0.31/0.47 thf(fact_245_expr_Odistinct_I29_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X52: expr @ R @ L @ V] :
% 0.31/0.47 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( read @ R @ L @ V @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(29)
% 0.31/0.47 thf(fact_246_expr_Odistinct_I45_J,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,X52: expr @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 0.31/0.47 ( ( read @ R @ L @ V @ X52 )
% 0.31/0.47 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(45)
% 0.31/0.47 thf(fact_247_option_Oexhaust__sel,axiom,
% 0.31/0.47 ! [A: $tType,Option: option @ A] :
% 0.31/0.47 ( ( Option
% 0.31/0.47 != ( none @ A ) )
% 0.31/0.47 => ( Option
% 0.31/0.47 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust_sel
% 0.31/0.47 thf(fact_248_option_Osel,axiom,
% 0.31/0.47 ! [A: $tType,X22: A] :
% 0.31/0.47 ( ( the @ A @ ( some @ A @ X22 ) )
% 0.31/0.47 = X22 ) ).
% 0.31/0.47
% 0.31/0.47 % option.sel
% 0.31/0.47 thf(fact_249_RID_092_060_094sub_062GE,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,R2: A,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) )] :
% 0.31/0.47 ( ( member @ A @ R2 @ ( rID_G @ A @ B @ C @ S ) )
% 0.31/0.47 => ( ~ ( member @ A @ R2 @ ( dom @ A @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) @ S ) )
% 0.31/0.47 => ~ ! [R9: A,Ls3: product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) )] :
% 0.31/0.47 ( ( ( S @ R9 )
% 0.31/0.47 = ( some @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) @ Ls3 ) )
% 0.31/0.47 => ~ ( member @ A @ R2 @ ( rID_L @ B @ A @ C @ Ls3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>GE
% 0.31/0.47 thf(fact_250_substitution_O_092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( domain398919503obally @ R @ L @ V @ S )
% 0.31/0.47 => ( ( member @ R @ R2 @ ( dom @ R @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ S ) )
% 0.31/0.47 => ( subsumes_accessible @ R @ L @ V @ R2 @ R2 @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.\<S>\<^sub>G_imp_\<A>_refl
% 0.31/0.47 thf(fact_251_substitution_Osubsumes__accessible__globally__def,axiom,
% 0.31/0.47 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 0.31/0.47 = ( ! [R_12: R,R_22: R] :
% 0.31/0.47 ( ( member @ R @ R_12 @ ( dom @ R @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ S ) )
% 0.31/0.47 => ( ( member @ R @ R_22 @ ( dom @ R @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ S ) )
% 0.31/0.47 => ( subsumes_accessible @ R @ L @ V @ R_12 @ R_22 @ S ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.subsumes_accessible_globally_def
% 0.31/0.47 thf(fact_252_substitution_Orevision__step__relaxed_Oget,axiom,
% 0.31/0.47 ! [R: $tType,V: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( read @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( the @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.get
% 0.31/0.47 thf(fact_253_substitution_Oget__deterministic,axiom,
% 0.31/0.47 ! [R: $tType,V: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( read @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.31/0.47 = ( ( member @ L @ L2 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( the @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.get_deterministic
% 0.31/0.47 thf(fact_254_substitution_Orevision__step_Oget,axiom,
% 0.31/0.47 ! [R: $tType,V: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L] :
% 0.31/0.47 ( ( substitution @ R @ L @ V @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( read @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( member @ L @ L2 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau ) ) )
% 0.31/0.47 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( the @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.get
% 0.31/0.47
% 0.31/0.47 % Type constructors (3)
% 0.31/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/0.47 ! [A6: $tType,A7: $tType] :
% 0.31/0.47 ( ( order @ A7 )
% 0.31/0.47 => ( order @ ( A6 > A7 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 0.31/0.47 ! [A6: $tType] : ( order @ ( set @ A6 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 0.31/0.47 order @ $o ).
% 0.31/0.47
% 0.31/0.47 % Helper facts (3)
% 0.31/0.47 thf(help_If_3_1_T,axiom,
% 0.31/0.47 ! [P: $o] :
% 0.31/0.47 ( ( P = $true )
% 0.31/0.47 | ( P = $false ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_2_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.31/0.47 ( ( if @ A @ $false @ X2 @ Y )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_1_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.31/0.47 ( ( if @ A @ $true @ X2 @ Y )
% 0.31/0.47 = X2 ) ).
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ( ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ x ) ) @ r3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ r4 ) ) ) ) ) ) ) @ r4
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ sigma @ tau )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.31/0.47 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.31/0.47 @ e2 ) ) ) )
% 0.31/0.47 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )
% 0.31/0.47 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ r4 ) ) ) ) ) ) ) @ r4
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ sigma @ tau )
% 0.31/0.47 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.31/0.47 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.31/0.47 @ e2 ) ) ) )
% 0.31/0.47 @ r2
% 0.31/0.47 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ x ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 3.28/1.66 ---- Embedded in THF ---
% 3.28/1.66 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.28/1.66 %%% Generated on Tue Feb 24 08:24:24 EST 2026
% 3.28/1.66 %%% using '$$dhol' embedding, version 1.3.0.
% 3.28/1.66 %%% Logic specification used:
% 3.28/1.66 %%% thf(spec, logic, $$dhol).
% 3.28/1.66
% 3.28/1.66 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qbB1WGygH8/DTF2DTF7240.p
% 3.28/1.66 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.28/1.66 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 3.28/1.66 thf(ty_t_Data_Oconst, type, const: $tType).
% 3.28/1.66 thf(ty_t_Data_Ocntxt, type, cntxt: ($tType > ($tType > ($tType > $tType)))).
% 3.28/1.66 thf(ty_t_Data_Oexpr, type, expr: ($tType > ($tType > ($tType > $tType)))).
% 3.28/1.66 thf(ty_t_Data_Oval, type, val: ($tType > ($tType > ($tType > $tType)))).
% 3.28/1.66 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.28/1.66 thf(ty_tf_v, type, v: $tType).
% 3.28/1.66 thf(ty_tf_r, type, r: $tType).
% 3.28/1.66 thf(ty_tf_l, type, l: $tType).
% 3.28/1.66 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.28/1.66 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.28/1.66 thf(sy_c_Data_Ocombine, type, combine: (!> [A:$tType,B:$tType]: (((A > (option @ B)) > ((A > (option @ B)) > (A > (option @ B))))))).
% 3.28/1.66 thf(sy_c_Data_Oconst_OF, type, f: const).
% 3.28/1.66 thf(sy_c_Data_Oconst_OT, type, t: const).
% 3.28/1.66 thf(sy_c_Data_Oconst_OUnit, type, unit: const).
% 3.28/1.66 thf(sy_c_Data_Odoms, type, doms: (!> [L:$tType,R:$tType,V:$tType]: ((((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) > (set @ L))))).
% 3.28/1.66 thf(sy_c_Data_Oexpr_OAssign, type, assign: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))))).
% 3.28/1.66 thf(sy_c_Data_Oexpr_OIte, type, ite: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > ((((expr @ R) @ L) @ V) > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))))).
% 3.28/1.66 thf(sy_c_Data_Oexpr_ORead, type, read: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.28/1.66 thf(sy_c_Data_Oexpr_ORef, type, ref: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.28/1.66 thf(sy_c_Data_Oexpr_ORfork, type, rfork: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.28/1.66 thf(sy_c_Data_Oexpr_ORjoin, type, rjoin: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.28/1.66 thf(sy_c_Data_Oexpr_OVE, type, ve: (!> [R:$tType,L:$tType,V:$tType]: (((((val @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.28/1.66 thf(sy_c_Data_Oplug, type, plug: (!> [R:$tType,L:$tType,V:$tType]: (((((cntxt @ R) @ L) @ V) > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))))).
% 3.28/1.66 thf(sy_c_Data_Oval_OCV, type, cv: (!> [R:$tType,L:$tType,V:$tType]: ((const > (((val @ R) @ L) @ V))))).
% 3.28/1.66 thf(sy_c_Data_Oval_OLoc, type, loc: (!> [L:$tType,R:$tType,V:$tType]: ((L > (((val @ R) @ L) @ V))))).
% 3.28/1.66 thf(sy_c_Data_Oval_ORid, type, rid: (!> [R:$tType,L:$tType,V:$tType]: ((R > (((val @ R) @ L) @ V))))).
% 3.28/1.66 thf(sy_c_Executions_Osubstitution_Oexecution, type, execution: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > ((((expr @ R) @ L) @ V) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o))))))).
% 3.28/1.66 thf(sy_c_Executions_Osubstitution_Oinductive__invariant, type, inductive_invariant: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > (((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o) > $o))))).
% 3.28/1.66 thf(sy_c_Executions_Osubstitution_Omaximal__execution, type, maximal_execution: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > ((((expr @ R) @ L) @ V) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o))))))).
% 3.28/1.66 thf(sy_c_Executions_Osubstitution_Oreachable, type, reachable: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o))))).
% 3.28/1.66 thf(sy_c_Executions_Osubstitution_Osteps, type, steps: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > (set @ ((product_prod @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))))))).
% 3.28/1.66 thf(sy_c_Executions_Osubstitution_Oterminates__in, type, terminates_in: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > ((((expr @ R) @ L) @ V) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o)))))).
% 3.28/1.66 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.28/1.66 thf(sy_c_Fun_Ofun__upd, type, fun_upd: (!> [A:$tType,B:$tType]: (((A > B) > (A > (B > (A > B))))))).
% 3.28/1.66 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.28/1.66 thf(sy_c_Map_Odom, type, dom: (!> [A:$tType,B:$tType]: (((A > (option @ B)) > (set @ A))))).
% 3.28/1.66 thf(sy_c_Occurrences_OLID_092_060_094sub_062G, type, lID_G: (!> [R:$tType,L:$tType,V:$tType]: (((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > (set @ L))))).
% 3.28/1.66 thf(sy_c_Occurrences_OLID_092_060_094sub_062L, type, lID_L: (!> [L:$tType,R:$tType,V:$tType]: ((((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) > (set @ L))))).
% 3.28/1.66 thf(sy_c_Occurrences_ORID_092_060_094sub_062G, type, rID_G: (!> [R:$tType,L:$tType,V:$tType]: (((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > (set @ R))))).
% 3.28/1.66 thf(sy_c_Occurrences_ORID_092_060_094sub_062L, type, rID_L: (!> [L:$tType,R:$tType,V:$tType]: ((((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) > (set @ R))))).
% 3.28/1.66 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume, type, domains_subsume: (!> [L:$tType,R:$tType,V:$tType]: ((((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) > $o)))).
% 3.28/1.66 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally, type, domain398919503obally: (!> [R:$tType,L:$tType,V:$tType]: (((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o)))).
% 3.28/1.66 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step, type, revision_step: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > (R > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o))))))).
% 3.28/1.66 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed, type, revisi1433015572elaxed: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > (R > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o))))))).
% 3.28/1.66 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible, type, subsumes_accessible: (!> [R:$tType,L:$tType,V:$tType]: ((R > (R > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o)))))).
% 3.28/1.66 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally, type, subsum380726323obally: (!> [R:$tType,L:$tType,V:$tType]: (((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o)))).
% 3.28/1.66 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 3.28/1.66 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 3.28/1.66 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 3.28/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.28/1.66 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 3.28/1.66 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.28/1.66 thf(sy_c_Renaming_Oeq__states, type, eq_states: (!> [R:$tType,L:$tType,V:$tType]: (((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > ((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o))))).
% 3.28/1.66 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.28/1.66 thf(sy_c_Substitution_Osubstitution, type, substitution: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > $o)))).
% 3.28/1.66 thf(sy_c_Transitive__Closure_Ortrancl, type, transitive_rtrancl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ A) @ A)))))).
% 3.28/1.66 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.28/1.66 thf(sy_v__092_060E_062, type, e: (((cntxt @ r) @ l) @ v)).
% 3.28/1.66 thf(sy_v__092_060sigma_062, type, sigma: (l > (option @ (((val @ r) @ l) @ v)))).
% 3.28/1.66 thf(sy_v__092_060tau_062, type, tau: (l > (option @ (((val @ r) @ l) @ v)))).
% 3.28/1.66 thf(sy_v_e, type, e2: (((expr @ r) @ l) @ v)).
% 3.28/1.66 thf(sy_v_r, type, r2: r).
% 3.28/1.66 thf(sy_v_r_H, type, r3: r).
% 3.28/1.66 thf(sy_v_r_H_H, type, r4: r).
% 3.28/1.66 thf(sy_v_s_092_060_094sub_0621, type, s_1: (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))).
% 3.28/1.66 thf(sy_v_s_092_060_094sub_0622, type, s_2: (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))).
% 3.28/1.66 thf(sy_v_s_092_060_094sub_0622_H, type, s_22: (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))).
% 3.28/1.66 thf(sy_v_subst, type, subst: ((((expr @ r) @ l) @ v) > (v > ((((expr @ r) @ l) @ v) > (((expr @ r) @ l) @ v))))).
% 3.28/1.66 thf(sy_v_x, type, x: ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))).
% 3.28/1.66 thf(fact_0_assms_I4_J, axiom, (~ ((((member @ r) @ r4) @ ((((rID_G @ r) @ l) @ v) @ s_2))))).
% 3.28/1.66 thf(fact_1_assms_I7_J, axiom, (r2 != r4)).
% 3.28/1.66 thf(fact_2_assms_I6_J, axiom, (r2 != r3)).
% 3.28/1.66 thf(fact_3_assms_I1_J, axiom, (s_2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ s_1) @ r2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ x)))).
% 3.28/1.66 thf(fact_4_assms_I3_J, axiom, ((s_2 @ r3) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ tau) @ (((((plug @ r) @ l) @ v) @ e) @ ((((rfork @ r) @ l) @ v) @ e2))))))).
% 3.28/1.66 thf(fact_5_assms_I2_J, axiom, (s_22 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ s_1) @ r3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ tau) @ (((((plug @ r) @ l) @ v) @ e) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ r4)))))))) @ r4) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ sigma) @ tau)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ e2)))))).
% 3.28/1.66 thf(fact_6_revision__step_Ofork, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E2:(((expr @ r) @ l) @ v),R3:r]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rfork @ r) @ l) @ v) @ E2)))))) => ((~ ((((member @ r) @ R3) @ ((((rID_G @ r) @ l) @ v) @ S)))) => (((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R3)))))))) @ R3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ E2)))))))))).
% 3.28/1.66 thf(fact_7_assms_I5_J, axiom, (((((((revision_step @ r) @ l) @ v) @ subst) @ r2) @ s_22) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ s_1) @ r3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ tau) @ (((((plug @ r) @ l) @ v) @ e) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ r4)))))))) @ r4) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ sigma) @ tau)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ e2))))) @ r2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ x)))).
% 3.28/1.66 thf(fact_8_restrictions__inwards, axiom, (! [A:$tType,B:$tType,X2:A,X3:A,F:(A > (option @ B)),Y:B]: (((X2 != X3) => ((((((fun_upd @ A) @ (option @ B)) @ (((((fun_upd @ A) @ (option @ B)) @ F) @ X2) @ ((some @ B) @ Y))) @ X3) @ (none @ B)) = (((((fun_upd @ A) @ (option @ B)) @ (((((fun_upd @ A) @ (option @ B)) @ F) @ X3) @ (none @ B))) @ X2) @ ((some @ B) @ Y))))))).
% 3.28/1.66 thf(fact_9_empty__upd__none, axiom, (! [B:$tType,A:$tType,X2:A]: (((((((fun_upd @ A) @ (option @ B)) @ (^ [X:A]: ((none @ B)))) @ X2) @ (none @ B)) = (^ [X:A]: ((none @ B))))))).
% 3.28/1.66 thf(fact_10_not__None__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((X2 != (none @ A)) = (? [Y2:A]: ((X2 = ((some @ A) @ Y2)))))))).
% 3.28/1.66 thf(fact_11_not__Some__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((! [Y2:A]: ((X2 != ((some @ A) @ Y2)))) = (X2 = (none @ A)))))).
% 3.28/1.66 thf(fact_12_map__upd__nonempty, axiom, (! [B:$tType,A:$tType,T:(A > (option @ B)),K:A,X2:B]: (((((((fun_upd @ A) @ (option @ B)) @ T) @ K) @ ((some @ B) @ X2)) != (^ [X:A]: ((none @ B))))))).
% 3.28/1.66 thf(fact_13_fork__pseudodeterministic, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E2:(((expr @ r) @ l) @ v),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rfork @ r) @ l) @ v) @ E2)))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = (? [R4:r]: (((~ ((((member @ r) @ R4) @ ((((rID_G @ r) @ l) @ v) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rfork @ r) @ l) @ v) @ E2)))))))))) & (S2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R4)))))))) @ R4) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ E2))))))))))))).
% 3.28/1.66 thf(fact_14_revision__step__relaxed_Ofork, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E2:(((expr @ r) @ l) @ v),R3:r]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rfork @ r) @ l) @ v) @ E2)))))) => ((~ ((((member @ r) @ R3) @ ((((rID_G @ r) @ l) @ v) @ S)))) => (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R3)))))))) @ R3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ E2)))))))))).
% 3.28/1.66 thf(fact_15_val_Oinject_I4_J, axiom, (! [V:$tType,L:$tType,R:$tType,X4:R,Y4:R]: (((((((rid @ R) @ L) @ V) @ X4) = ((((rid @ R) @ L) @ V) @ Y4)) = (X4 = Y4))))).
% 3.28/1.66 thf(fact_16_injective__cntxt, axiom, (! [C:$tType,B:$tType,A:$tType,E:(((cntxt @ A) @ B) @ C),E1:(((expr @ A) @ B) @ C),E22:(((expr @ A) @ B) @ C)]: ((((((((plug @ A) @ B) @ C) @ E) @ E1) = (((((plug @ A) @ B) @ C) @ E) @ E22)) = (E1 = E22))))).
% 3.28/1.66 thf(fact_17_expr_Oinject_I1_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),Y1:(((val @ R) @ L) @ V)]: (((((((ve @ R) @ L) @ V) @ X1) = ((((ve @ R) @ L) @ V) @ Y1)) = (X1 = Y1))))).
% 3.28/1.66 thf(fact_18_fun__upd__upd, axiom, (! [A:$tType,B:$tType,F:(A > B),X2:A,Y:B,Z:B]: (((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ F) @ X2) @ Y)) @ X2) @ Z) = (((((fun_upd @ A) @ B) @ F) @ X2) @ Z))))).
% 3.28/1.66 thf(fact_19_fun__upd__triv, axiom, (! [B:$tType,A:$tType,F:(A > B),X2:A]: (((((((fun_upd @ A) @ B) @ F) @ X2) @ (F @ X2)) = F)))).
% 3.28/1.66 thf(fact_20_option_Oinject, axiom, (! [A:$tType,X22:A,Y22:A]: (((((some @ A) @ X22) = ((some @ A) @ Y22)) = (X22 = Y22))))).
% 3.28/1.66 thf(fact_21_fun__upd__apply, axiom, (! [A:$tType,B:$tType]: ((((fun_upd @ B) @ A) = (^ [F2:(B > A),X:B,Y2:A,Z2:B]: (((((if @ A) @ (Z2 = X)) @ Y2) @ (F2 @ Z2)))))))).
% 3.28/1.66 thf(fact_22_expr_Oinject_I7_J, axiom, (! [V:$tType,L:$tType,R:$tType,X7:(((expr @ R) @ L) @ V),Y7:(((expr @ R) @ L) @ V)]: (((((((rfork @ R) @ L) @ V) @ X7) = ((((rfork @ R) @ L) @ V) @ Y7)) = (X7 = Y7))))).
% 3.28/1.66 thf(fact_23_RID_092_060_094sub_062GI_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R2:B,V2:((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))]: ((((S @ R2) = ((some @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))) @ V2)) => (((member @ B) @ R2) @ ((((rID_G @ B) @ A) @ C) @ S)))))).
% 3.28/1.66 thf(fact_24_in__restricted__global__in__unrestricted__global_I1_J, axiom, (! [C:$tType,B:$tType,A:$tType,R3:A,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A]: (((((member @ A) @ R3) @ ((((rID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))) => (((member @ A) @ R3) @ ((((rID_G @ A) @ B) @ C) @ S)))))).
% 3.28/1.66 thf(fact_25_only__fork__introduces__rids_H, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R3:r]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => ((! [Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),E4:(((expr @ r) @ l) @ v)]: (((S @ R2) != ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((rfork @ r) @ l) @ v) @ E4)))))))) => ((~ ((((member @ r) @ R3) @ ((((rID_G @ r) @ l) @ v) @ S)))) => (~ ((((member @ r) @ R3) @ ((((rID_G @ r) @ l) @ v) @ S2)))))))))).
% 3.28/1.66 thf(fact_26_in__restricted__global__in__updated__global_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,R3:A,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A,Ls:((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))]: (((((member @ A) @ R3) @ ((((rID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))) => (((member @ A) @ R3) @ ((((rID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ ((some @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))) @ Ls)))))))).
% 3.28/1.66 thf(fact_27_substitution__axioms, axiom, ((((substitution @ r) @ l) @ v) @ subst)).
% 3.28/1.66 thf(fact_28_expr_Odistinct_I11_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X7:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != ((((rfork @ R) @ L) @ V) @ X7))))).
% 3.28/1.66 thf(fact_29_fun__upd__idem__iff, axiom, (! [A:$tType,B:$tType,F:(A > B),X2:A,Y:B]: ((((((((fun_upd @ A) @ B) @ F) @ X2) @ Y) = F) = ((F @ X2) = Y))))).
% 3.28/1.66 thf(fact_30_fun__upd__twist, axiom, (! [A:$tType,B:$tType,A2:A,C2:A,M:(A > B),B2:B,D:B]: (((A2 != C2) => ((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M) @ A2) @ B2)) @ C2) @ D) = (((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M) @ C2) @ D)) @ A2) @ B2)))))).
% 3.28/1.66 thf(fact_31_fun__upd__other, axiom, (! [B:$tType,A:$tType,Z:A,X2:A,F:(A > B),Y:B]: (((Z != X2) => (((((((fun_upd @ A) @ B) @ F) @ X2) @ Y) @ Z) = (F @ Z)))))).
% 3.28/1.66 thf(fact_32_fun__upd__same, axiom, (! [B:$tType,A:$tType,F:(B > A),X2:B,Y:A]: ((((((((fun_upd @ B) @ A) @ F) @ X2) @ Y) @ X2) = Y)))).
% 3.28/1.66 thf(fact_33_fun__upd__idem, axiom, (! [A:$tType,B:$tType,F:(B > A),X2:B,Y:A]: ((((F @ X2) = Y) => ((((((fun_upd @ B) @ A) @ F) @ X2) @ Y) = F))))).
% 3.28/1.66 thf(fact_34_fun__upd__eqD, axiom, (! [A:$tType,B:$tType,F:(A > B),X2:A,Y:B,G:(A > B),Z:B]: ((((((((fun_upd @ A) @ B) @ F) @ X2) @ Y) = (((((fun_upd @ A) @ B) @ G) @ X2) @ Z)) => (Y = Z))))).
% 3.28/1.66 thf(fact_35_fun__upd__def, axiom, (! [B:$tType,A:$tType]: ((((fun_upd @ A) @ B) = (^ [F2:(A > B),A3:A,B3:B,X:A]: (((((if @ B) @ (X = A3)) @ B3) @ (F2 @ X)))))))).
% 3.28/1.66 thf(fact_36_combine__options__cases, axiom, (! [A:$tType,B:$tType,X2:(option @ A),P:((option @ A) > ((option @ B) > $o)),Y:(option @ B)]: ((((X2 = (none @ A)) => ((P @ X2) @ Y)) => (((Y = (none @ B)) => ((P @ X2) @ Y)) => ((! [A4:A,B4:B]: (((X2 = ((some @ A) @ A4)) => ((Y = ((some @ B) @ B4)) => ((P @ X2) @ Y))))) => ((P @ X2) @ Y))))))).
% 3.28/1.66 thf(fact_37_split__option__all, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((! [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) & (! [X:A]: ((P3 @ ((some @ A) @ X))))))))))).
% 3.28/1.66 thf(fact_38_split__option__ex, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((? [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) | (? [X:A]: ((P3 @ ((some @ A) @ X))))))))))).
% 3.28/1.66 thf(fact_39_option_Oinducts, axiom, (! [A:$tType,P:((option @ A) > $o),Option:(option @ A)]: (((P @ (none @ A)) => ((! [X6:A]: ((P @ ((some @ A) @ X6)))) => (P @ Option)))))).
% 3.28/1.66 thf(fact_40_option_Oexhaust, axiom, (! [A:$tType,Y:(option @ A)]: (((Y != (none @ A)) => (~ ((! [X23:A]: ((Y != ((some @ A) @ X23)))))))))).
% 3.28/1.66 thf(fact_41_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X22:A]: (((Option = ((some @ A) @ X22)) => (Option != (none @ A)))))).
% 3.28/1.66 thf(fact_42_option_Odistinct_I1_J, axiom, (! [A:$tType,X22:A]: (((none @ A) != ((some @ A) @ X22))))).
% 3.28/1.66 thf(fact_43_combine_Ocases, axiom, (! [B:$tType,A:$tType,X2:((product_prod @ (A > (option @ B))) @ ((product_prod @ (A > (option @ B))) @ A))]: ((~ ((! [F3:(A > (option @ B)),G2:(A > (option @ B)),X6:A]: ((X2 != ((((product_Pair @ (A > (option @ B))) @ ((product_prod @ (A > (option @ B))) @ A)) @ F3) @ ((((product_Pair @ (A > (option @ B))) @ A) @ G2) @ X6)))))))))).
% 3.28/1.66 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.28/1.66 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A5)))) = A5)))).
% 3.28/1.66 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X6:A]: (((P @ X6) = (Q @ X6)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.28/1.66 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X6:A]: (((F @ X6) = (G @ X6)))) => (F = G))))).
% 3.28/1.66 thf(fact_48_map__upd__Some__unfold, axiom, (! [B:$tType,A:$tType,M:(B > (option @ A)),A2:B,B2:A,X2:B,Y:A]: (((((((((fun_upd @ B) @ (option @ A)) @ M) @ A2) @ ((some @ A) @ B2)) @ X2) = ((some @ A) @ Y)) = (((X2 = A2) & (B2 = Y)) | ((X2 != A2) & ((M @ X2) = ((some @ A) @ Y)))))))).
% 3.28/1.66 thf(fact_49_map__upd__triv, axiom, (! [A:$tType,B:$tType,T:(B > (option @ A)),K:B,X2:A]: ((((T @ K) = ((some @ A) @ X2)) => ((((((fun_upd @ B) @ (option @ A)) @ T) @ K) @ ((some @ A) @ X2)) = T))))).
% 3.28/1.66 thf(fact_50_map__upd__eqD1, axiom, (! [A:$tType,B:$tType,M:(A > (option @ B)),A2:A,X2:B,N:(A > (option @ B)),Y:B]: ((((((((fun_upd @ A) @ (option @ B)) @ M) @ A2) @ ((some @ B) @ X2)) = (((((fun_upd @ A) @ (option @ B)) @ N) @ A2) @ ((some @ B) @ Y))) => (X2 = Y))))).
% 3.28/1.66 thf(fact_51_LID__local__store_Oinduct, axiom, (! [V:$tType,R:$tType,L:$tType,P:(((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) > $o),A0:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))]: (((! [Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E4:(((expr @ R) @ L) @ V)]: ((P @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ E4))))) => (P @ A0))))).
% 3.28/1.66 thf(fact_52_LID__local__store_Ocases, axiom, (! [V:$tType,L:$tType,R:$tType,X2:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))]: ((~ ((! [Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E4:(((expr @ R) @ L) @ V)]: ((X2 != ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ E4)))))))))).
% 3.28/1.66 thf(fact_53_combine_Osimps, axiom, (! [B:$tType,A:$tType]: ((((combine @ A) @ B) = (^ [F2:(A > (option @ B)),G3:(A > (option @ B)),X:A]: (((((if @ (option @ B)) @ ((G3 @ X) = (none @ B))) @ (F2 @ X)) @ (G3 @ X)))))))).
% 3.28/1.66 thf(fact_54_combine_Oelims, axiom, (! [B:$tType,A:$tType,X2:(A > (option @ B)),Xa:(A > (option @ B)),Xb:A,Y:(option @ B)]: ((((((((combine @ A) @ B) @ X2) @ Xa) @ Xb) = Y) => ((((Xa @ Xb) = (none @ B)) => (Y = (X2 @ Xb))) & (((Xa @ Xb) != (none @ B)) => (Y = (Xa @ Xb)))))))).
% 3.28/1.66 thf(fact_55_local__steps__commute, axiom, (! [S_2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_1:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,X2:((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))),S_22:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R3:r,Y:((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))]: (((S_2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ X2))) => ((S_22 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ Y))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ X2))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ X2))) @ R3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ Y))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ Y))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ Y))) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ X2))) => (? [S_3:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_32:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((eq_states @ r) @ l) @ v) @ S_3) @ S_32) & (((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_3) | (S_2 = S_3)) & ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_32) | (S_22 = S_32))))))))))))).
% 3.28/1.66 thf(fact_56_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R3:r]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R3)))))))) => (((S @ R3) = (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) => (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ (^ [X:r]: ((none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))))))))).
% 3.28/1.66 thf(fact_57_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R3:r]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R3)))))))) => (((S @ R3) = (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) => (((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ (^ [X:r]: ((none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))))))))).
% 3.28/1.66 thf(fact_58_transition__relations__equivalent, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2)))))).
% 3.28/1.66 thf(fact_59_SLC__commute, axiom, (! [S_33:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_34:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R3:r,S_2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,S_22:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((S_33 = S_34) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_33) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_34) => ((((((eq_states @ r) @ l) @ v) @ S_33) @ S_34) & (((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_33) | (S_2 = S_33)) & ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_34) | (S_22 = S_34)))))))))).
% 3.28/1.66 thf(fact_60_SLC__sym, axiom, (! [R3:r,S_2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,S_22:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((? [S_35:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_36:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((eq_states @ r) @ l) @ v) @ S_35) @ S_36) & (((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_35) | (S_2 = S_35)) & ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_36) | (S_22 = S_36)))))) => (? [S_3:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_32:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((eq_states @ r) @ l) @ v) @ S_3) @ S_32) & (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_3) | (S_22 = S_3)) & ((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_32) | (S_2 = S_32)))))))))).
% 3.28/1.66 thf(fact_61_local__determinism, axiom, (! [R2:r,S_1:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_22:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_1) @ S_2) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_1) @ S_22) => (((((eq_states @ r) @ l) @ v) @ S_2) @ S_22)))))).
% 3.28/1.66 thf(fact_62_reachability__closed__under__execution__step, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => (((((reachable @ r) @ l) @ v) @ subst) @ S2)))))).
% 3.28/1.66 thf(fact_63_only__fork__introduces__rids, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => ((! [Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),E4:(((expr @ r) @ l) @ v)]: (((S @ R2) != ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((rfork @ r) @ l) @ v) @ E4)))))))) => (((ord_less_eq @ (set @ r)) @ ((((rID_G @ r) @ l) @ v) @ S2)) @ ((((rID_G @ r) @ l) @ v) @ S))))))).
% 3.28/1.66 thf(fact_64_substitution_Ofork__pseudodeterministic, axiom, (! [L:$tType,V:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E2:(((expr @ R) @ L) @ V),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rfork @ R) @ L) @ V) @ E2)))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (? [R4:R]: (((~ ((((member @ R) @ R4) @ ((((rID_G @ R) @ L) @ V) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rfork @ R) @ L) @ V) @ E2)))))))))) & (S2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R4)))))))) @ R4) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau)) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (^ [X:L]: ((none @ (((val @ R) @ L) @ V))))) @ E2)))))))))))))).
% 3.28/1.66 thf(fact_65_expr_Oinject_I8_J, axiom, (! [V:$tType,L:$tType,R:$tType,X8:(((expr @ R) @ L) @ V),Y8:(((expr @ R) @ L) @ V)]: (((((((rjoin @ R) @ L) @ V) @ X8) = ((((rjoin @ R) @ L) @ V) @ Y8)) = (X8 = Y8))))).
% 3.28/1.66 thf(fact_66_SLC__join_092_060_094sub_062_092_060epsilon_062, axiom, (! [S_1:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R5:r,S_2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R3:r,S_22:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S_1 @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R5)))))))) => ((S_2 = (^ [X:r]: ((none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))))) => (((S_1 @ R5) = (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_1) @ S_22) => ((R2 != R3) => (? [S_3:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_32:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((eq_states @ r) @ l) @ v) @ S_3) @ S_32) & (((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_3) | (S_2 = S_3)) & ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_32) | (S_22 = S_32)))))))))))))).
% 3.28/1.66 thf(fact_67_reachable__def, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) = (? [E5:(((expr @ r) @ l) @ v),S3:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((((((execution @ r) @ l) @ v) @ subst) @ E5) @ S3) @ S))))))).
% 3.28/1.66 thf(fact_68_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R3:r,S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R3)))))))) => (((S @ R3) = (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = (S2 = (^ [X:r]: ((none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))))))))))).
% 3.28/1.66 thf(fact_69_substitution_Olocal__determinism, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S_1:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_22:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_1) @ S_2) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_1) @ S_22) => (((((eq_states @ R) @ L) @ V) @ S_2) @ S_22))))))).
% 3.28/1.66 thf(fact_70_substitution_OSLC__commute, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S_33:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_34:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R3:R,S_2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,S_22:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((S_33 = S_34) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_33) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_34) => ((((((eq_states @ R) @ L) @ V) @ S_33) @ S_34) & (((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_33) | (S_2 = S_33)) & ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_34) | (S_22 = S_34))))))))))).
% 3.28/1.66 thf(fact_71_substitution_OSLC__sym, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R3:R,S_2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,S_22:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((? [S_35:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_36:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: (((((((eq_states @ R) @ L) @ V) @ S_35) @ S_36) & (((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_35) | (S_2 = S_35)) & ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_36) | (S_22 = S_36)))))) => (? [S_3:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_32:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: (((((((eq_states @ R) @ L) @ V) @ S_3) @ S_32) & (((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_3) | (S_22 = S_3)) & ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_32) | (S_2 = S_32))))))))))).
% 3.28/1.66 thf(fact_72_expr_Odistinct_I13_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.28/1.66 thf(fact_73_expr_Odistinct_I55_J, axiom, (! [V:$tType,L:$tType,R:$tType,X7:(((expr @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: ((((((rfork @ R) @ L) @ V) @ X7) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.28/1.66 thf(fact_74_substitution_Olocal__steps__commute, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S_2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_1:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,X2:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))),S_22:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R3:R,Y:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((S_2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ X2))) => ((S_22 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R3) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ Y))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ X2))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ X2))) @ R3) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ Y))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R3) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ Y))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R3) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ Y))) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ X2))) => (? [S_3:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_32:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: (((((((eq_states @ R) @ L) @ V) @ S_3) @ S_32) & (((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_3) | (S_2 = S_3)) & ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_32) | (S_22 = S_32)))))))))))))).
% 3.28/1.66 thf(fact_75_ID__restricted__global__subset__unrestricted_I2_J, axiom, (! [C:$tType,A:$tType,B:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R2:B]: ((((ord_less_eq @ (set @ B)) @ ((((rID_G @ B) @ A) @ C) @ (((((fun_upd @ B) @ (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))))) @ ((((rID_G @ B) @ A) @ C) @ S))))).
% 3.28/1.66 thf(fact_76_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S_1:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R5:R,S_2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R3:R,S_22:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S_1 @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R5)))))))) => ((S_2 = (^ [X:R]: ((none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))) => (((S_1 @ R5) = (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_1) @ S_22) => ((R2 != R3) => (? [S_3:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_32:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: (((((((eq_states @ R) @ L) @ V) @ S_3) @ S_32) & (((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_3) | (S_2 = S_3)) & ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_32) | (S_22 = S_32))))))))))))))).
% 3.28/1.66 thf(fact_77_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic, axiom, (! [L:$tType,V:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R3:R,S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) => (((S @ R3) = (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (S2 = (^ [X:R]: ((none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))))))))))).
% 3.28/1.66 thf(fact_78_inductive__invariant__is__execution__invariant, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),P:((r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) > $o)]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((((((inductive_invariant @ r) @ l) @ v) @ subst) @ P) => (P @ S)))))).
% 3.28/1.66 thf(fact_79_substitution_Orevision__step__relaxed_Ofork, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E2:(((expr @ R) @ L) @ V),R3:R]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rfork @ R) @ L) @ V) @ E2)))))) => ((~ ((((member @ R) @ R3) @ ((((rID_G @ R) @ L) @ V) @ S)))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) @ R3) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau)) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (^ [X:L]: ((none @ (((val @ R) @ L) @ V))))) @ E2))))))))))).
% 3.28/1.66 thf(fact_80_substitution_Orevision__step_Ofork, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E2:(((expr @ R) @ L) @ V),R3:R]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rfork @ R) @ L) @ V) @ E2)))))) => ((~ ((((member @ R) @ R3) @ ((((rID_G @ R) @ L) @ V) @ S)))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) @ R3) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau)) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (^ [X:L]: ((none @ (((val @ R) @ L) @ V))))) @ E2))))))))))).
% 3.28/1.66 thf(fact_81_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062, axiom, (! [L:$tType,V:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R3:R]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) => (((S @ R3) = (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (^ [X:R]: ((none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))))))))).
% 3.28/1.66 thf(fact_82_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062, axiom, (! [L:$tType,V:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R3:R]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) => (((S @ R3) = (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (^ [X:R]: ((none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))))))))).
% 3.28/1.66 thf(fact_83_substitution_Oonly__fork__introduces__rids, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => ((! [Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E4:(((expr @ R) @ L) @ V)]: (((S @ R2) != ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((rfork @ R) @ L) @ V) @ E4)))))))) => (((ord_less_eq @ (set @ R)) @ ((((rID_G @ R) @ L) @ V) @ S2)) @ ((((rID_G @ R) @ L) @ V) @ S)))))))).
% 3.28/1.66 thf(fact_84_reachable__imp___092_060S_062_092_060_094sub_062G, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((((domain398919503obally @ r) @ l) @ v) @ S))))).
% 3.28/1.66 thf(fact_85_domains__subsume__globally__def, axiom, ((((domain398919503obally @ r) @ l) @ v) = (^ [S4:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((! [R6:r,Ls2:((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))]: ((((S4 @ R6) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ Ls2)) => ((((domains_subsume @ l) @ r) @ v) @ Ls2)))))))).
% 3.28/1.66 thf(fact_86_substitution_Orevision__step_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((revision_step @ R) @ L) @ V) = (((revision_step @ R) @ L) @ V))))).
% 3.28/1.66 thf(fact_87_substitution_Orevision__step__relaxed_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((revisi1433015572elaxed @ R) @ L) @ V) = (((revisi1433015572elaxed @ R) @ L) @ V))))).
% 3.28/1.66 thf(fact_88_substitution_Oonly__fork__introduces__rids_H, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R3:R]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => ((! [Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E4:(((expr @ R) @ L) @ V)]: (((S @ R2) != ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((rfork @ R) @ L) @ V) @ E4)))))))) => ((~ ((((member @ R) @ R3) @ ((((rID_G @ R) @ L) @ V) @ S)))) => (~ ((((member @ R) @ R3) @ ((((rID_G @ R) @ L) @ V) @ S2))))))))))).
% 3.28/1.66 thf(fact_89_nice__ind__inv__is__inductive__invariant, axiom, (((((inductive_invariant @ r) @ l) @ v) @ subst) @ (^ [S4:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((((domain398919503obally @ r) @ l) @ v) @ S4) & ((((subsum380726323obally @ r) @ l) @ v) @ S4)))))).
% 3.28/1.66 thf(fact_90_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => (((((domain398919503obally @ r) @ l) @ v) @ S) => (((((subsum380726323obally @ r) @ l) @ v) @ S) => ((((subsum380726323obally @ r) @ l) @ v) @ S2))))))).
% 3.28/1.66 thf(fact_91_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => (((((domain398919503obally @ r) @ l) @ v) @ S) => (((((subsum380726323obally @ r) @ l) @ v) @ S) => ((((domain398919503obally @ r) @ l) @ v) @ S2))))))).
% 3.28/1.66 thf(fact_92_valid__stepE, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((member @ ((product_prod @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))))) @ ((((product_Pair @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ S) @ S2)) @ ((((steps @ r) @ l) @ v) @ subst)) => (? [R7:r]: ((((((((revision_step @ r) @ l) @ v) @ subst) @ R7) @ S) @ S2))))))).
% 3.28/1.66 thf(fact_93_substitution_Odomains__subsume__globallyI, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((! [R7:R,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E4:(((expr @ R) @ L) @ V)]: ((((S @ R7) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ E4)))) => ((((domains_subsume @ L) @ R) @ V) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ E4)))))) => ((((domain398919503obally @ R) @ L) @ V) @ S)))))).
% 3.28/1.66 thf(fact_94_substitution_Otransition__relations__equivalent, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2))))))).
% 3.28/1.66 thf(fact_95_valid__stepI, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => (((member @ ((product_prod @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))))) @ ((((product_Pair @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ S) @ S2)) @ ((((steps @ r) @ l) @ v) @ subst)))))).
% 3.28/1.66 thf(fact_96_domains__subsume__globallyI, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((! [R7:r,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E4:(((expr @ r) @ l) @ v)]: ((((S @ R7) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ E4)))) => ((((domains_subsume @ l) @ r) @ v) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ E4)))))) => ((((domain398919503obally @ r) @ l) @ v) @ S))))).
% 3.28/1.66 thf(fact_97_maximal__execution__def, axiom, (! [E2:(((expr @ r) @ l) @ v),S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((maximal_execution @ r) @ l) @ v) @ subst) @ E2) @ S) @ S2) = ((((((((execution @ r) @ l) @ v) @ subst) @ E2) @ S) @ S2) & (~ ((? [S5:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((member @ ((product_prod @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))))) @ ((((product_Pair @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ S2) @ S5)) @ ((((steps @ r) @ l) @ v) @ subst))))))))))).
% 3.28/1.66 thf(fact_98_substitution_Osteps_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((steps @ R) @ L) @ V) = (((steps @ R) @ L) @ V))))).
% 3.28/1.66 thf(fact_99_substitution_Ovalid__stepE, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((member @ ((product_prod @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))) @ ((((product_Pair @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ S) @ S2)) @ ((((steps @ R) @ L) @ V) @ Subst)) => (? [R7:R]: ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R7) @ S) @ S2)))))))).
% 3.28/1.66 thf(fact_100_substitution_Ovalid__stepI, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => (((member @ ((product_prod @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))) @ ((((product_Pair @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ S) @ S2)) @ ((((steps @ R) @ L) @ V) @ Subst))))))).
% 3.28/1.66 thf(fact_101_substitution_Oreachable_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((reachable @ R) @ L) @ V) = (((reachable @ R) @ L) @ V))))).
% 3.28/1.66 thf(fact_102_substitution_Oinductive__invariant_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((inductive_invariant @ R) @ L) @ V) = (((inductive_invariant @ R) @ L) @ V))))).
% 3.28/1.66 thf(fact_103_substitution_Oexecution_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((execution @ R) @ L) @ V) = (((execution @ R) @ L) @ V))))).
% 3.28/1.66 thf(fact_104_substitution_Onice__ind__inv__is__inductive__invariant, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((((inductive_invariant @ R) @ L) @ V) @ Subst) @ (^ [S4:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((domain398919503obally @ R) @ L) @ V) @ S4) & ((((subsum380726323obally @ R) @ L) @ V) @ S4))))))))).
% 3.28/1.66 thf(fact_105_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => (((((domain398919503obally @ R) @ L) @ V) @ S) => (((((subsum380726323obally @ R) @ L) @ V) @ S) => ((((subsum380726323obally @ R) @ L) @ V) @ S2)))))))).
% 3.28/1.66 thf(fact_106_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => (((((domain398919503obally @ R) @ L) @ V) @ S) => (((((subsum380726323obally @ R) @ L) @ V) @ S) => ((((domain398919503obally @ R) @ L) @ V) @ S2)))))))).
% 3.28/1.66 thf(fact_107_substitution_Odomains__subsume__globally__def, axiom, (! [L:$tType,V:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((((domain398919503obally @ R) @ L) @ V) @ S) = (! [R6:R,Ls2:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))]: ((((S @ R6) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ Ls2)) => ((((domains_subsume @ L) @ R) @ V) @ Ls2))))))))).
% 3.28/1.66 thf(fact_108_substitution_Oreachability__closed__under__execution__step, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => (((((reachable @ R) @ L) @ V) @ Subst) @ S2))))))).
% 3.28/1.66 thf(fact_109_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((((domain398919503obally @ R) @ L) @ V) @ S)))))).
% 3.28/1.66 thf(fact_110_substitution_Oinductive__invariant__is__execution__invariant, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),P:((R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) > $o)]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((((((inductive_invariant @ R) @ L) @ V) @ Subst) @ P) => (P @ S))))))).
% 3.28/1.66 thf(fact_111_substitution_Oreachable__def, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) = (? [E5:(((expr @ R) @ L) @ V),S3:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((((execution @ R) @ L) @ V) @ Subst) @ E5) @ S3) @ S)))))))).
% 3.28/1.66 thf(fact_112_SLC__join, axiom, (! [S_1:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R5:r,S_2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),Tau3:(l > (option @ (((val @ r) @ l) @ v))),Sigma3:(l > (option @ (((val @ r) @ l) @ v))),V2:(((val @ r) @ l) @ v),R3:r,S_22:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S_1 @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R5)))))))) => ((S_2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))) @ R5) @ (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) => (((S_1 @ R5) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma3) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau3) @ ((((ve @ r) @ l) @ v) @ V2))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_1) @ S_22) => ((R2 != R3) => (? [S_3:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_32:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((eq_states @ r) @ l) @ v) @ S_3) @ S_32) & (((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_3) | (S_2 = S_3)) & ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_32) | (S_22 = S_32)))))))))))))).
% 3.28/1.66 thf(fact_113_join__and__local__commute, axiom, (! [S_2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_1:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),Tau3:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R5:r,S_22:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R3:r,Ls:((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))),Sigma3:(l > (option @ (((val @ r) @ l) @ v))),V2:(((val @ r) @ l) @ v)]: (((S_2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))) @ R5) @ (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) => ((S_22 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ Ls))) => ((R2 != R3) => ((R3 != R5) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))) @ R5) @ (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ R3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ Ls))) => (((S_22 @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R5)))))))) => (((S_22 @ R5) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma3) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau3) @ ((((ve @ r) @ l) @ v) @ V2))))) => (? [S_3:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S_32:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((eq_states @ r) @ l) @ v) @ S_3) @ S_32) & (((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_3) | (S_2 = S_3)) & ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_32) | (S_22 = S_32)))))))))))))))).
% 3.28/1.66 thf(fact_114_substitution_Omaximal__execution__def, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),E2:(((expr @ R) @ L) @ V),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((maximal_execution @ R) @ L) @ V) @ Subst) @ E2) @ S) @ S2) = ((((((((execution @ R) @ L) @ V) @ Subst) @ E2) @ S) @ S2) & (~ ((? [S5:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((member @ ((product_prod @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))) @ ((((product_Pair @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ S2) @ S5)) @ ((((steps @ R) @ L) @ V) @ Subst)))))))))))).
% 3.28/1.66 thf(fact_115_substitution_Osubsumes__accessible__globallyI, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ 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 @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma_1) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau_1) @ E_1)))) => (((S @ R_2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma_2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau_2) @ E_2)))) => ((((((subsumes_accessible @ R) @ L) @ V) @ R_1) @ R_2) @ S))))) => ((((subsum380726323obally @ R) @ L) @ V) @ S)))))).
% 3.28/1.66 thf(fact_116_revision__step__relaxed_Ojoin, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R3:r,Sigma3:(l > (option @ (((val @ r) @ l) @ v))),Tau3:(l > (option @ (((val @ r) @ l) @ v))),V2:(((val @ r) @ l) @ v)]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R3)))))))) => (((S @ R3) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma3) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau3) @ ((((ve @ r) @ l) @ v) @ V2))))) => (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))) @ R3) @ (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))))))))).
% 3.28/1.66 thf(fact_117_val_Oinject_I1_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:const,Y1:const]: (((((((cv @ R) @ L) @ V) @ X1) = ((((cv @ R) @ L) @ V) @ Y1)) = (X1 = Y1))))).
% 3.28/1.66 thf(fact_118_terminates__in__def, axiom, (! [E2:(((expr @ r) @ l) @ v),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((((((terminates_in @ r) @ l) @ v) @ subst) @ E2) @ S2) = (? [S4:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((((((maximal_execution @ r) @ l) @ v) @ subst) @ E2) @ S4) @ S2))))))).
% 3.28/1.66 thf(fact_119_revision__step_Ojoin, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R3:r,Sigma3:(l > (option @ (((val @ r) @ l) @ v))),Tau3:(l > (option @ (((val @ r) @ l) @ v))),V2:(((val @ r) @ l) @ v)]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R3)))))))) => (((S @ R3) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma3) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau3) @ ((((ve @ r) @ l) @ v) @ V2))))) => (((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))) @ R3) @ (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))))))))).
% 3.28/1.66 thf(fact_120_subsumes__accessible__globallyI, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ 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 @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma_1) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau_1) @ E_1)))) => (((S @ R_2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma_2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau_2) @ E_2)))) => ((((((subsumes_accessible @ r) @ l) @ v) @ R_1) @ R_2) @ S))))) => ((((subsum380726323obally @ r) @ l) @ v) @ S))))).
% 3.28/1.66 thf(fact_121_rjoin__deterministic, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),R3:r,Sigma3:(l > (option @ (((val @ r) @ l) @ v))),Tau3:(l > (option @ (((val @ r) @ l) @ v))),V2:(((val @ r) @ l) @ v),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((rjoin @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R3)))))))) => (((S @ R3) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma3) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau3) @ ((((ve @ r) @ l) @ v) @ V2))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = (S2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))) @ R3) @ (none @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))))))))).
% 3.28/1.66 thf(fact_122_substitution_Omaximal__execution_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((maximal_execution @ R) @ L) @ V) = (((maximal_execution @ R) @ L) @ V))))).
% 3.28/1.66 thf(fact_123_val_Odistinct_I5_J, axiom, (! [L:$tType,V:$tType,R:$tType,X1:const,X4:R]: ((((((cv @ R) @ L) @ V) @ X1) != ((((rid @ R) @ L) @ V) @ X4))))).
% 3.28/1.66 thf(fact_124_substitution_Orevision__step_Ojoin, axiom, (! [V:$tType,R:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R3:R,Sigma3:(L > (option @ (((val @ R) @ L) @ V))),Tau3:(L > (option @ (((val @ R) @ L) @ V))),V2:(((val @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) => (((S @ R3) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma3) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau3) @ ((((ve @ R) @ L) @ V) @ V2))))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))) @ R3) @ (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))))))))).
% 3.28/1.66 thf(fact_125_substitution_Orjoin__deterministic, axiom, (! [V:$tType,R:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R3:R,Sigma3:(L > (option @ (((val @ R) @ L) @ V))),Tau3:(L > (option @ (((val @ R) @ L) @ V))),V2:(((val @ R) @ L) @ V),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) => (((S @ R3) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma3) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau3) @ ((((ve @ R) @ L) @ V) @ V2))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (S2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))) @ R3) @ (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))))))))).
% 3.28/1.66 thf(fact_126_substitution_Orevision__step__relaxed_Ojoin, axiom, (! [V:$tType,R:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R3:R,Sigma3:(L > (option @ (((val @ R) @ L) @ V))),Tau3:(L > (option @ (((val @ R) @ L) @ V))),V2:(((val @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) => (((S @ R3) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma3) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau3) @ ((((ve @ R) @ L) @ V) @ V2))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))) @ R3) @ (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))))))))).
% 3.28/1.66 thf(fact_127_substitution_Ojoin__and__local__commute, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S_2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_1:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),Tau3:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R5:R,S_22:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R3:R,Ls:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))),Sigma3:(L > (option @ (((val @ R) @ L) @ V))),V2:(((val @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((S_2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))) @ R5) @ (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) => ((S_22 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R3) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ Ls))) => ((R2 != R3) => ((R3 != R5) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))) @ R5) @ (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ R3) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ Ls))) => (((S_22 @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R5)))))))) => (((S_22 @ R5) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma3) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau3) @ ((((ve @ R) @ L) @ V) @ V2))))) => (? [S_3:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_32:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: (((((((eq_states @ R) @ L) @ V) @ S_3) @ S_32) & (((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_3) | (S_2 = S_3)) & ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_32) | (S_22 = S_32))))))))))))))))).
% 3.28/1.66 thf(fact_128_substitution_OSLC__join, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S_1:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),R5:R,S_2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),Tau3:(L > (option @ (((val @ R) @ L) @ V))),Sigma3:(L > (option @ (((val @ R) @ L) @ V))),V2:(((val @ R) @ L) @ V),R3:R,S_22:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S_1 @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R5)))))))) => ((S_2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S_1) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))) @ R5) @ (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) => (((S_1 @ R5) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma3) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau3) @ ((((ve @ R) @ L) @ V) @ V2))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_1) @ S_22) => ((R2 != R3) => (? [S_3:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_32:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: (((((((eq_states @ R) @ L) @ V) @ S_3) @ S_32) & (((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_3) | (S_2 = S_3)) & ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_32) | (S_22 = S_32))))))))))))))).
% 3.28/1.66 thf(fact_129_reachable__imp__identifiers__finite_I1_J, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((finite_finite @ r) @ ((((rID_G @ r) @ l) @ v) @ S)))))).
% 3.28/1.66 thf(fact_130_RID_092_060_094sub_062G__finite__invariant, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => (((finite_finite @ r) @ ((((rID_G @ r) @ l) @ v) @ S)) => ((finite_finite @ r) @ ((((rID_G @ r) @ l) @ v) @ S2))))))).
% 3.28/1.66 thf(fact_131_reachability__closed__under__execution, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((((member @ ((product_prod @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))))) @ ((((product_Pair @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ S) @ S2)) @ ((transitive_rtrancl @ (r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))) @ ((((steps @ r) @ l) @ v) @ subst))) => (((((reachable @ r) @ l) @ v) @ subst) @ S2)))))).
% 3.28/1.66 thf(fact_132_revision__step__relaxed_OifTrue, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E1:(((expr @ r) @ l) @ v),E22:(((expr @ r) @ l) @ v)]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((((ite @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ t))) @ E1) @ E22)))))) => (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ E1)))))))))).
% 3.28/1.66 thf(fact_133_empty__map__finite_I3_J, axiom, (! [H:$tType,I:$tType,G4:$tType]: (((finite_finite @ G4) @ ((((rID_G @ G4) @ H) @ I) @ (^ [X:G4]: ((none @ ((product_prod @ (H > (option @ (((val @ G4) @ H) @ I)))) @ ((product_prod @ (H > (option @ (((val @ G4) @ H) @ I)))) @ (((expr @ G4) @ H) @ I))))))))))).
% 3.28/1.66 thf(fact_134_expr_Oinject_I3_J, axiom, (! [V:$tType,L:$tType,R:$tType,X31:(((expr @ R) @ L) @ V),X32:(((expr @ R) @ L) @ V),X33:(((expr @ R) @ L) @ V),Y31:(((expr @ R) @ L) @ V),Y32:(((expr @ R) @ L) @ V),Y33:(((expr @ R) @ L) @ V)]: (((((((((ite @ R) @ L) @ V) @ X31) @ X32) @ X33) = ((((((ite @ R) @ L) @ V) @ Y31) @ Y32) @ Y33)) = ((X31 = Y31) & ((X32 = Y32) & (X33 = Y33))))))).
% 3.28/1.66 thf(fact_135_revision__step_OifTrue, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E1:(((expr @ r) @ l) @ v),E22:(((expr @ r) @ l) @ v)]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((((ite @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ t))) @ E1) @ E22)))))) => (((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ E1)))))))))).
% 3.28/1.66 thf(fact_136_finite__state__imp__restriction__finite_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A]: ((((finite_finite @ A) @ ((((rID_G @ A) @ B) @ C) @ S)) => ((finite_finite @ A) @ ((((rID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))))))).
% 3.28/1.66 thf(fact_137_ifTrue__deterministic, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E1:(((expr @ r) @ l) @ v),E22:(((expr @ r) @ l) @ v),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((((ite @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ t))) @ E1) @ E22)))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = (S2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ E1))))))))))).
% 3.28/1.66 thf(fact_138_expr_Odistinct_I3_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X31:(((expr @ R) @ L) @ V),X32:(((expr @ R) @ L) @ V),X33:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != ((((((ite @ R) @ L) @ V) @ X31) @ X32) @ X33))))).
% 3.28/1.66 thf(fact_139_expr_Odistinct_I35_J, axiom, (! [V:$tType,L:$tType,R:$tType,X31:(((expr @ R) @ L) @ V),X32:(((expr @ R) @ L) @ V),X33:(((expr @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: ((((((((ite @ R) @ L) @ V) @ X31) @ X32) @ X33) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.28/1.66 thf(fact_140_expr_Odistinct_I33_J, axiom, (! [V:$tType,L:$tType,R:$tType,X31:(((expr @ R) @ L) @ V),X32:(((expr @ R) @ L) @ V),X33:(((expr @ R) @ L) @ V),X7:(((expr @ R) @ L) @ V)]: ((((((((ite @ R) @ L) @ V) @ X31) @ X32) @ X33) != ((((rfork @ R) @ L) @ V) @ X7))))).
% 3.28/1.66 thf(fact_141_substitution_Oterminates__in_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((terminates_in @ R) @ L) @ V) = (((terminates_in @ R) @ L) @ V))))).
% 3.28/1.66 thf(fact_142_const_Odistinct_I3_J, axiom, (unit != t)).
% 3.28/1.66 thf(fact_143_substitution_ORID_092_060_094sub_062G__finite__invariant, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => (((finite_finite @ R) @ ((((rID_G @ R) @ L) @ V) @ S)) => ((finite_finite @ R) @ ((((rID_G @ R) @ L) @ V) @ S2)))))))).
% 3.28/1.66 thf(fact_144_substitution_Oreachable__imp__identifiers__finite_I1_J, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((finite_finite @ R) @ ((((rID_G @ R) @ L) @ V) @ S))))))).
% 3.28/1.66 thf(fact_145_substitution_Oempty__map__finite_I3_J, axiom, (! [R:$tType,L:$tType,V:$tType,H:$tType,I:$tType,G4:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((finite_finite @ G4) @ ((((rID_G @ G4) @ H) @ I) @ (^ [X:G4]: ((none @ ((product_prod @ (H > (option @ (((val @ G4) @ H) @ I)))) @ ((product_prod @ (H > (option @ (((val @ G4) @ H) @ I)))) @ (((expr @ G4) @ H) @ I)))))))))))).
% 3.28/1.66 thf(fact_146_substitution_Oreachability__closed__under__execution, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((((member @ ((product_prod @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))) @ ((((product_Pair @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ S) @ S2)) @ ((transitive_rtrancl @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ ((((steps @ R) @ L) @ V) @ Subst))) => (((((reachable @ R) @ L) @ V) @ Subst) @ S2))))))).
% 3.28/1.66 thf(fact_147_substitution_Ofinite__state__imp__restriction__finite_I1_J, axiom, (! [V:$tType,L:$tType,R:$tType,C:$tType,A:$tType,B:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((finite_finite @ A) @ ((((rID_G @ A) @ B) @ C) @ S)) => ((finite_finite @ A) @ ((((rID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))))))))))).
% 3.28/1.66 thf(fact_148_substitution_OifTrue__deterministic, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ t))) @ E1) @ E22)))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (S2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ E1)))))))))))).
% 3.28/1.66 thf(fact_149_substitution_Orevision__step_OifTrue, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ t))) @ E1) @ E22)))))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ E1))))))))))).
% 3.28/1.66 thf(fact_150_substitution_Orevision__step__relaxed_OifTrue, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ t))) @ E1) @ E22)))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ E1))))))))))).
% 3.28/1.66 thf(fact_151_substitution_Oterminates__in__def, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),E2:(((expr @ R) @ L) @ V),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((((((terminates_in @ R) @ L) @ V) @ Subst) @ E2) @ S2) = (? [S4:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((((maximal_execution @ R) @ L) @ V) @ Subst) @ E2) @ S4) @ S2)))))))).
% 3.28/1.66 thf(fact_152_revision__step__relaxed_OifFalse, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E1:(((expr @ r) @ l) @ v),E22:(((expr @ r) @ l) @ v)]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((((ite @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ f))) @ E1) @ E22)))))) => (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ E22)))))))))).
% 3.28/1.66 thf(fact_153_revision__step_OifFalse, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E1:(((expr @ r) @ l) @ v),E22:(((expr @ r) @ l) @ v)]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((((ite @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ f))) @ E1) @ E22)))))) => (((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ E22)))))))))).
% 3.28/1.66 thf(fact_154_ifFalse__deterministic, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E1:(((expr @ r) @ l) @ v),E22:(((expr @ r) @ l) @ v),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((((ite @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ f))) @ E1) @ E22)))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = (S2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ E22))))))))))).
% 3.28/1.66 thf(fact_155_finite__Collect__subsets, axiom, (! [A:$tType,A5:(set @ A)]: ((((finite_finite @ A) @ A5) => ((finite_finite @ (set @ A)) @ ((collect @ (set @ A)) @ (^ [B5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B5) @ A5))))))))).
% 3.28/1.66 thf(fact_156_finite__Collect__disjI, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((finite_finite @ A) @ ((collect @ A) @ (^ [X:A]: (((P @ X) | (Q @ X)))))) = (((finite_finite @ A) @ ((collect @ A) @ P)) & ((finite_finite @ A) @ ((collect @ A) @ Q))))))).
% 3.28/1.66 thf(fact_157_finite__Collect__conjI, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((finite_finite @ A) @ ((collect @ A) @ P)) | ((finite_finite @ A) @ ((collect @ A) @ Q))) => ((finite_finite @ A) @ ((collect @ A) @ (^ [X:A]: (((P @ X) & (Q @ X)))))))))).
% 3.28/1.66 thf(fact_158_const_Odistinct_I1_J, axiom, (unit != f)).
% 3.28/1.66 thf(fact_159_const_Odistinct_I5_J, axiom, (f != t)).
% 3.28/1.66 thf(fact_160_const_Oinduct, axiom, (! [P:(const > $o),Const:const]: (((P @ unit) => ((P @ f) => ((P @ t) => (P @ Const))))))).
% 3.28/1.66 thf(fact_161_const_Oexhaust, axiom, (! [Y:const]: (((Y != unit) => ((Y != f) => (Y = t)))))).
% 3.28/1.66 thf(fact_162_pigeonhole__infinite__rel, axiom, (! [B:$tType,A:$tType,A5:(set @ A),B6:(set @ B),R8:(A > (B > $o))]: (((~ (((finite_finite @ A) @ A5))) => (((finite_finite @ B) @ B6) => ((! [X6:A]: (((((member @ A) @ X6) @ A5) => (? [Xa2:B]: (((((member @ B) @ Xa2) @ B6) & ((R8 @ X6) @ Xa2))))))) => (? [X6:B]: (((((member @ B) @ X6) @ B6) & (~ (((finite_finite @ A) @ ((collect @ A) @ (^ [A3:A]: (((((member @ A) @ A3) @ A5) & ((R8 @ A3) @ X6))))))))))))))))).
% 3.28/1.66 thf(fact_163_not__finite__existsD, axiom, (! [A:$tType,P:(A > $o)]: (((~ (((finite_finite @ A) @ ((collect @ A) @ P)))) => (? [X_1:A]: ((P @ X_1))))))).
% 3.28/1.66 thf(fact_164_finite__has__maximal2, axiom, (! [A:$tType]: (((order @ A) => (! [A5:(set @ A),A2:A]: ((((finite_finite @ A) @ A5) => ((((member @ A) @ A2) @ A5) => (? [X6:A]: (((((member @ A) @ X6) @ A5) & ((((ord_less_eq @ A) @ A2) @ X6) & (! [Xa2:A]: (((((member @ A) @ Xa2) @ A5) => ((((ord_less_eq @ A) @ X6) @ Xa2) => (X6 = Xa2))))))))))))))))).
% 3.28/1.66 thf(fact_165_finite__has__minimal2, axiom, (! [A:$tType]: (((order @ A) => (! [A5:(set @ A),A2:A]: ((((finite_finite @ A) @ A5) => ((((member @ A) @ A2) @ A5) => (? [X6:A]: (((((member @ A) @ X6) @ A5) & ((((ord_less_eq @ A) @ X6) @ A2) & (! [Xa2:A]: (((((member @ A) @ Xa2) @ A5) => ((((ord_less_eq @ A) @ Xa2) @ X6) => (X6 = Xa2))))))))))))))))).
% 3.28/1.66 thf(fact_166_finite__subset, axiom, (! [A:$tType,A5:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B6) => (((finite_finite @ A) @ B6) => ((finite_finite @ A) @ A5)))))).
% 3.28/1.66 thf(fact_167_infinite__super, axiom, (! [A:$tType,S6:(set @ A),T2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ S6) @ T2) => ((~ (((finite_finite @ A) @ S6))) => (~ (((finite_finite @ A) @ T2)))))))).
% 3.28/1.66 thf(fact_168_rev__finite__subset, axiom, (! [A:$tType,B6:(set @ A),A5:(set @ A)]: ((((finite_finite @ A) @ B6) => ((((ord_less_eq @ (set @ A)) @ A5) @ B6) => ((finite_finite @ A) @ A5)))))).
% 3.28/1.66 thf(fact_169_finite__update__induct, axiom, (! [B:$tType,A:$tType,F:(A > B),C2:B,P:((A > B) > $o)]: ((((finite_finite @ A) @ ((collect @ A) @ (^ [A3:A]: (((F @ A3) != C2))))) => ((P @ (^ [A3:A]: (C2))) => ((! [A4:A,B4:B,F3:(A > B)]: ((((finite_finite @ A) @ ((collect @ A) @ (^ [C3:A]: (((F3 @ C3) != C2))))) => (((F3 @ A4) = C2) => ((B4 != C2) => ((P @ F3) => (P @ (((((fun_upd @ A) @ B) @ F3) @ A4) @ B4)))))))) => (P @ F))))))).
% 3.28/1.66 thf(fact_170_substitution_Orevision__step_OifFalse, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ f))) @ E1) @ E22)))))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ E22))))))))))).
% 3.28/1.66 thf(fact_171_substitution_OifFalse__deterministic, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ f))) @ E1) @ E22)))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (S2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ E22)))))))))))).
% 3.28/1.66 thf(fact_172_substitution_Orevision__step__relaxed_OifFalse, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ f))) @ E1) @ E22)))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ E22))))))))))).
% 3.28/1.66 thf(fact_173_reachable__imp__identifiers__available_I1_J, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((~ (((finite_finite @ r) @ (top_top @ (set @ r))))) => (? [R7:r]: ((~ ((((member @ r) @ R7) @ ((((rID_G @ r) @ l) @ v) @ S))))))))))).
% 3.28/1.66 thf(fact_174_local__state__of__finite__restricted__global__state__is__finite_I1_J, axiom, (! [C:$tType,B:$tType,A:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R3:B,Ls:((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))),R2:B]: ((((S @ R3) = ((some @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))) @ Ls)) => (((finite_finite @ B) @ ((((rID_G @ B) @ A) @ C) @ (((((fun_upd @ B) @ (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))))) => ((R2 != R3) => ((finite_finite @ B) @ ((((rID_L @ A) @ B) @ C) @ Ls)))))))).
% 3.28/1.66 thf(fact_175_empty__map__finite_I4_J, axiom, (! [J:$tType,M2:$tType,K2:$tType]: (((finite_finite @ J) @ ((((lID_G @ K2) @ J) @ M2) @ (^ [X:K2]: ((none @ ((product_prod @ (J > (option @ (((val @ K2) @ J) @ M2)))) @ ((product_prod @ (J > (option @ (((val @ K2) @ J) @ M2)))) @ (((expr @ K2) @ J) @ M2))))))))))).
% 3.28/1.66 thf(fact_176_RID_092_060_094sub_062L__finite__invariant, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => (((finite_finite @ l) @ ((((lID_G @ r) @ l) @ v) @ S)) => ((finite_finite @ l) @ ((((lID_G @ r) @ l) @ v) @ S2))))))).
% 3.28/1.66 thf(fact_177_reachable__imp__identifiers__finite_I2_J, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((finite_finite @ l) @ ((((lID_G @ r) @ l) @ v) @ S)))))).
% 3.28/1.66 thf(fact_178_finite__option__UNIV, axiom, (! [A:$tType]: ((((finite_finite @ (option @ A)) @ (top_top @ (set @ (option @ A)))) = ((finite_finite @ A) @ (top_top @ (set @ A))))))).
% 3.28/1.66 thf(fact_179_finite__Collect__not, axiom, (! [A:$tType,P:(A > $o)]: ((((finite_finite @ A) @ ((collect @ A) @ P)) => (((finite_finite @ A) @ ((collect @ A) @ (^ [X:A]: ((~ ((P @ X))))))) = ((finite_finite @ A) @ (top_top @ (set @ A)))))))).
% 3.28/1.66 thf(fact_180_in__restricted__global__in__unrestricted__global_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,L2:B,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A]: (((((member @ B) @ L2) @ ((((lID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))) => (((member @ B) @ L2) @ ((((lID_G @ A) @ B) @ C) @ S)))))).
% 3.28/1.66 thf(fact_181_RID_092_060_094sub_062GI_I2_J, axiom, (! [C:$tType,A:$tType,B:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R3:B,Ls:((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))),R2:B]: ((((S @ R3) = ((some @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))) @ Ls)) => ((((member @ B) @ R2) @ ((((rID_L @ A) @ B) @ C) @ Ls)) => (((member @ B) @ R2) @ ((((rID_G @ B) @ A) @ C) @ S))))))).
% 3.28/1.66 thf(fact_182_finite__state__imp__restriction__finite_I2_J, axiom, (! [C:$tType,A:$tType,B:$tType,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A]: ((((finite_finite @ B) @ ((((lID_G @ A) @ B) @ C) @ S)) => ((finite_finite @ B) @ ((((lID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))))))).
% 3.28/1.66 thf(fact_183_in__restricted__global__in__updated__global_I2_J, axiom, (! [C:$tType,A:$tType,B:$tType,L2:B,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A,Ls:((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))]: (((((member @ B) @ L2) @ ((((lID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))) => (((member @ B) @ L2) @ ((((lID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ ((some @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))) @ Ls)))))))).
% 3.28/1.66 thf(fact_184_substitution_Oreachable__imp__identifiers__available_I2_J, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((~ (((finite_finite @ L) @ (top_top @ (set @ L))))) => (? [L3:L]: ((~ ((((member @ L) @ L3) @ ((((lID_G @ R) @ L) @ V) @ S)))))))))))).
% 3.28/1.66 thf(fact_185_substitution_ORID_092_060_094sub_062L__finite__invariant, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => (((finite_finite @ L) @ ((((lID_G @ R) @ L) @ V) @ S)) => ((finite_finite @ L) @ ((((lID_G @ R) @ L) @ V) @ S2)))))))).
% 3.28/1.66 thf(fact_186_ID__restricted__global__subset__unrestricted_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R2:B]: ((((ord_less_eq @ (set @ A)) @ ((((lID_G @ B) @ A) @ C) @ (((((fun_upd @ B) @ (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))))) @ ((((lID_G @ B) @ A) @ C) @ S))))).
% 3.28/1.66 thf(fact_187_substitution_Oreachable__imp__identifiers__finite_I2_J, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((finite_finite @ L) @ ((((lID_G @ R) @ L) @ V) @ S))))))).
% 3.28/1.66 thf(fact_188_substitution_Oempty__map__finite_I4_J, axiom, (! [R:$tType,L:$tType,V:$tType,J:$tType,M2:$tType,K2:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((finite_finite @ J) @ ((((lID_G @ K2) @ J) @ M2) @ (^ [X:K2]: ((none @ ((product_prod @ (J > (option @ (((val @ K2) @ J) @ M2)))) @ ((product_prod @ (J > (option @ (((val @ K2) @ J) @ M2)))) @ (((expr @ K2) @ J) @ M2)))))))))))).
% 3.28/1.66 thf(fact_189_substitution_Oreachable__imp__identifiers__available_I1_J, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((~ (((finite_finite @ R) @ (top_top @ (set @ R))))) => (? [R7:R]: ((~ ((((member @ R) @ R7) @ ((((rID_G @ R) @ L) @ V) @ S)))))))))))).
% 3.28/1.66 thf(fact_190_substitution_Ofinite__state__imp__restriction__finite_I2_J, axiom, (! [V:$tType,L:$tType,R:$tType,C:$tType,A:$tType,B:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((finite_finite @ B) @ ((((lID_G @ A) @ B) @ C) @ S)) => ((finite_finite @ B) @ ((((lID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))))))))))).
% 3.28/1.66 thf(fact_191_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J, axiom, (! [V:$tType,L:$tType,R:$tType,C:$tType,B:$tType,A:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R3:B,Ls:((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))),R2:B]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R3) = ((some @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))) @ Ls)) => (((finite_finite @ B) @ ((((rID_G @ B) @ A) @ C) @ (((((fun_upd @ B) @ (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))))) => ((R2 != R3) => ((finite_finite @ B) @ ((((rID_L @ A) @ B) @ C) @ Ls))))))))).
% 3.28/1.66 thf(fact_192_only__new__introduces__lids_H, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),L2:l]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => ((! [Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),V3:(((val @ r) @ l) @ v)]: (((S @ R2) != ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ref @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ V3))))))))) => ((~ ((((member @ l) @ L2) @ ((((lID_G @ r) @ l) @ v) @ S)))) => (~ ((((member @ l) @ L2) @ ((((lID_G @ r) @ l) @ v) @ S2)))))))))).
% 3.28/1.66 thf(fact_193_local__state__of__finite__restricted__global__state__is__finite_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R3:B,Ls:((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))),R2:B]: ((((S @ R3) = ((some @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))) @ Ls)) => (((finite_finite @ A) @ ((((lID_G @ B) @ A) @ C) @ (((((fun_upd @ B) @ (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))))) => ((R2 != R3) => ((finite_finite @ A) @ ((((lID_L @ A) @ B) @ C) @ Ls)))))))).
% 3.28/1.66 thf(fact_194_only__new__introduces__lids, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => ((! [Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),V3:(((val @ r) @ l) @ v)]: (((S @ R2) != ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ref @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ V3))))))))) => (((ord_less_eq @ (set @ l)) @ ((((lID_G @ r) @ l) @ v) @ S2)) @ ((((lID_G @ r) @ l) @ v) @ S))))))).
% 3.28/1.66 thf(fact_195_expr_Oinject_I4_J, axiom, (! [V:$tType,L:$tType,R:$tType,X4:(((expr @ R) @ L) @ V),Y4:(((expr @ R) @ L) @ V)]: (((((((ref @ R) @ L) @ V) @ X4) = ((((ref @ R) @ L) @ V) @ Y4)) = (X4 = Y4))))).
% 3.28/1.66 thf(fact_196_reachable__imp__identifiers__available_I2_J, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((~ (((finite_finite @ l) @ (top_top @ (set @ l))))) => (? [L3:l]: ((~ ((((member @ l) @ L3) @ ((((lID_G @ r) @ l) @ v) @ S))))))))))).
% 3.28/1.66 thf(fact_197_LID_092_060_094sub_062GI, axiom, (! [C:$tType,A:$tType,B:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R2:B,Ls:((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))),L2:A]: ((((S @ R2) = ((some @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))) @ Ls)) => ((((member @ A) @ L2) @ ((((lID_L @ A) @ B) @ C) @ Ls)) => (((member @ A) @ L2) @ ((((lID_G @ B) @ A) @ C) @ S))))))).
% 3.28/1.66 thf(fact_198_expr_Odistinct_I41_J, axiom, (! [V:$tType,L:$tType,R:$tType,X4:(((expr @ R) @ L) @ V),X7:(((expr @ R) @ L) @ V)]: ((((((ref @ R) @ L) @ V) @ X4) != ((((rfork @ R) @ L) @ V) @ X7))))).
% 3.28/1.66 thf(fact_199_expr_Odistinct_I43_J, axiom, (! [V:$tType,L:$tType,R:$tType,X4:(((expr @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: ((((((ref @ R) @ L) @ V) @ X4) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.28/1.66 thf(fact_200_expr_Odistinct_I5_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X4:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != ((((ref @ R) @ L) @ V) @ X4))))).
% 3.28/1.66 thf(fact_201_expr_Odistinct_I27_J, axiom, (! [V:$tType,L:$tType,R:$tType,X31:(((expr @ R) @ L) @ V),X32:(((expr @ R) @ L) @ V),X33:(((expr @ R) @ L) @ V),X4:(((expr @ R) @ L) @ V)]: ((((((((ite @ R) @ L) @ V) @ X31) @ X32) @ X33) != ((((ref @ R) @ L) @ V) @ X4))))).
% 3.28/1.66 thf(fact_202_LID_092_060_094sub_062GE, axiom, (! [C:$tType,B:$tType,A:$tType,L2:A,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))))]: (((((member @ A) @ L2) @ ((((lID_G @ B) @ A) @ C) @ S)) => (~ ((! [R7:B,Ls3:((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))]: ((((S @ R7) = ((some @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))) @ Ls3)) => (~ ((((member @ A) @ L2) @ ((((lID_L @ A) @ B) @ C) @ Ls3))))))))))))).
% 3.28/1.66 thf(fact_203_substitution_Oonly__new__introduces__lids_H, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),L2:L]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => ((! [Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),V3:(((val @ R) @ L) @ V)]: (((S @ R2) != ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ref @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ V3))))))))) => ((~ ((((member @ L) @ L2) @ ((((lID_G @ R) @ L) @ V) @ S)))) => (~ ((((member @ L) @ L2) @ ((((lID_G @ R) @ L) @ V) @ S2))))))))))).
% 3.28/1.66 thf(fact_204_substitution_Oonly__new__introduces__lids, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => ((! [Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),V3:(((val @ R) @ L) @ V)]: (((S @ R2) != ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ref @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ V3))))))))) => (((ord_less_eq @ (set @ L)) @ ((((lID_G @ R) @ L) @ V) @ S2)) @ ((((lID_G @ R) @ L) @ V) @ S)))))))).
% 3.28/1.66 thf(fact_205_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J, axiom, (! [V:$tType,L:$tType,R:$tType,C:$tType,B:$tType,A:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R3:B,Ls:((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))),R2:B]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R3) = ((some @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C)))) @ Ls)) => (((finite_finite @ A) @ ((((lID_G @ B) @ A) @ C) @ (((((fun_upd @ B) @ (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))))) => ((R2 != R3) => ((finite_finite @ A) @ ((((lID_L @ A) @ B) @ C) @ Ls))))))))).
% 3.28/1.66 thf(fact_206_domains__subsume__def, axiom, ((((domains_subsume @ l) @ r) @ v) = (^ [Ls2:((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))]: ((((ord_less_eq @ (set @ l)) @ ((((lID_L @ l) @ r) @ v) @ Ls2)) @ ((((doms @ l) @ r) @ v) @ Ls2)))))).
% 3.28/1.66 thf(fact_207_revision__step_Onew, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),V2:(((val @ r) @ l) @ v),L2:l]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ref @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ V2))))))) => ((~ ((((member @ l) @ L2) @ ((((lID_G @ r) @ l) @ v) @ S)))) => (((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau) @ L2) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L2))))))))))))).
% 3.28/1.66 thf(fact_208_val_Oinject_I3_J, axiom, (! [V:$tType,R:$tType,L:$tType,X34:L,Y3:L]: (((((((loc @ L) @ R) @ V) @ X34) = ((((loc @ L) @ R) @ V) @ Y3)) = (X34 = Y3))))).
% 3.28/1.66 thf(fact_209_new__pseudodeterministic, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),V2:(((val @ r) @ l) @ v),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ref @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ V2))))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = (? [L4:l]: (((~ ((((member @ l) @ L4) @ ((((lID_G @ r) @ l) @ v) @ S)))) & (S2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau) @ L4) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L4)))))))))))))))).
% 3.28/1.66 thf(fact_210_val_Odistinct_I15_J, axiom, (! [L:$tType,V:$tType,R:$tType,X34:L,X4:R]: ((((((loc @ L) @ R) @ V) @ X34) != ((((rid @ R) @ L) @ V) @ X4))))).
% 3.28/1.66 thf(fact_211_val_Odistinct_I3_J, axiom, (! [R:$tType,V:$tType,L:$tType,X1:const,X34:L]: ((((((cv @ R) @ L) @ V) @ X1) != ((((loc @ L) @ R) @ V) @ X34))))).
% 3.28/1.66 thf(fact_212_substitution_Odomains__subsume__def, axiom, (! [V:$tType,R:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),Ls:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((((domains_subsume @ L) @ R) @ V) @ Ls) = (((ord_less_eq @ (set @ L)) @ ((((lID_L @ L) @ R) @ V) @ Ls)) @ ((((doms @ L) @ R) @ V) @ Ls))))))).
% 3.28/1.66 thf(fact_213_substitution_Onew__pseudodeterministic, axiom, (! [V:$tType,R:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),V2:(((val @ R) @ L) @ V),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ref @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ V2))))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (? [L4:L]: (((~ ((((member @ L) @ L4) @ ((((lID_G @ R) @ L) @ V) @ S)))) & (S2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau) @ L4) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L4))))))))))))))))).
% 3.28/1.66 thf(fact_214_substitution_Orevision__step_Onew, axiom, (! [R:$tType,V:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),V2:(((val @ R) @ L) @ V),L2:L]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ref @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ V2))))))) => ((~ ((((member @ L) @ L2) @ ((((lID_G @ R) @ L) @ V) @ S)))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau) @ L2) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L2)))))))))))))).
% 3.28/1.66 thf(fact_215_revision__step__relaxed_Oset, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),L2:l,V2:(((val @ r) @ l) @ v)]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ (((((assign @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L2))) @ ((((ve @ r) @ l) @ v) @ V2))))))) => (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau) @ L2) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))))))).
% 3.28/1.66 thf(fact_216_substitution_Orevision__step__relaxed_Oset, axiom, (! [R:$tType,L:$tType,V:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),L2:L,V2:(((val @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ (((((assign @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L2))) @ ((((ve @ R) @ L) @ V) @ V2))))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau) @ L2) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit))))))))))))).
% 3.28/1.66 thf(fact_217_expr_Oinject_I6_J, axiom, (! [V:$tType,L:$tType,R:$tType,X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V),Y61:(((expr @ R) @ L) @ V),Y62:(((expr @ R) @ L) @ V)]: ((((((((assign @ R) @ L) @ V) @ X61) @ X62) = (((((assign @ R) @ L) @ V) @ Y61) @ Y62)) = ((X61 = Y61) & (X62 = Y62)))))).
% 3.28/1.66 thf(fact_218_expr_Odistinct_I39_J, axiom, (! [V:$tType,L:$tType,R:$tType,X4:(((expr @ R) @ L) @ V),X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V)]: ((((((ref @ R) @ L) @ V) @ X4) != (((((assign @ R) @ L) @ V) @ X61) @ X62))))).
% 3.28/1.66 thf(fact_219_expr_Odistinct_I51_J, axiom, (! [V:$tType,L:$tType,R:$tType,X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V),X7:(((expr @ R) @ L) @ V)]: (((((((assign @ R) @ L) @ V) @ X61) @ X62) != ((((rfork @ R) @ L) @ V) @ X7))))).
% 3.28/1.66 thf(fact_220_expr_Odistinct_I53_J, axiom, (! [V:$tType,L:$tType,R:$tType,X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: (((((((assign @ R) @ L) @ V) @ X61) @ X62) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.28/1.66 thf(fact_221_expr_Odistinct_I9_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != (((((assign @ R) @ L) @ V) @ X61) @ X62))))).
% 3.28/1.66 thf(fact_222_expr_Odistinct_I31_J, axiom, (! [V:$tType,L:$tType,R:$tType,X31:(((expr @ R) @ L) @ V),X32:(((expr @ R) @ L) @ V),X33:(((expr @ R) @ L) @ V),X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V)]: ((((((((ite @ R) @ L) @ V) @ X31) @ X32) @ X33) != (((((assign @ R) @ L) @ V) @ X61) @ X62))))).
% 3.28/1.66 thf(fact_223_revision__step_Oset, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),L2:l,V2:(((val @ r) @ l) @ v)]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ (((((assign @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L2))) @ ((((ve @ r) @ l) @ v) @ V2))))))) => ((((member @ l) @ L2) @ (((dom @ l) @ (((val @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau))) => (((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau) @ L2) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit))))))))))))).
% 3.28/1.66 thf(fact_224_set__deterministic, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),L2:l,V2:(((val @ r) @ l) @ v),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ (((((assign @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L2))) @ ((((ve @ r) @ l) @ v) @ V2))))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = ((((member @ l) @ L2) @ (((dom @ l) @ (((val @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau))) & (S2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau) @ L2) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))))))))).
% 3.28/1.66 thf(fact_225_dom__const, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((dom @ A) @ B) @ (^ [X:A]: (((some @ B) @ (F @ X))))) = (top_top @ (set @ A)))))).
% 3.28/1.66 thf(fact_226_domI, axiom, (! [A:$tType,B:$tType,M:(B > (option @ A)),A2:B,B2:A]: ((((M @ A2) = ((some @ A) @ B2)) => (((member @ B) @ A2) @ (((dom @ B) @ A) @ M)))))).
% 3.28/1.66 thf(fact_227_domD, axiom, (! [A:$tType,B:$tType,A2:A,M:(A > (option @ B))]: (((((member @ A) @ A2) @ (((dom @ A) @ B) @ M)) => (? [B4:B]: (((M @ A2) = ((some @ B) @ B4)))))))).
% 3.28/1.66 thf(fact_228_dom__def, axiom, (! [B:$tType,A:$tType]: ((((dom @ A) @ B) = (^ [M3:(A > (option @ B))]: (((collect @ A) @ (^ [A3:A]: (((M3 @ A3) != (none @ B))))))))))).
% 3.28/1.66 thf(fact_229_domIff, axiom, (! [A:$tType,B:$tType,A2:A,M:(A > (option @ B))]: (((((member @ A) @ A2) @ (((dom @ A) @ B) @ M)) = ((M @ A2) != (none @ B)))))).
% 3.28/1.66 thf(fact_230_finite__map__freshness, axiom, (! [A:$tType,B:$tType,F:(A > (option @ B))]: ((((finite_finite @ A) @ (((dom @ A) @ B) @ F)) => ((~ (((finite_finite @ A) @ (top_top @ (set @ A))))) => (? [X6:A]: (((F @ X6) = (none @ B))))))))).
% 3.28/1.66 thf(fact_231_substitution_Oset__deterministic, axiom, (! [R:$tType,L:$tType,V:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),L2:L,V2:(((val @ R) @ L) @ V),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ (((((assign @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L2))) @ ((((ve @ R) @ L) @ V) @ V2))))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = ((((member @ L) @ L2) @ (((dom @ L) @ (((val @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau))) & (S2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau) @ L2) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit))))))))))))))).
% 3.28/1.66 thf(fact_232_substitution_Orevision__step_Oset, axiom, (! [R:$tType,L:$tType,V:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),L2:L,V2:(((val @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ (((((assign @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L2))) @ ((((ve @ R) @ L) @ V) @ V2))))))) => ((((member @ L) @ L2) @ (((dom @ L) @ (((val @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau) @ L2) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))))))))).
% 3.28/1.66 thf(fact_233_revision__step_Oget, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),L2:l]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((read @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L2)))))))) => ((((member @ l) @ L2) @ (((dom @ l) @ (((val @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau))) => (((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((the @ (((val @ r) @ l) @ v)) @ (((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau) @ L2)))))))))))))).
% 3.28/1.66 thf(fact_234_revision__step__relaxed_Oget, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),L2:l]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((read @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L2)))))))) => (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((the @ (((val @ r) @ l) @ v)) @ (((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau) @ L2))))))))))))).
% 3.28/1.66 thf(fact_235__092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r]: ((((((domain398919503obally @ r) @ l) @ v) @ S) => ((((member @ r) @ R2) @ (((dom @ r) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ S)) => ((((((subsumes_accessible @ r) @ l) @ v) @ R2) @ R2) @ S)))))).
% 3.28/1.66 thf(fact_236_subsumes__accessible__globally__def, axiom, ((((subsum380726323obally @ r) @ l) @ v) = (^ [S4:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((! [R_12:r,R_22:r]: (((((member @ r) @ R_12) @ (((dom @ r) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ S4)) => ((((member @ r) @ R_22) @ (((dom @ r) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ S4)) => ((((((subsumes_accessible @ r) @ l) @ v) @ R_12) @ R_22) @ S4))))))))).
% 3.28/1.66 thf(fact_237_expr_Oinject_I5_J, axiom, (! [V:$tType,L:$tType,R:$tType,X52:(((expr @ R) @ L) @ V),Y5:(((expr @ R) @ L) @ V)]: (((((((read @ R) @ L) @ V) @ X52) = ((((read @ R) @ L) @ V) @ Y5)) = (X52 = Y5))))).
% 3.28/1.66 thf(fact_238_option_Ocollapse, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (((some @ A) @ ((the @ A) @ Option)) = Option))))).
% 3.28/1.66 thf(fact_239_get__deterministic, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),L2:l,S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((S @ R2) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((read @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L2)))))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = ((((member @ l) @ L2) @ (((dom @ l) @ (((val @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau))) & (S2 = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ S) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ (((((plug @ r) @ l) @ v) @ E) @ ((((ve @ r) @ l) @ v) @ ((the @ (((val @ r) @ l) @ v)) @ (((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma) @ Tau) @ L2))))))))))))))).
% 3.28/1.66 thf(fact_240_expr_Odistinct_I37_J, axiom, (! [V:$tType,L:$tType,R:$tType,X4:(((expr @ R) @ L) @ V),X52:(((expr @ R) @ L) @ V)]: ((((((ref @ R) @ L) @ V) @ X4) != ((((read @ R) @ L) @ V) @ X52))))).
% 3.28/1.66 thf(fact_241_option_Oexpand, axiom, (! [A:$tType,Option:(option @ A),Option2:(option @ A)]: ((((Option = (none @ A)) = (Option2 = (none @ A))) => (((Option != (none @ A)) => ((Option2 != (none @ A)) => (((the @ A) @ Option) = ((the @ A) @ Option2)))) => (Option = Option2)))))).
% 3.28/1.66 thf(fact_242_expr_Odistinct_I47_J, axiom, (! [V:$tType,L:$tType,R:$tType,X52:(((expr @ R) @ L) @ V),X7:(((expr @ R) @ L) @ V)]: ((((((read @ R) @ L) @ V) @ X52) != ((((rfork @ R) @ L) @ V) @ X7))))).
% 3.28/1.66 thf(fact_243_expr_Odistinct_I49_J, axiom, (! [V:$tType,L:$tType,R:$tType,X52:(((expr @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: ((((((read @ R) @ L) @ V) @ X52) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.28/1.66 thf(fact_244_expr_Odistinct_I7_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X52:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != ((((read @ R) @ L) @ V) @ X52))))).
% 3.28/1.66 thf(fact_245_expr_Odistinct_I29_J, axiom, (! [V:$tType,L:$tType,R:$tType,X31:(((expr @ R) @ L) @ V),X32:(((expr @ R) @ L) @ V),X33:(((expr @ R) @ L) @ V),X52:(((expr @ R) @ L) @ V)]: ((((((((ite @ R) @ L) @ V) @ X31) @ X32) @ X33) != ((((read @ R) @ L) @ V) @ X52))))).
% 3.28/1.66 thf(fact_246_expr_Odistinct_I45_J, axiom, (! [V:$tType,L:$tType,R:$tType,X52:(((expr @ R) @ L) @ V),X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V)]: ((((((read @ R) @ L) @ V) @ X52) != (((((assign @ R) @ L) @ V) @ X61) @ X62))))).
% 3.28/1.66 thf(fact_247_option_Oexhaust__sel, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (Option = ((some @ A) @ ((the @ A) @ Option))))))).
% 3.28/1.66 thf(fact_248_option_Osel, axiom, (! [A:$tType,X22:A]: ((((the @ A) @ ((some @ A) @ X22)) = X22)))).
% 3.28/1.66 thf(fact_249_RID_092_060_094sub_062GE, axiom, (! [C:$tType,A:$tType,B:$tType,R2:A,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))))]: (((((member @ A) @ R2) @ ((((rID_G @ A) @ B) @ C) @ S)) => ((~ ((((member @ A) @ R2) @ (((dom @ A) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))) @ S)))) => (~ ((! [R9:A,Ls3:((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))]: ((((S @ R9) = ((some @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))) @ Ls3)) => (~ ((((member @ A) @ R2) @ ((((rID_L @ B) @ A) @ C) @ Ls3)))))))))))))).
% 3.28/1.66 thf(fact_250_substitution_O_092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((((domain398919503obally @ R) @ L) @ V) @ S) => ((((member @ R) @ R2) @ (((dom @ R) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ S)) => ((((((subsumes_accessible @ R) @ L) @ V) @ R2) @ R2) @ S))))))).
% 3.28/1.66 thf(fact_251_substitution_Osubsumes__accessible__globally__def, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((((subsum380726323obally @ R) @ L) @ V) @ S) = (! [R_12:R,R_22:R]: (((((member @ R) @ R_12) @ (((dom @ R) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ S)) => ((((member @ R) @ R_22) @ (((dom @ R) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ S)) => ((((((subsumes_accessible @ R) @ L) @ V) @ R_12) @ R_22) @ S)))))))))).
% 3.28/1.66 thf(fact_252_substitution_Orevision__step__relaxed_Oget, axiom, (! [R:$tType,V:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),L2:L]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((read @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L2)))))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((the @ (((val @ R) @ L) @ V)) @ (((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau) @ L2)))))))))))))).
% 3.28/1.66 thf(fact_253_substitution_Oget__deterministic, axiom, (! [R:$tType,V:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),L2:L,S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((read @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L2)))))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = ((((member @ L) @ L2) @ (((dom @ L) @ (((val @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau))) & (S2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((the @ (((val @ R) @ L) @ V)) @ (((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau) @ L2)))))))))))))))).
% 3.28/1.66 thf(fact_254_substitution_Orevision__step_Oget, axiom, (! [R:$tType,V:$tType,L:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),L2:L]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((read @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L2)))))))) => ((((member @ L) @ L2) @ (((dom @ L) @ (((val @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ve @ R) @ L) @ V) @ ((the @ (((val @ R) @ L) @ V)) @ (((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma) @ Tau) @ L2))))))))))))))).
% 3.28/1.66 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: (((order @ A7) => (order @ (A6 > A7)))))).
% 3.28/1.66 thf(tcon_Set_Oset___Orderings_Oorder_1, axiom, (! [A6:$tType]: ((order @ (set @ A6))))).
% 3.28/1.66 thf(tcon_HOL_Obool___Orderings_Oorder_2, axiom, (order @ $o)).
% 3.28/1.66 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.28/1.66 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 3.28/1.66 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 3.28/1.66 thf(conj_0, conjecture, ((((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ s_1) @ r2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ x))) @ r3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ tau) @ (((((plug @ r) @ l) @ v) @ e) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ r4)))))))) @ r4) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ sigma) @ tau)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ e2)))) = (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ (((((fun_upd @ r) @ (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))) @ s_1) @ r3) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ tau) @ (((((plug @ r) @ l) @ v) @ e) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ r4)))))))) @ r4) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ sigma) @ tau)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ e2))))) @ r2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ x)))).
% 3.28/1.66 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.qbB1WGygH8/DTF2DTF7240.p
% 3.28/1.66 ------------------------
% 3.44/1.78 ---- Cleaned THF ---
% 3.44/1.78 thf(ty_t_Product__Type_Oprod,type,
% 3.44/1.78 product_prod: $tType > $tType > $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_t_Option_Ooption,type,
% 3.44/1.78 option: $tType > $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_t_Data_Oconst,type,
% 3.44/1.78 const: $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_t_Data_Ocntxt,type,
% 3.44/1.78 cntxt: $tType > $tType > $tType > $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_t_Data_Oexpr,type,
% 3.44/1.78 expr: $tType > $tType > $tType > $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_t_Data_Oval,type,
% 3.44/1.78 val: $tType > $tType > $tType > $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_t_Set_Oset,type,
% 3.44/1.78 set: $tType > $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_tf_v,type,
% 3.44/1.78 v: $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_tf_r,type,
% 3.44/1.78 r: $tType ).
% 3.44/1.78
% 3.44/1.78 thf(ty_tf_l,type,
% 3.44/1.78 l: $tType ).
% 3.44/1.78
% 3.44/1.78 thf(sy_cl_HOL_Otype,type,
% 3.44/1.78 type:
% 3.44/1.78 !>[A: $tType] : $o ).
% 3.44/1.78
% 3.44/1.78 thf(sy_cl_Orderings_Oorder,type,
% 3.44/1.78 order:
% 3.44/1.78 !>[A: $tType] : $o ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Ocombine,type,
% 3.44/1.78 combine:
% 3.44/1.78 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( A > ( option @ B ) ) > A > ( option @ B ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oconst_OF,type,
% 3.44/1.78 f: const ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oconst_OT,type,
% 3.44/1.78 t: const ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oconst_OUnit,type,
% 3.44/1.78 unit: const ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Odoms,type,
% 3.44/1.78 doms:
% 3.44/1.78 !>[L: $tType,R: $tType,V: $tType] : ( ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > ( set @ L ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oexpr_OAssign,type,
% 3.44/1.78 assign:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oexpr_OIte,type,
% 3.44/1.78 ite:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oexpr_ORead,type,
% 3.44/1.78 read:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oexpr_ORef,type,
% 3.44/1.78 ref:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oexpr_ORfork,type,
% 3.44/1.78 rfork:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oexpr_ORjoin,type,
% 3.44/1.78 rjoin:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oexpr_OVE,type,
% 3.44/1.78 ve:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( val @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oplug,type,
% 3.44/1.78 plug:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( cntxt @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oval_OCV,type,
% 3.44/1.78 cv:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( const > ( val @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oval_OLoc,type,
% 3.44/1.78 loc:
% 3.44/1.78 !>[L: $tType,R: $tType,V: $tType] : ( L > ( val @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Data_Oval_ORid,type,
% 3.44/1.78 rid:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( R > ( val @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Executions_Osubstitution_Oexecution,type,
% 3.44/1.78 execution:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( expr @ R @ L @ V ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Executions_Osubstitution_Oinductive__invariant,type,
% 3.44/1.78 inductive_invariant:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Executions_Osubstitution_Omaximal__execution,type,
% 3.44/1.78 maximal_execution:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( expr @ R @ L @ V ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Executions_Osubstitution_Oreachable,type,
% 3.44/1.78 reachable:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Executions_Osubstitution_Osteps,type,
% 3.44/1.78 steps:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( set @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Executions_Osubstitution_Oterminates__in,type,
% 3.44/1.78 terminates_in:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > ( expr @ R @ L @ V ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Finite__Set_Ofinite,type,
% 3.44/1.78 finite_finite:
% 3.44/1.78 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Fun_Ofun__upd,type,
% 3.44/1.78 fun_upd:
% 3.44/1.78 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_If,type,
% 3.44/1.78 if:
% 3.44/1.78 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Map_Odom,type,
% 3.44/1.78 dom:
% 3.44/1.78 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Occurrences_OLID_092_060_094sub_062G,type,
% 3.44/1.78 lID_G:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( set @ L ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Occurrences_OLID_092_060_094sub_062L,type,
% 3.44/1.78 lID_L:
% 3.44/1.78 !>[L: $tType,R: $tType,V: $tType] : ( ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > ( set @ L ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Occurrences_ORID_092_060_094sub_062G,type,
% 3.44/1.78 rID_G:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( set @ R ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Occurrences_ORID_092_060_094sub_062L,type,
% 3.44/1.78 rID_L:
% 3.44/1.78 !>[L: $tType,R: $tType,V: $tType] : ( ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > ( set @ R ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume,type,
% 3.44/1.78 domains_subsume:
% 3.44/1.78 !>[L: $tType,R: $tType,V: $tType] : ( ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally,type,
% 3.44/1.78 domain398919503obally:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step,type,
% 3.44/1.78 revision_step:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > R > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed,type,
% 3.44/1.78 revisi1433015572elaxed:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > R > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible,type,
% 3.44/1.78 subsumes_accessible:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( R > R > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally,type,
% 3.44/1.78 subsum380726323obally:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Option_Ooption_ONone,type,
% 3.44/1.78 none:
% 3.44/1.78 !>[A: $tType] : ( option @ A ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Option_Ooption_OSome,type,
% 3.44/1.78 some:
% 3.44/1.78 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Option_Ooption_Othe,type,
% 3.44/1.78 the:
% 3.44/1.78 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.44/1.78 ord_less_eq:
% 3.44/1.78 !>[A: $tType] : ( A > A > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Orderings_Otop__class_Otop,type,
% 3.44/1.78 top_top:
% 3.44/1.78 !>[A: $tType] : A ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Product__Type_OPair,type,
% 3.44/1.78 product_Pair:
% 3.44/1.78 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Renaming_Oeq__states,type,
% 3.44/1.78 eq_states:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Set_OCollect,type,
% 3.44/1.78 collect:
% 3.44/1.78 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Substitution_Osubstitution,type,
% 3.44/1.78 substitution:
% 3.44/1.78 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_Transitive__Closure_Ortrancl,type,
% 3.44/1.78 transitive_rtrancl:
% 3.44/1.78 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_c_member,type,
% 3.44/1.78 member:
% 3.44/1.78 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v__092_060E_062,type,
% 3.44/1.78 e: cntxt @ r @ l @ v ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v__092_060sigma_062,type,
% 3.44/1.78 sigma: l > ( option @ ( val @ r @ l @ v ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v__092_060tau_062,type,
% 3.44/1.78 tau: l > ( option @ ( val @ r @ l @ v ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_e,type,
% 3.44/1.78 e2: expr @ r @ l @ v ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_r,type,
% 3.44/1.78 r2: r ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_r_H,type,
% 3.44/1.78 r3: r ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_r_H_H,type,
% 3.44/1.78 r4: r ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_s_092_060_094sub_0621,type,
% 3.44/1.78 s_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_s_092_060_094sub_0622,type,
% 3.44/1.78 s_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_s_092_060_094sub_0622_H,type,
% 3.44/1.78 s_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_subst,type,
% 3.44/1.78 subst: ( expr @ r @ l @ v ) > v > ( expr @ r @ l @ v ) > ( expr @ r @ l @ v ) ).
% 3.44/1.78
% 3.44/1.78 thf(sy_v_x,type,
% 3.44/1.78 x: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_0_assms_I4_J,axiom,
% 3.44/1.78 ~ ( member @ r @ r4 @ ( rID_G @ r @ l @ v @ s_2 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_1_assms_I7_J,axiom,
% 3.44/1.78 r2 != r4 ).
% 3.44/1.78
% 3.44/1.78 thf(fact_2_assms_I6_J,axiom,
% 3.44/1.78 r2 != r3 ).
% 3.44/1.78
% 3.44/1.78 thf(fact_3_assms_I1_J,axiom,
% 3.44/1.78 ( s_2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ x ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_4_assms_I3_J,axiom,
% 3.44/1.78 ( ( s_2 @ r3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( rfork @ r @ l @ v @ e2 ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_5_assms_I2_J,axiom,
% 3.44/1.78 ( s_22
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ r4 ) ) ) ) ) ) ) @ r4
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ sigma @ tau )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.44/1.78 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.44/1.78 @ e2 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_6_revision__step_Ofork,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v,R3: r] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rfork @ r @ l @ v @ E2 ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 3.44/1.78 => ( revision_step @ r @ l @ v @ subst @ R2 @ S
% 3.44/1.78 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) @ R3
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.44/1.78 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.44/1.78 @ E2 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_7_assms_I5_J,axiom,
% 3.44/1.78 ( revision_step @ r @ l @ v @ subst @ r2 @ s_22
% 3.44/1.78 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )
% 3.44/1.78 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ r4 ) ) ) ) ) ) ) @ r4
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ sigma @ tau )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.44/1.78 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.44/1.78 @ e2 ) ) ) )
% 3.44/1.78 @ r2
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ x ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_8_restrictions__inwards,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,X2: A,X3: A,F: A > ( option @ B ),Y: B] :
% 3.44/1.78 ( ( X2 != X3 )
% 3.44/1.78 => ( ( fun_upd @ A @ ( option @ B ) @ ( fun_upd @ A @ ( option @ B ) @ F @ X2 @ ( some @ B @ Y ) ) @ X3 @ ( none @ B ) )
% 3.44/1.78 = ( fun_upd @ A @ ( option @ B ) @ ( fun_upd @ A @ ( option @ B ) @ F @ X3 @ ( none @ B ) ) @ X2 @ ( some @ B @ Y ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_9_empty__upd__none,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,X2: A] :
% 3.44/1.78 ( ( fun_upd @ A @ ( option @ B )
% 3.44/1.78 @ ^ [X: A] : ( none @ B )
% 3.44/1.78 @ X2
% 3.44/1.78 @ ( none @ B ) )
% 3.44/1.78 = ( ^ [X: A] : ( none @ B ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_10_not__None__eq,axiom,
% 3.44/1.78 ! [A: $tType,X2: option @ A] :
% 3.44/1.78 ( ( X2
% 3.44/1.78 != ( none @ A ) )
% 3.44/1.78 = ( ? [Y2: A] :
% 3.44/1.78 ( X2
% 3.44/1.78 = ( some @ A @ Y2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_11_not__Some__eq,axiom,
% 3.44/1.78 ! [A: $tType,X2: option @ A] :
% 3.44/1.78 ( ( ! [Y2: A] :
% 3.44/1.78 ( X2
% 3.44/1.78 != ( some @ A @ Y2 ) ) )
% 3.44/1.78 = ( X2
% 3.44/1.78 = ( none @ A ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_12_map__upd__nonempty,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,T: A > ( option @ B ),K: A,X2: B] :
% 3.44/1.78 ( ( fun_upd @ A @ ( option @ B ) @ T @ K @ ( some @ B @ X2 ) )
% 3.44/1.78 != ( ^ [X: A] : ( none @ B ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_13_fork__pseudodeterministic,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rfork @ r @ l @ v @ E2 ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( ? [R4: r] :
% 3.44/1.78 ( ~ ( member @ r @ R4 @ ( rID_G @ r @ l @ v @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rfork @ r @ l @ v @ E2 ) ) ) ) ) ) ) )
% 3.44/1.78 & ( S2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R4 ) ) ) ) ) ) ) @ R4
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.44/1.78 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.44/1.78 @ E2 ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_14_revision__step__relaxed_Ofork,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v,R3: r] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rfork @ r @ l @ v @ E2 ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S
% 3.44/1.78 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) @ R3
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.44/1.78 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.44/1.78 @ E2 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_15_val_Oinject_I4_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X4: R,Y4: R] :
% 3.44/1.78 ( ( ( rid @ R @ L @ V @ X4 )
% 3.44/1.78 = ( rid @ R @ L @ V @ Y4 ) )
% 3.44/1.78 = ( X4 = Y4 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_16_injective__cntxt,axiom,
% 3.44/1.78 ! [C: $tType,B: $tType,A: $tType,E: cntxt @ A @ B @ C,E1: expr @ A @ B @ C,E22: expr @ A @ B @ C] :
% 3.44/1.78 ( ( ( plug @ A @ B @ C @ E @ E1 )
% 3.44/1.78 = ( plug @ A @ B @ C @ E @ E22 ) )
% 3.44/1.78 = ( E1 = E22 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_17_expr_Oinject_I1_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,Y1: val @ R @ L @ V] :
% 3.44/1.78 ( ( ( ve @ R @ L @ V @ X1 )
% 3.44/1.78 = ( ve @ R @ L @ V @ Y1 ) )
% 3.44/1.78 = ( X1 = Y1 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_18_fun__upd__upd,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B,Z: B] :
% 3.44/1.78 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X2 @ Y ) @ X2 @ Z )
% 3.44/1.78 = ( fun_upd @ A @ B @ F @ X2 @ Z ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_19_fun__upd__triv,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,F: A > B,X2: A] :
% 3.44/1.78 ( ( fun_upd @ A @ B @ F @ X2 @ ( F @ X2 ) )
% 3.44/1.78 = F ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_20_option_Oinject,axiom,
% 3.44/1.78 ! [A: $tType,X22: A,Y22: A] :
% 3.44/1.78 ( ( ( some @ A @ X22 )
% 3.44/1.78 = ( some @ A @ Y22 ) )
% 3.44/1.78 = ( X22 = Y22 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_21_fun__upd__apply,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType] :
% 3.44/1.78 ( ( fun_upd @ B @ A )
% 3.44/1.78 = ( ^ [F2: B > A,X: B,Y2: A,Z2: B] : ( if @ A @ ( Z2 = X ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_22_expr_Oinject_I7_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X7: expr @ R @ L @ V,Y7: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ( rfork @ R @ L @ V @ X7 )
% 3.44/1.78 = ( rfork @ R @ L @ V @ Y7 ) )
% 3.44/1.78 = ( X7 = Y7 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_23_RID_092_060_094sub_062GI_I1_J,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R2: B,V2: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ V2 ) )
% 3.44/1.78 => ( member @ B @ R2 @ ( rID_G @ B @ A @ C @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_24_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 3.44/1.78 ! [C: $tType,B: $tType,A: $tType,R3: A,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 3.44/1.78 ( ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) )
% 3.44/1.78 => ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_25_only__fork__introduces__rids_H,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ! [Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: expr @ r @ l @ v] :
% 3.44/1.78 ( ( S @ R2 )
% 3.44/1.78 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( rfork @ r @ l @ v @ E4 ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 3.44/1.78 => ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S2 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_26_in__restricted__global__in__updated__global_I1_J,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,R3: A,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A,Ls: product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) )] :
% 3.44/1.78 ( ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) )
% 3.44/1.78 => ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) @ Ls ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_27_substitution__axioms,axiom,
% 3.44/1.78 substitution @ r @ l @ v @ subst ).
% 3.44/1.78
% 3.44/1.78 thf(fact_28_expr_Odistinct_I11_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X7: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ve @ R @ L @ V @ X1 )
% 3.44/1.78 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_29_fun__upd__idem__iff,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B] :
% 3.44/1.78 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y )
% 3.44/1.78 = F )
% 3.44/1.78 = ( ( F @ X2 )
% 3.44/1.78 = Y ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_30_fun__upd__twist,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,A2: A,C2: A,M: A > B,B2: B,D: B] :
% 3.44/1.78 ( ( A2 != C2 )
% 3.44/1.78 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ A2 @ B2 ) @ C2 @ D )
% 3.44/1.78 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ C2 @ D ) @ A2 @ B2 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_31_fun__upd__other,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,Z: A,X2: A,F: A > B,Y: B] :
% 3.44/1.78 ( ( Z != X2 )
% 3.44/1.78 => ( ( fun_upd @ A @ B @ F @ X2 @ Y @ Z )
% 3.44/1.78 = ( F @ Z ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_32_fun__upd__same,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,F: B > A,X2: B,Y: A] :
% 3.44/1.78 ( ( fun_upd @ B @ A @ F @ X2 @ Y @ X2 )
% 3.44/1.78 = Y ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_33_fun__upd__idem,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,F: B > A,X2: B,Y: A] :
% 3.44/1.78 ( ( ( F @ X2 )
% 3.44/1.78 = Y )
% 3.44/1.78 => ( ( fun_upd @ B @ A @ F @ X2 @ Y )
% 3.44/1.78 = F ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_34_fun__upd__eqD,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B,G: A > B,Z: B] :
% 3.44/1.78 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y )
% 3.44/1.78 = ( fun_upd @ A @ B @ G @ X2 @ Z ) )
% 3.44/1.78 => ( Y = Z ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_35_fun__upd__def,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType] :
% 3.44/1.78 ( ( fun_upd @ A @ B )
% 3.44/1.78 = ( ^ [F2: A > B,A3: A,B3: B,X: A] : ( if @ B @ ( X = A3 ) @ B3 @ ( F2 @ X ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_36_combine__options__cases,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,X2: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 3.44/1.78 ( ( ( X2
% 3.44/1.78 = ( none @ A ) )
% 3.44/1.78 => ( P @ X2 @ Y ) )
% 3.44/1.78 => ( ( ( Y
% 3.44/1.78 = ( none @ B ) )
% 3.44/1.78 => ( P @ X2 @ Y ) )
% 3.44/1.78 => ( ! [A4: A,B4: B] :
% 3.44/1.78 ( ( X2
% 3.44/1.78 = ( some @ A @ A4 ) )
% 3.44/1.78 => ( ( Y
% 3.44/1.78 = ( some @ B @ B4 ) )
% 3.44/1.78 => ( P @ X2 @ Y ) ) )
% 3.44/1.78 => ( P @ X2 @ Y ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_37_split__option__all,axiom,
% 3.44/1.78 ! [A: $tType] :
% 3.44/1.78 ( ( ^ [P2: ( option @ A ) > $o] :
% 3.44/1.78 ! [X5: option @ A] : ( P2 @ X5 ) )
% 3.44/1.78 = ( ^ [P3: ( option @ A ) > $o] :
% 3.44/1.78 ( ( P3 @ ( none @ A ) )
% 3.44/1.78 & ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_38_split__option__ex,axiom,
% 3.44/1.78 ! [A: $tType] :
% 3.44/1.78 ( ( ^ [P2: ( option @ A ) > $o] :
% 3.44/1.78 ? [X5: option @ A] : ( P2 @ X5 ) )
% 3.44/1.78 = ( ^ [P3: ( option @ A ) > $o] :
% 3.44/1.78 ( ( P3 @ ( none @ A ) )
% 3.44/1.78 | ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_39_option_Oinducts,axiom,
% 3.44/1.78 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 3.44/1.78 ( ( P @ ( none @ A ) )
% 3.44/1.78 => ( ! [X6: A] : ( P @ ( some @ A @ X6 ) )
% 3.44/1.78 => ( P @ Option ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_40_option_Oexhaust,axiom,
% 3.44/1.78 ! [A: $tType,Y: option @ A] :
% 3.44/1.78 ( ( Y
% 3.44/1.78 != ( none @ A ) )
% 3.44/1.78 => ~ ! [X23: A] :
% 3.44/1.78 ( Y
% 3.44/1.78 != ( some @ A @ X23 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_41_option_OdiscI,axiom,
% 3.44/1.78 ! [A: $tType,Option: option @ A,X22: A] :
% 3.44/1.78 ( ( Option
% 3.44/1.78 = ( some @ A @ X22 ) )
% 3.44/1.78 => ( Option
% 3.44/1.78 != ( none @ A ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_42_option_Odistinct_I1_J,axiom,
% 3.44/1.78 ! [A: $tType,X22: A] :
% 3.44/1.78 ( ( none @ A )
% 3.44/1.78 != ( some @ A @ X22 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_43_combine_Ocases,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,X2: product_prod @ ( A > ( option @ B ) ) @ ( product_prod @ ( A > ( option @ B ) ) @ A )] :
% 3.44/1.78 ~ ! [F3: A > ( option @ B ),G2: A > ( option @ B ),X6: A] :
% 3.44/1.78 ( X2
% 3.44/1.78 != ( product_Pair @ ( A > ( option @ B ) ) @ ( product_prod @ ( A > ( option @ B ) ) @ A ) @ F3 @ ( product_Pair @ ( A > ( option @ B ) ) @ A @ G2 @ X6 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_44_mem__Collect__eq,axiom,
% 3.44/1.78 ! [A: $tType,A2: A,P: A > $o] :
% 3.44/1.78 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.44/1.78 = ( P @ A2 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_45_Collect__mem__eq,axiom,
% 3.44/1.78 ! [A: $tType,A5: set @ A] :
% 3.44/1.78 ( ( collect @ A
% 3.44/1.78 @ ^ [X: A] : ( member @ A @ X @ A5 ) )
% 3.44/1.78 = A5 ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_46_Collect__cong,axiom,
% 3.44/1.78 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.44/1.78 ( ! [X6: A] :
% 3.44/1.78 ( ( P @ X6 )
% 3.44/1.78 = ( Q @ X6 ) )
% 3.44/1.78 => ( ( collect @ A @ P )
% 3.44/1.78 = ( collect @ A @ Q ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_47_ext,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.44/1.78 ( ! [X6: A] :
% 3.44/1.78 ( ( F @ X6 )
% 3.44/1.78 = ( G @ X6 ) )
% 3.44/1.78 => ( F = G ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_48_map__upd__Some__unfold,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,M: B > ( option @ A ),A2: B,B2: A,X2: B,Y: A] :
% 3.44/1.78 ( ( ( fun_upd @ B @ ( option @ A ) @ M @ A2 @ ( some @ A @ B2 ) @ X2 )
% 3.44/1.78 = ( some @ A @ Y ) )
% 3.44/1.78 = ( ( ( X2 = A2 )
% 3.44/1.78 & ( B2 = Y ) )
% 3.44/1.78 | ( ( X2 != A2 )
% 3.44/1.78 & ( ( M @ X2 )
% 3.44/1.78 = ( some @ A @ Y ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_49_map__upd__triv,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,T: B > ( option @ A ),K: B,X2: A] :
% 3.44/1.78 ( ( ( T @ K )
% 3.44/1.78 = ( some @ A @ X2 ) )
% 3.44/1.78 => ( ( fun_upd @ B @ ( option @ A ) @ T @ K @ ( some @ A @ X2 ) )
% 3.44/1.78 = T ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_50_map__upd__eqD1,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,M: A > ( option @ B ),A2: A,X2: B,N: A > ( option @ B ),Y: B] :
% 3.44/1.78 ( ( ( fun_upd @ A @ ( option @ B ) @ M @ A2 @ ( some @ B @ X2 ) )
% 3.44/1.78 = ( fun_upd @ A @ ( option @ B ) @ N @ A2 @ ( some @ B @ Y ) ) )
% 3.44/1.78 => ( X2 = Y ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_51_LID__local__store_Oinduct,axiom,
% 3.44/1.78 ! [V: $tType,R: $tType,L: $tType,P: ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) > $o,A0: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 3.44/1.78 ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E4: expr @ R @ L @ V] : ( P @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ E4 ) ) )
% 3.44/1.78 => ( P @ A0 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_52_LID__local__store_Ocases,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X2: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 3.44/1.78 ~ ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E4: expr @ R @ L @ V] :
% 3.44/1.78 ( X2
% 3.44/1.78 != ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ E4 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_53_combine_Osimps,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType] :
% 3.44/1.78 ( ( combine @ A @ B )
% 3.44/1.78 = ( ^ [F2: A > ( option @ B ),G3: A > ( option @ B ),X: A] :
% 3.44/1.78 ( if @ ( option @ B )
% 3.44/1.78 @ ( ( G3 @ X )
% 3.44/1.78 = ( none @ B ) )
% 3.44/1.78 @ ( F2 @ X )
% 3.44/1.78 @ ( G3 @ X ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_54_combine_Oelims,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,X2: A > ( option @ B ),Xa: A > ( option @ B ),Xb: A,Y: option @ B] :
% 3.44/1.78 ( ( ( combine @ A @ B @ X2 @ Xa @ Xb )
% 3.44/1.78 = Y )
% 3.44/1.78 => ( ( ( ( Xa @ Xb )
% 3.44/1.78 = ( none @ B ) )
% 3.44/1.78 => ( Y
% 3.44/1.78 = ( X2 @ Xb ) ) )
% 3.44/1.78 & ( ( ( Xa @ Xb )
% 3.44/1.78 != ( none @ B ) )
% 3.44/1.78 => ( Y
% 3.44/1.78 = ( Xa @ Xb ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_55_local__steps__commute,axiom,
% 3.44/1.78 ! [S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,X2: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ),S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r,Y: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) )] :
% 3.44/1.78 ( ( S_2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) )
% 3.44/1.78 => ( ( S_22
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Y ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Y ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Y ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Y ) ) @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) )
% 3.44/1.78 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.44/1.78 | ( S_2 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.44/1.78 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_56_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S
% 3.44/1.78 @ ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_57_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 3.44/1.78 => ( revision_step @ r @ l @ v @ subst @ R2 @ S
% 3.44/1.78 @ ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_58_transition__relations__equivalent,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ S2 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_59_SLC__commute,axiom,
% 3.44/1.78 ! [S_33: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_34: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r,S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( S_33 = S_34 )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_33 )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_34 )
% 3.44/1.78 => ( ( eq_states @ r @ l @ v @ S_33 @ S_34 )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_33 )
% 3.44/1.78 | ( S_2 = S_33 ) )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_34 )
% 3.44/1.78 | ( S_22 = S_34 ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_60_SLC__sym,axiom,
% 3.44/1.78 ! [R3: r,S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ? [S_35: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_36: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ r @ l @ v @ S_35 @ S_36 )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_35 )
% 3.44/1.78 | ( S_2 = S_35 ) )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_36 )
% 3.44/1.78 | ( S_22 = S_36 ) ) )
% 3.44/1.78 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_3 )
% 3.44/1.78 | ( S_22 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_32 )
% 3.44/1.78 | ( S_2 = S_32 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_61_local__determinism,axiom,
% 3.44/1.78 ! [R2: r,S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_1 @ S_2 )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_1 @ S_22 )
% 3.44/1.78 => ( eq_states @ r @ l @ v @ S_2 @ S_22 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_62_reachability__closed__under__execution__step,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( reachable @ r @ l @ v @ subst @ S2 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_63_only__fork__introduces__rids,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ! [Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: expr @ r @ l @ v] :
% 3.44/1.78 ( ( S @ R2 )
% 3.44/1.78 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( rfork @ r @ l @ v @ E4 ) ) ) ) ) )
% 3.44/1.78 => ( ord_less_eq @ ( set @ r ) @ ( rID_G @ r @ l @ v @ S2 ) @ ( rID_G @ r @ l @ v @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_64_substitution_Ofork__pseudodeterministic,axiom,
% 3.44/1.78 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rfork @ R @ L @ V @ E2 ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( ? [R4: R] :
% 3.44/1.78 ( ~ ( member @ R @ R4 @ ( rID_G @ R @ L @ V @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rfork @ R @ L @ V @ E2 ) ) ) ) ) ) ) )
% 3.44/1.78 & ( S2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R4 ) ) ) ) ) ) ) @ R4
% 3.44/1.78 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 3.44/1.78 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau )
% 3.44/1.78 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 3.44/1.78 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 3.44/1.78 @ E2 ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_65_expr_Oinject_I8_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X8: expr @ R @ L @ V,Y8: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ( rjoin @ R @ L @ V @ X8 )
% 3.44/1.78 = ( rjoin @ R @ L @ V @ Y8 ) )
% 3.44/1.78 = ( X8 = Y8 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_66_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.44/1.78 ! [S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R5: r,S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S_1 @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( S_2
% 3.44/1.78 = ( ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S_1 @ R5 )
% 3.44/1.78 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.44/1.78 | ( S_2 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.44/1.78 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_67_reachable__def,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 = ( ? [E5: expr @ r @ l @ v,S3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] : ( execution @ r @ l @ v @ subst @ E5 @ S3 @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_68_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( S2
% 3.44/1.78 = ( ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_69_substitution_Olocal__determinism,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_1 @ S_2 )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_1 @ S_22 )
% 3.44/1.78 => ( eq_states @ R @ L @ V @ S_2 @ S_22 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_70_substitution_OSLC__commute,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_33: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_34: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R,S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( S_33 = S_34 )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_33 )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_34 )
% 3.44/1.78 => ( ( eq_states @ R @ L @ V @ S_33 @ S_34 )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_33 )
% 3.44/1.78 | ( S_2 = S_33 ) )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_34 )
% 3.44/1.78 | ( S_22 = S_34 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_71_substitution_OSLC__sym,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R3: R,S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ? [S_35: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_36: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ R @ L @ V @ S_35 @ S_36 )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_35 )
% 3.44/1.78 | ( S_2 = S_35 ) )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_36 )
% 3.44/1.78 | ( S_22 = S_36 ) ) )
% 3.44/1.78 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_3 )
% 3.44/1.78 | ( S_22 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_32 )
% 3.44/1.78 | ( S_2 = S_32 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_72_expr_Odistinct_I13_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ve @ R @ L @ V @ X1 )
% 3.44/1.78 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_73_expr_Odistinct_I55_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X7: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.44/1.78 ( ( rfork @ R @ L @ V @ X7 )
% 3.44/1.78 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_74_substitution_Olocal__steps__commute,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,X2: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ),S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R,Y: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( S_2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) )
% 3.44/1.78 => ( ( S_22
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Y ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Y ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Y ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Y ) ) @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) )
% 3.44/1.78 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.44/1.78 | ( S_2 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.44/1.78 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_75_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R2: B] : ( ord_less_eq @ ( set @ B ) @ ( rID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) @ ( rID_G @ B @ A @ C @ S ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_76_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R5: R,S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S_1 @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( S_2
% 3.44/1.78 = ( ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S_1 @ R5 )
% 3.44/1.78 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.44/1.78 | ( S_2 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.44/1.78 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_77_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 3.44/1.78 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( S2
% 3.44/1.78 = ( ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_78_inductive__invariant__is__execution__invariant,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),P: ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) > $o] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( ( inductive_invariant @ r @ l @ v @ subst @ P )
% 3.44/1.78 => ( P @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_79_substitution_Orevision__step__relaxed_Ofork,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V,R3: R] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rfork @ R @ L @ V @ E2 ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S
% 3.44/1.78 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) @ R3
% 3.44/1.78 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 3.44/1.78 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau )
% 3.44/1.78 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 3.44/1.78 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 3.44/1.78 @ E2 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_80_substitution_Orevision__step_Ofork,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V,R3: R] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rfork @ R @ L @ V @ E2 ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 3.44/1.78 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S
% 3.44/1.78 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) @ R3
% 3.44/1.78 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 3.44/1.78 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau )
% 3.44/1.78 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 3.44/1.78 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 3.44/1.78 @ E2 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_81_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.44/1.78 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S
% 3.44/1.78 @ ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_82_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.44/1.78 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 3.44/1.78 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S
% 3.44/1.78 @ ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_83_substitution_Oonly__fork__introduces__rids,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: expr @ R @ L @ V] :
% 3.44/1.78 ( ( S @ R2 )
% 3.44/1.78 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( rfork @ R @ L @ V @ E4 ) ) ) ) ) )
% 3.44/1.78 => ( ord_less_eq @ ( set @ R ) @ ( rID_G @ R @ L @ V @ S2 ) @ ( rID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_84_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( domain398919503obally @ r @ l @ v @ S ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_85_domains__subsume__globally__def,axiom,
% 3.44/1.78 ( ( domain398919503obally @ r @ l @ v )
% 3.44/1.78 = ( ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ! [R6: r,Ls2: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) )] :
% 3.44/1.78 ( ( ( S4 @ R6 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Ls2 ) )
% 3.44/1.78 => ( domains_subsume @ l @ r @ v @ Ls2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_86_substitution_Orevision__step_Ocong,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType] :
% 3.44/1.78 ( ( revision_step @ R @ L @ V )
% 3.44/1.78 = ( revision_step @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_87_substitution_Orevision__step__relaxed_Ocong,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType] :
% 3.44/1.78 ( ( revisi1433015572elaxed @ R @ L @ V )
% 3.44/1.78 = ( revisi1433015572elaxed @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_88_substitution_Oonly__fork__introduces__rids_H,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: expr @ R @ L @ V] :
% 3.44/1.78 ( ( S @ R2 )
% 3.44/1.78 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( rfork @ R @ L @ V @ E4 ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 3.44/1.78 => ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S2 ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_89_nice__ind__inv__is__inductive__invariant,axiom,
% 3.44/1.78 ( inductive_invariant @ r @ l @ v @ subst
% 3.44/1.78 @ ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( domain398919503obally @ r @ l @ v @ S4 )
% 3.44/1.78 & ( subsum380726323obally @ r @ l @ v @ S4 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_90_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ( domain398919503obally @ r @ l @ v @ S )
% 3.44/1.78 => ( ( subsum380726323obally @ r @ l @ v @ S )
% 3.44/1.78 => ( subsum380726323obally @ r @ l @ v @ S2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_91_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ( domain398919503obally @ r @ l @ v @ S )
% 3.44/1.78 => ( ( subsum380726323obally @ r @ l @ v @ S )
% 3.44/1.78 => ( domain398919503obally @ r @ l @ v @ S2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_92_valid__stepE,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( member @ ( product_prod @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) @ ( product_Pair @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ S @ S2 ) @ ( steps @ r @ l @ v @ subst ) )
% 3.44/1.78 => ? [R7: r] : ( revision_step @ r @ l @ v @ subst @ R7 @ S @ S2 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_93_substitution_Odomains__subsume__globallyI,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ! [R7: R,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E4: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ( S @ R7 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ E4 ) ) ) )
% 3.44/1.78 => ( domains_subsume @ L @ R @ V @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ E4 ) ) ) )
% 3.44/1.78 => ( domain398919503obally @ R @ L @ V @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_94_substitution_Otransition__relations__equivalent,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ S2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_95_valid__stepI,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( member @ ( product_prod @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) @ ( product_Pair @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ S @ S2 ) @ ( steps @ r @ l @ v @ subst ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_96_domains__subsume__globallyI,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ! [R7: r,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E4: expr @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R7 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ E4 ) ) ) )
% 3.44/1.78 => ( domains_subsume @ l @ r @ v @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ E4 ) ) ) )
% 3.44/1.78 => ( domain398919503obally @ r @ l @ v @ S ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_97_maximal__execution__def,axiom,
% 3.44/1.78 ! [E2: expr @ r @ l @ v,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( maximal_execution @ r @ l @ v @ subst @ E2 @ S @ S2 )
% 3.44/1.78 = ( ( execution @ r @ l @ v @ subst @ E2 @ S @ S2 )
% 3.44/1.78 & ~ ? [S5: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] : ( member @ ( product_prod @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) @ ( product_Pair @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ S2 @ S5 ) @ ( steps @ r @ l @ v @ subst ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_98_substitution_Osteps_Ocong,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType] :
% 3.44/1.78 ( ( steps @ R @ L @ V )
% 3.44/1.78 = ( steps @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_99_substitution_Ovalid__stepE,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( member @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) @ ( product_Pair @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ S @ S2 ) @ ( steps @ R @ L @ V @ Subst ) )
% 3.44/1.78 => ? [R7: R] : ( revision_step @ R @ L @ V @ Subst @ R7 @ S @ S2 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_100_substitution_Ovalid__stepI,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( member @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) @ ( product_Pair @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ S @ S2 ) @ ( steps @ R @ L @ V @ Subst ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_101_substitution_Oreachable_Ocong,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType] :
% 3.44/1.78 ( ( reachable @ R @ L @ V )
% 3.44/1.78 = ( reachable @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_102_substitution_Oinductive__invariant_Ocong,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType] :
% 3.44/1.78 ( ( inductive_invariant @ R @ L @ V )
% 3.44/1.78 = ( inductive_invariant @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_103_substitution_Oexecution_Ocong,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType] :
% 3.44/1.78 ( ( execution @ R @ L @ V )
% 3.44/1.78 = ( execution @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_104_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( inductive_invariant @ R @ L @ V @ Subst
% 3.44/1.78 @ ^ [S4: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( domain398919503obally @ R @ L @ V @ S4 )
% 3.44/1.78 & ( subsum380726323obally @ R @ L @ V @ S4 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_105_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ( domain398919503obally @ R @ L @ V @ S )
% 3.44/1.78 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 3.44/1.78 => ( subsum380726323obally @ R @ L @ V @ S2 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_106_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ( domain398919503obally @ R @ L @ V @ S )
% 3.44/1.78 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 3.44/1.78 => ( domain398919503obally @ R @ L @ V @ S2 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_107_substitution_Odomains__subsume__globally__def,axiom,
% 3.44/1.78 ! [L: $tType,V: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( domain398919503obally @ R @ L @ V @ S )
% 3.44/1.78 = ( ! [R6: R,Ls2: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 3.44/1.78 ( ( ( S @ R6 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Ls2 ) )
% 3.44/1.78 => ( domains_subsume @ L @ R @ V @ Ls2 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_108_substitution_Oreachability__closed__under__execution__step,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( reachable @ R @ L @ V @ Subst @ S2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_109_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( domain398919503obally @ R @ L @ V @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_110_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),P: ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) > $o] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( ( inductive_invariant @ R @ L @ V @ Subst @ P )
% 3.44/1.78 => ( P @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_111_substitution_Oreachable__def,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 = ( ? [E5: expr @ R @ L @ V,S3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] : ( execution @ R @ L @ V @ Subst @ E5 @ S3 @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_112_SLC__join,axiom,
% 3.44/1.78 ! [S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R5: r,S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),Sigma3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v,R3: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S_1 @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( S_2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S_1 @ R5 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.44/1.78 | ( S_2 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.44/1.78 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_113_join__and__local__commute,axiom,
% 3.44/1.78 ! [S_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R5: r,S_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R3: r,Ls: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ),Sigma3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v] :
% 3.44/1.78 ( ( S_2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) )
% 3.44/1.78 => ( ( S_22
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Ls ) ) )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ( ( R3 != R5 )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ R3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Ls ) ) )
% 3.44/1.78 => ( ( ( S_22 @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S_22 @ R5 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 3.44/1.78 => ? [S_3: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S_32: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.44/1.78 | ( S_2 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.44/1.78 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_114_substitution_Omaximal__execution__def,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),E2: expr @ R @ L @ V,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( maximal_execution @ R @ L @ V @ Subst @ E2 @ S @ S2 )
% 3.44/1.78 = ( ( execution @ R @ L @ V @ Subst @ E2 @ S @ S2 )
% 3.44/1.78 & ~ ? [S5: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] : ( member @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) @ ( product_Pair @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ S2 @ S5 ) @ ( steps @ R @ L @ V @ Subst ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_115_substitution_Osubsumes__accessible__globallyI,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ! [R_1: R,Sigma_1: L > ( option @ ( val @ R @ L @ V ) ),Tau_1: L > ( option @ ( val @ R @ L @ V ) ),E_1: expr @ R @ L @ V,R_2: R,Sigma_2: L > ( option @ ( val @ R @ L @ V ) ),Tau_2: L > ( option @ ( val @ R @ L @ V ) ),E_2: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ( S @ R_1 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma_1 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau_1 @ E_1 ) ) ) )
% 3.44/1.78 => ( ( ( S @ R_2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma_2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau_2 @ E_2 ) ) ) )
% 3.44/1.78 => ( subsumes_accessible @ R @ L @ V @ R_1 @ R_2 @ S ) ) )
% 3.44/1.78 => ( subsum380726323obally @ R @ L @ V @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_116_revision__step__relaxed_Ojoin,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r,Sigma3: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_117_val_Oinject_I1_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X1: const,Y1: const] :
% 3.44/1.78 ( ( ( cv @ R @ L @ V @ X1 )
% 3.44/1.78 = ( cv @ R @ L @ V @ Y1 ) )
% 3.44/1.78 = ( X1 = Y1 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_118_terminates__in__def,axiom,
% 3.44/1.78 ! [E2: expr @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( terminates_in @ r @ l @ v @ subst @ E2 @ S2 )
% 3.44/1.78 = ( ? [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] : ( maximal_execution @ r @ l @ v @ subst @ E2 @ S4 @ S2 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_119_revision__step_Ojoin,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r,Sigma3: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 3.44/1.78 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_120_subsumes__accessible__globallyI,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ! [R_1: r,Sigma_1: l > ( option @ ( val @ r @ l @ v ) ),Tau_1: l > ( option @ ( val @ r @ l @ v ) ),E_1: expr @ r @ l @ v,R_2: r,Sigma_2: l > ( option @ ( val @ r @ l @ v ) ),Tau_2: l > ( option @ ( val @ r @ l @ v ) ),E_2: expr @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R_1 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma_1 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau_1 @ E_1 ) ) ) )
% 3.44/1.78 => ( ( ( S @ R_2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma_2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau_2 @ E_2 ) ) ) )
% 3.44/1.78 => ( subsumes_accessible @ r @ l @ v @ R_1 @ R_2 @ S ) ) )
% 3.44/1.78 => ( subsum380726323obally @ r @ l @ v @ S ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_121_rjoin__deterministic,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,R3: r,Sigma3: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),V2: val @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma3 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau3 @ ( ve @ r @ l @ v @ V2 ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( S2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau @ Tau3 ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_122_substitution_Omaximal__execution_Ocong,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType] :
% 3.44/1.78 ( ( maximal_execution @ R @ L @ V )
% 3.44/1.78 = ( maximal_execution @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_123_val_Odistinct_I5_J,axiom,
% 3.44/1.78 ! [L: $tType,V: $tType,R: $tType,X1: const,X4: R] :
% 3.44/1.78 ( ( cv @ R @ L @ V @ X1 )
% 3.44/1.78 != ( rid @ R @ L @ V @ X4 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_124_substitution_Orevision__step_Ojoin,axiom,
% 3.44/1.78 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R,Sigma3: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 3.44/1.78 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_125_substitution_Orjoin__deterministic,axiom,
% 3.44/1.78 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R,Sigma3: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( S2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_126_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 3.44/1.78 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R3: R,Sigma3: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R3 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_127_substitution_Ojoin__and__local__commute,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R5: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R3: R,Ls: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ),Sigma3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( S_2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) )
% 3.44/1.78 => ( ( S_22
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Ls ) ) )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ( ( R3 != R5 )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ R3 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Ls ) ) )
% 3.44/1.78 => ( ( ( S_22 @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S_22 @ R5 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 3.44/1.78 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.44/1.78 | ( S_2 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.44/1.78 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_128_substitution_OSLC__join,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S_1: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,R5: R,S_2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),Sigma3: L > ( option @ ( val @ R @ L @ V ) ),V2: val @ R @ L @ V,R3: R,S_22: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S_1 @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( S_2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S_1 @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau @ Tau3 ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) @ R5 @ ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) )
% 3.44/1.78 => ( ( ( S_1 @ R5 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma3 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau3 @ ( ve @ R @ L @ V @ V2 ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ? [S_3: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S_32: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.44/1.78 | ( S_2 = S_3 ) )
% 3.44/1.78 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.44/1.78 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_129_reachable__imp__identifiers__finite_I1_J,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( finite_finite @ r @ ( rID_G @ r @ l @ v @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_130_RID_092_060_094sub_062G__finite__invariant,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ( finite_finite @ r @ ( rID_G @ r @ l @ v @ S ) )
% 3.44/1.78 => ( finite_finite @ r @ ( rID_G @ r @ l @ v @ S2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_131_reachability__closed__under__execution,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( ( member @ ( product_prod @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) @ ( product_Pair @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ S @ S2 ) @ ( transitive_rtrancl @ ( r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) @ ( steps @ r @ l @ v @ subst ) ) )
% 3.44/1.78 => ( reachable @ r @ l @ v @ subst @ S2 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_132_revision__step__relaxed_OifTrue,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E1 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_133_empty__map__finite_I3_J,axiom,
% 3.44/1.78 ! [H: $tType,I: $tType,G4: $tType] :
% 3.44/1.78 ( finite_finite @ G4
% 3.44/1.78 @ ( rID_G @ G4 @ H @ I
% 3.44/1.78 @ ^ [X: G4] : ( none @ ( product_prod @ ( H > ( option @ ( val @ G4 @ H @ I ) ) ) @ ( product_prod @ ( H > ( option @ ( val @ G4 @ H @ I ) ) ) @ ( expr @ G4 @ H @ I ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_134_expr_Oinject_I3_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,Y31: expr @ R @ L @ V,Y32: expr @ R @ L @ V,Y33: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 3.44/1.78 = ( ite @ R @ L @ V @ Y31 @ Y32 @ Y33 ) )
% 3.44/1.78 = ( ( X31 = Y31 )
% 3.44/1.78 & ( X32 = Y32 )
% 3.44/1.78 & ( X33 = Y33 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_135_revision__step_OifTrue,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E1 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_136_finite__state__imp__restriction__finite_I1_J,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 3.44/1.78 ( ( finite_finite @ A @ ( rID_G @ A @ B @ C @ S ) )
% 3.44/1.78 => ( finite_finite @ A @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_137_ifTrue__deterministic,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( S2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E1 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_138_expr_Odistinct_I3_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ve @ R @ L @ V @ X1 )
% 3.44/1.78 != ( ite @ R @ L @ V @ X31 @ X32 @ X33 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_139_expr_Odistinct_I35_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 3.44/1.78 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_140_expr_Odistinct_I33_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 3.44/1.78 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_141_substitution_Oterminates__in_Ocong,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType] :
% 3.44/1.78 ( ( terminates_in @ R @ L @ V )
% 3.44/1.78 = ( terminates_in @ R @ L @ V ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_142_const_Odistinct_I3_J,axiom,
% 3.44/1.78 unit != t ).
% 3.44/1.78
% 3.44/1.78 thf(fact_143_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ( finite_finite @ R @ ( rID_G @ R @ L @ V @ S ) )
% 3.44/1.78 => ( finite_finite @ R @ ( rID_G @ R @ L @ V @ S2 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_144_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( finite_finite @ R @ ( rID_G @ R @ L @ V @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_145_substitution_Oempty__map__finite_I3_J,axiom,
% 3.44/1.78 ! [R: $tType,L: $tType,V: $tType,H: $tType,I: $tType,G4: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( finite_finite @ G4
% 3.44/1.78 @ ( rID_G @ G4 @ H @ I
% 3.44/1.78 @ ^ [X: G4] : ( none @ ( product_prod @ ( H > ( option @ ( val @ G4 @ H @ I ) ) ) @ ( product_prod @ ( H > ( option @ ( val @ G4 @ H @ I ) ) ) @ ( expr @ G4 @ H @ I ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_146_substitution_Oreachability__closed__under__execution,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( ( member @ ( product_prod @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) @ ( product_Pair @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ S @ S2 ) @ ( transitive_rtrancl @ ( R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) @ ( steps @ R @ L @ V @ Subst ) ) )
% 3.44/1.78 => ( reachable @ R @ L @ V @ Subst @ S2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_147_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,C: $tType,A: $tType,B: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( finite_finite @ A @ ( rID_G @ A @ B @ C @ S ) )
% 3.44/1.78 => ( finite_finite @ A @ ( rID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_148_substitution_OifTrue__deterministic,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( S2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E1 ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_149_substitution_Orevision__step_OifTrue,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E1 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_150_substitution_Orevision__step__relaxed_OifTrue,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E1 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_151_substitution_Oterminates__in__def,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),E2: expr @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( terminates_in @ R @ L @ V @ Subst @ E2 @ S2 )
% 3.44/1.78 = ( ? [S4: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] : ( maximal_execution @ R @ L @ V @ Subst @ E2 @ S4 @ S2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_152_revision__step__relaxed_OifFalse,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E22 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_153_revision__step_OifFalse,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E22 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_154_ifFalse__deterministic,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( S2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ E22 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_155_finite__Collect__subsets,axiom,
% 3.44/1.78 ! [A: $tType,A5: set @ A] :
% 3.44/1.78 ( ( finite_finite @ A @ A5 )
% 3.44/1.78 => ( finite_finite @ ( set @ A )
% 3.44/1.78 @ ( collect @ ( set @ A )
% 3.44/1.78 @ ^ [B5: set @ A] : ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_156_finite__Collect__disjI,axiom,
% 3.44/1.78 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.44/1.78 ( ( finite_finite @ A
% 3.44/1.78 @ ( collect @ A
% 3.44/1.78 @ ^ [X: A] :
% 3.44/1.78 ( ( P @ X )
% 3.44/1.78 | ( Q @ X ) ) ) )
% 3.44/1.78 = ( ( finite_finite @ A @ ( collect @ A @ P ) )
% 3.44/1.78 & ( finite_finite @ A @ ( collect @ A @ Q ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_157_finite__Collect__conjI,axiom,
% 3.44/1.78 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.44/1.78 ( ( ( finite_finite @ A @ ( collect @ A @ P ) )
% 3.44/1.78 | ( finite_finite @ A @ ( collect @ A @ Q ) ) )
% 3.44/1.78 => ( finite_finite @ A
% 3.44/1.78 @ ( collect @ A
% 3.44/1.78 @ ^ [X: A] :
% 3.44/1.78 ( ( P @ X )
% 3.44/1.78 & ( Q @ X ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_158_const_Odistinct_I1_J,axiom,
% 3.44/1.78 unit != f ).
% 3.44/1.78
% 3.44/1.78 thf(fact_159_const_Odistinct_I5_J,axiom,
% 3.44/1.78 f != t ).
% 3.44/1.78
% 3.44/1.78 thf(fact_160_const_Oinduct,axiom,
% 3.44/1.78 ! [P: const > $o,Const: const] :
% 3.44/1.78 ( ( P @ unit )
% 3.44/1.78 => ( ( P @ f )
% 3.44/1.78 => ( ( P @ t )
% 3.44/1.78 => ( P @ Const ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_161_const_Oexhaust,axiom,
% 3.44/1.78 ! [Y: const] :
% 3.44/1.78 ( ( Y != unit )
% 3.44/1.78 => ( ( Y != f )
% 3.44/1.78 => ( Y = t ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_162_pigeonhole__infinite__rel,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,A5: set @ A,B6: set @ B,R8: A > B > $o] :
% 3.44/1.78 ( ~ ( finite_finite @ A @ A5 )
% 3.44/1.78 => ( ( finite_finite @ B @ B6 )
% 3.44/1.78 => ( ! [X6: A] :
% 3.44/1.78 ( ( member @ A @ X6 @ A5 )
% 3.44/1.78 => ? [Xa2: B] :
% 3.44/1.78 ( ( member @ B @ Xa2 @ B6 )
% 3.44/1.78 & ( R8 @ X6 @ Xa2 ) ) )
% 3.44/1.78 => ? [X6: B] :
% 3.44/1.78 ( ( member @ B @ X6 @ B6 )
% 3.44/1.78 & ~ ( finite_finite @ A
% 3.44/1.78 @ ( collect @ A
% 3.44/1.78 @ ^ [A3: A] :
% 3.44/1.78 ( ( member @ A @ A3 @ A5 )
% 3.44/1.78 & ( R8 @ A3 @ X6 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_163_not__finite__existsD,axiom,
% 3.44/1.78 ! [A: $tType,P: A > $o] :
% 3.44/1.78 ( ~ ( finite_finite @ A @ ( collect @ A @ P ) )
% 3.44/1.78 => ? [X_1: A] : ( P @ X_1 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_164_finite__has__maximal2,axiom,
% 3.44/1.78 ! [A: $tType] :
% 3.44/1.78 ( ( order @ A )
% 3.44/1.78 => ! [A5: set @ A,A2: A] :
% 3.44/1.78 ( ( finite_finite @ A @ A5 )
% 3.44/1.78 => ( ( member @ A @ A2 @ A5 )
% 3.44/1.78 => ? [X6: A] :
% 3.44/1.78 ( ( member @ A @ X6 @ A5 )
% 3.44/1.78 & ( ord_less_eq @ A @ A2 @ X6 )
% 3.44/1.78 & ! [Xa2: A] :
% 3.44/1.78 ( ( member @ A @ Xa2 @ A5 )
% 3.44/1.78 => ( ( ord_less_eq @ A @ X6 @ Xa2 )
% 3.44/1.78 => ( X6 = Xa2 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_165_finite__has__minimal2,axiom,
% 3.44/1.78 ! [A: $tType] :
% 3.44/1.78 ( ( order @ A )
% 3.44/1.78 => ! [A5: set @ A,A2: A] :
% 3.44/1.78 ( ( finite_finite @ A @ A5 )
% 3.44/1.78 => ( ( member @ A @ A2 @ A5 )
% 3.44/1.78 => ? [X6: A] :
% 3.44/1.78 ( ( member @ A @ X6 @ A5 )
% 3.44/1.78 & ( ord_less_eq @ A @ X6 @ A2 )
% 3.44/1.78 & ! [Xa2: A] :
% 3.44/1.78 ( ( member @ A @ Xa2 @ A5 )
% 3.44/1.78 => ( ( ord_less_eq @ A @ Xa2 @ X6 )
% 3.44/1.78 => ( X6 = Xa2 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_166_finite__subset,axiom,
% 3.44/1.78 ! [A: $tType,A5: set @ A,B6: set @ A] :
% 3.44/1.78 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 3.44/1.78 => ( ( finite_finite @ A @ B6 )
% 3.44/1.78 => ( finite_finite @ A @ A5 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_167_infinite__super,axiom,
% 3.44/1.78 ! [A: $tType,S6: set @ A,T2: set @ A] :
% 3.44/1.78 ( ( ord_less_eq @ ( set @ A ) @ S6 @ T2 )
% 3.44/1.78 => ( ~ ( finite_finite @ A @ S6 )
% 3.44/1.78 => ~ ( finite_finite @ A @ T2 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_168_rev__finite__subset,axiom,
% 3.44/1.78 ! [A: $tType,B6: set @ A,A5: set @ A] :
% 3.44/1.78 ( ( finite_finite @ A @ B6 )
% 3.44/1.78 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 3.44/1.78 => ( finite_finite @ A @ A5 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_169_finite__update__induct,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,F: A > B,C2: B,P: ( A > B ) > $o] :
% 3.44/1.78 ( ( finite_finite @ A
% 3.44/1.78 @ ( collect @ A
% 3.44/1.78 @ ^ [A3: A] :
% 3.44/1.78 ( ( F @ A3 )
% 3.44/1.78 != C2 ) ) )
% 3.44/1.78 => ( ( P
% 3.44/1.78 @ ^ [A3: A] : C2 )
% 3.44/1.78 => ( ! [A4: A,B4: B,F3: A > B] :
% 3.44/1.78 ( ( finite_finite @ A
% 3.44/1.78 @ ( collect @ A
% 3.44/1.78 @ ^ [C3: A] :
% 3.44/1.78 ( ( F3 @ C3 )
% 3.44/1.78 != C2 ) ) )
% 3.44/1.78 => ( ( ( F3 @ A4 )
% 3.44/1.78 = C2 )
% 3.44/1.78 => ( ( B4 != C2 )
% 3.44/1.78 => ( ( P @ F3 )
% 3.44/1.78 => ( P @ ( fun_upd @ A @ B @ F3 @ A4 @ B4 ) ) ) ) ) )
% 3.44/1.78 => ( P @ F ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_170_substitution_Orevision__step_OifFalse,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E22 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_171_substitution_OifFalse__deterministic,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( S2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E22 ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_172_substitution_Orevision__step__relaxed_OifFalse,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ E22 ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_173_reachable__imp__identifiers__available_I1_J,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( ~ ( finite_finite @ r @ ( top_top @ ( set @ r ) ) )
% 3.44/1.78 => ? [R7: r] :
% 3.44/1.78 ~ ( member @ r @ R7 @ ( rID_G @ r @ l @ v @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_174_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 3.44/1.78 ! [C: $tType,B: $tType,A: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 3.44/1.78 ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.44/1.78 => ( ( finite_finite @ B @ ( rID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ( finite_finite @ B @ ( rID_L @ A @ B @ C @ Ls ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_175_empty__map__finite_I4_J,axiom,
% 3.44/1.78 ! [J: $tType,M2: $tType,K2: $tType] :
% 3.44/1.78 ( finite_finite @ J
% 3.44/1.78 @ ( lID_G @ K2 @ J @ M2
% 3.44/1.78 @ ^ [X: K2] : ( none @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( expr @ K2 @ J @ M2 ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_176_RID_092_060_094sub_062L__finite__invariant,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ( finite_finite @ l @ ( lID_G @ r @ l @ v @ S ) )
% 3.44/1.78 => ( finite_finite @ l @ ( lID_G @ r @ l @ v @ S2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_177_reachable__imp__identifiers__finite_I2_J,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( finite_finite @ l @ ( lID_G @ r @ l @ v @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_178_finite__option__UNIV,axiom,
% 3.44/1.78 ! [A: $tType] :
% 3.44/1.78 ( ( finite_finite @ ( option @ A ) @ ( top_top @ ( set @ ( option @ A ) ) ) )
% 3.44/1.78 = ( finite_finite @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_179_finite__Collect__not,axiom,
% 3.44/1.78 ! [A: $tType,P: A > $o] :
% 3.44/1.78 ( ( finite_finite @ A @ ( collect @ A @ P ) )
% 3.44/1.78 => ( ( finite_finite @ A
% 3.44/1.78 @ ( collect @ A
% 3.44/1.78 @ ^ [X: A] :
% 3.44/1.78 ~ ( P @ X ) ) )
% 3.44/1.78 = ( finite_finite @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_180_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 3.44/1.78 ! [C: $tType,B: $tType,A: $tType,L2: B,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 3.44/1.78 ( ( member @ B @ L2 @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) )
% 3.44/1.78 => ( member @ B @ L2 @ ( lID_G @ A @ B @ C @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_181_RID_092_060_094sub_062GI_I2_J,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 3.44/1.78 ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.44/1.78 => ( ( member @ B @ R2 @ ( rID_L @ A @ B @ C @ Ls ) )
% 3.44/1.78 => ( member @ B @ R2 @ ( rID_G @ B @ A @ C @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_182_finite__state__imp__restriction__finite_I2_J,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 3.44/1.78 ( ( finite_finite @ B @ ( lID_G @ A @ B @ C @ S ) )
% 3.44/1.78 => ( finite_finite @ B @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_183_in__restricted__global__in__updated__global_I2_J,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,L2: B,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A,Ls: product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) )] :
% 3.44/1.78 ( ( member @ B @ L2 @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) )
% 3.44/1.78 => ( member @ B @ L2 @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) @ Ls ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_184_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( ~ ( finite_finite @ L @ ( top_top @ ( set @ L ) ) )
% 3.44/1.78 => ? [L3: L] :
% 3.44/1.78 ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_185_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ( finite_finite @ L @ ( lID_G @ R @ L @ V @ S ) )
% 3.44/1.78 => ( finite_finite @ L @ ( lID_G @ R @ L @ V @ S2 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_186_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R2: B] : ( ord_less_eq @ ( set @ A ) @ ( lID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) @ ( lID_G @ B @ A @ C @ S ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_187_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( finite_finite @ L @ ( lID_G @ R @ L @ V @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_188_substitution_Oempty__map__finite_I4_J,axiom,
% 3.44/1.78 ! [R: $tType,L: $tType,V: $tType,J: $tType,M2: $tType,K2: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( finite_finite @ J
% 3.44/1.78 @ ( lID_G @ K2 @ J @ M2
% 3.44/1.78 @ ^ [X: K2] : ( none @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( expr @ K2 @ J @ M2 ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_189_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.44/1.78 => ( ~ ( finite_finite @ R @ ( top_top @ ( set @ R ) ) )
% 3.44/1.78 => ? [R7: R] :
% 3.44/1.78 ~ ( member @ R @ R7 @ ( rID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_190_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,C: $tType,A: $tType,B: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ),R2: A] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( finite_finite @ B @ ( lID_G @ A @ B @ C @ S ) )
% 3.44/1.78 => ( finite_finite @ B @ ( lID_G @ A @ B @ C @ ( fun_upd @ A @ ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_191_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,C: $tType,B: $tType,A: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.44/1.78 => ( ( finite_finite @ B @ ( rID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ( finite_finite @ B @ ( rID_L @ A @ B @ C @ Ls ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_192_only__new__introduces__lids_H,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),L2: l] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ! [Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,V3: val @ r @ l @ v] :
% 3.44/1.78 ( ( S @ R2 )
% 3.44/1.78 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ref @ r @ l @ v @ ( ve @ r @ l @ v @ V3 ) ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ l @ L2 @ ( lID_G @ r @ l @ v @ S ) )
% 3.44/1.78 => ~ ( member @ l @ L2 @ ( lID_G @ r @ l @ v @ S2 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_193_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 3.44/1.78 ! [C: $tType,B: $tType,A: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 3.44/1.78 ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.44/1.78 => ( ( finite_finite @ A @ ( lID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ( finite_finite @ A @ ( lID_L @ A @ B @ C @ Ls ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_194_only__new__introduces__lids,axiom,
% 3.44/1.78 ! [R2: r,S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ! [Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,V3: val @ r @ l @ v] :
% 3.44/1.78 ( ( S @ R2 )
% 3.44/1.78 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ref @ r @ l @ v @ ( ve @ r @ l @ v @ V3 ) ) ) ) ) ) )
% 3.44/1.78 => ( ord_less_eq @ ( set @ l ) @ ( lID_G @ r @ l @ v @ S2 ) @ ( lID_G @ r @ l @ v @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_195_expr_Oinject_I4_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,Y4: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ( ref @ R @ L @ V @ X4 )
% 3.44/1.78 = ( ref @ R @ L @ V @ Y4 ) )
% 3.44/1.78 = ( X4 = Y4 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_196_reachable__imp__identifiers__available_I2_J,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.44/1.78 => ( ~ ( finite_finite @ l @ ( top_top @ ( set @ l ) ) )
% 3.44/1.78 => ? [L3: l] :
% 3.44/1.78 ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_197_LID_092_060_094sub_062GI,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R2: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),L2: A] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.44/1.78 => ( ( member @ A @ L2 @ ( lID_L @ A @ B @ C @ Ls ) )
% 3.44/1.78 => ( member @ A @ L2 @ ( lID_G @ B @ A @ C @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_198_expr_Odistinct_I41_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ref @ R @ L @ V @ X4 )
% 3.44/1.78 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_199_expr_Odistinct_I43_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ref @ R @ L @ V @ X4 )
% 3.44/1.78 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_200_expr_Odistinct_I5_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X4: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ve @ R @ L @ V @ X1 )
% 3.44/1.78 != ( ref @ R @ L @ V @ X4 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_201_expr_Odistinct_I27_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X4: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 3.44/1.78 != ( ref @ R @ L @ V @ X4 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_202_LID_092_060_094sub_062GE,axiom,
% 3.44/1.78 ! [C: $tType,B: $tType,A: $tType,L2: A,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) )] :
% 3.44/1.78 ( ( member @ A @ L2 @ ( lID_G @ B @ A @ C @ S ) )
% 3.44/1.78 => ~ ! [R7: B,Ls3: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) )] :
% 3.44/1.78 ( ( ( S @ R7 )
% 3.44/1.78 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls3 ) )
% 3.44/1.78 => ~ ( member @ A @ L2 @ ( lID_L @ A @ B @ C @ Ls3 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_203_substitution_Oonly__new__introduces__lids_H,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),L2: L] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,V3: val @ R @ L @ V] :
% 3.44/1.78 ( ( S @ R2 )
% 3.44/1.78 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ref @ R @ L @ V @ ( ve @ R @ L @ V @ V3 ) ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ L @ L2 @ ( lID_G @ R @ L @ V @ S ) )
% 3.44/1.78 => ~ ( member @ L @ L2 @ ( lID_G @ R @ L @ V @ S2 ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_204_substitution_Oonly__new__introduces__lids,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),R2: R,S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 => ( ! [Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,V3: val @ R @ L @ V] :
% 3.44/1.78 ( ( S @ R2 )
% 3.44/1.78 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ref @ R @ L @ V @ ( ve @ R @ L @ V @ V3 ) ) ) ) ) ) )
% 3.44/1.78 => ( ord_less_eq @ ( set @ L ) @ ( lID_G @ R @ L @ V @ S2 ) @ ( lID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_205_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,C: $tType,B: $tType,A: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ),R3: B,Ls: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ),R2: B] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R3 )
% 3.44/1.78 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.44/1.78 => ( ( finite_finite @ A @ ( lID_G @ B @ A @ C @ ( fun_upd @ B @ ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) @ S @ R2 @ ( none @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) ) ) ) )
% 3.44/1.78 => ( ( R2 != R3 )
% 3.44/1.78 => ( finite_finite @ A @ ( lID_L @ A @ B @ C @ Ls ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_206_domains__subsume__def,axiom,
% 3.44/1.78 ( ( domains_subsume @ l @ r @ v )
% 3.44/1.78 = ( ^ [Ls2: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) )] : ( ord_less_eq @ ( set @ l ) @ ( lID_L @ l @ r @ v @ Ls2 ) @ ( doms @ l @ r @ v @ Ls2 ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_207_revision__step_Onew,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,V2: val @ r @ l @ v,L2: l] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ref @ r @ l @ v @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ l @ L2 @ ( lID_G @ r @ l @ v @ S ) )
% 3.44/1.78 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L2 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_208_val_Oinject_I3_J,axiom,
% 3.44/1.78 ! [V: $tType,R: $tType,L: $tType,X34: L,Y3: L] :
% 3.44/1.78 ( ( ( loc @ L @ R @ V @ X34 )
% 3.44/1.78 = ( loc @ L @ R @ V @ Y3 ) )
% 3.44/1.78 = ( X34 = Y3 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_209_new__pseudodeterministic,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,V2: val @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ref @ r @ l @ v @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( ? [L4: l] :
% 3.44/1.78 ( ~ ( member @ l @ L4 @ ( lID_G @ r @ l @ v @ S ) )
% 3.44/1.78 & ( S2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L4 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_210_val_Odistinct_I15_J,axiom,
% 3.44/1.78 ! [L: $tType,V: $tType,R: $tType,X34: L,X4: R] :
% 3.44/1.78 ( ( loc @ L @ R @ V @ X34 )
% 3.44/1.78 != ( rid @ R @ L @ V @ X4 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_211_val_Odistinct_I3_J,axiom,
% 3.44/1.78 ! [R: $tType,V: $tType,L: $tType,X1: const,X34: L] :
% 3.44/1.78 ( ( cv @ R @ L @ V @ X1 )
% 3.44/1.78 != ( loc @ L @ R @ V @ X34 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_212_substitution_Odomains__subsume__def,axiom,
% 3.44/1.78 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),Ls: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( domains_subsume @ L @ R @ V @ Ls )
% 3.44/1.78 = ( ord_less_eq @ ( set @ L ) @ ( lID_L @ L @ R @ V @ Ls ) @ ( doms @ L @ R @ V @ Ls ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_213_substitution_Onew__pseudodeterministic,axiom,
% 3.44/1.78 ! [V: $tType,R: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,V2: val @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ref @ R @ L @ V @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( ? [L4: L] :
% 3.44/1.78 ( ~ ( member @ L @ L4 @ ( lID_G @ R @ L @ V @ S ) )
% 3.44/1.78 & ( S2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L4 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L4 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_214_substitution_Orevision__step_Onew,axiom,
% 3.44/1.78 ! [R: $tType,V: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,V2: val @ R @ L @ V,L2: L] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ref @ R @ L @ V @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( ~ ( member @ L @ L2 @ ( lID_G @ R @ L @ V @ S ) )
% 3.44/1.78 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L2 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_215_revision__step__relaxed_Oset,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l,V2: val @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L2 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_216_substitution_Orevision__step__relaxed_Oset,axiom,
% 3.44/1.78 ! [R: $tType,L: $tType,V: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L,V2: val @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L2 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_217_expr_Oinject_I6_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,Y61: expr @ R @ L @ V,Y62: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ( assign @ R @ L @ V @ X61 @ X62 )
% 3.44/1.78 = ( assign @ R @ L @ V @ Y61 @ Y62 ) )
% 3.44/1.78 = ( ( X61 = Y61 )
% 3.44/1.78 & ( X62 = Y62 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_218_expr_Odistinct_I39_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ref @ R @ L @ V @ X4 )
% 3.44/1.78 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_219_expr_Odistinct_I51_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 3.44/1.78 ( ( assign @ R @ L @ V @ X61 @ X62 )
% 3.44/1.78 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_220_expr_Odistinct_I53_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.44/1.78 ( ( assign @ R @ L @ V @ X61 @ X62 )
% 3.44/1.78 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_221_expr_Odistinct_I9_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ve @ R @ L @ V @ X1 )
% 3.44/1.78 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_222_expr_Odistinct_I31_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 3.44/1.78 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_223_revision__step_Oset,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l,V2: val @ r @ l @ v] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( ( member @ l @ L2 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau ) ) )
% 3.44/1.78 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L2 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_224_set__deterministic,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l,V2: val @ r @ l @ v,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( ( member @ l @ L2 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau ) ) )
% 3.44/1.78 & ( S2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau @ L2 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_225_dom__const,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType,F: A > B] :
% 3.44/1.78 ( ( dom @ A @ B
% 3.44/1.78 @ ^ [X: A] : ( some @ B @ ( F @ X ) ) )
% 3.44/1.78 = ( top_top @ ( set @ A ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_226_domI,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,M: B > ( option @ A ),A2: B,B2: A] :
% 3.44/1.78 ( ( ( M @ A2 )
% 3.44/1.78 = ( some @ A @ B2 ) )
% 3.44/1.78 => ( member @ B @ A2 @ ( dom @ B @ A @ M ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_227_domD,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,A2: A,M: A > ( option @ B )] :
% 3.44/1.78 ( ( member @ A @ A2 @ ( dom @ A @ B @ M ) )
% 3.44/1.78 => ? [B4: B] :
% 3.44/1.78 ( ( M @ A2 )
% 3.44/1.78 = ( some @ B @ B4 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_228_dom__def,axiom,
% 3.44/1.78 ! [B: $tType,A: $tType] :
% 3.44/1.78 ( ( dom @ A @ B )
% 3.44/1.78 = ( ^ [M3: A > ( option @ B )] :
% 3.44/1.78 ( collect @ A
% 3.44/1.78 @ ^ [A3: A] :
% 3.44/1.78 ( ( M3 @ A3 )
% 3.44/1.78 != ( none @ B ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_229_domIff,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,A2: A,M: A > ( option @ B )] :
% 3.44/1.78 ( ( member @ A @ A2 @ ( dom @ A @ B @ M ) )
% 3.44/1.78 = ( ( M @ A2 )
% 3.44/1.78 != ( none @ B ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_230_finite__map__freshness,axiom,
% 3.44/1.78 ! [A: $tType,B: $tType,F: A > ( option @ B )] :
% 3.44/1.78 ( ( finite_finite @ A @ ( dom @ A @ B @ F ) )
% 3.44/1.78 => ( ~ ( finite_finite @ A @ ( top_top @ ( set @ A ) ) )
% 3.44/1.78 => ? [X6: A] :
% 3.44/1.78 ( ( F @ X6 )
% 3.44/1.78 = ( none @ B ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_231_substitution_Oset__deterministic,axiom,
% 3.44/1.78 ! [R: $tType,L: $tType,V: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L,V2: val @ R @ L @ V,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( ( member @ L @ L2 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau ) ) )
% 3.44/1.78 & ( S2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L2 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_232_substitution_Orevision__step_Oset,axiom,
% 3.44/1.78 ! [R: $tType,L: $tType,V: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L,V2: val @ R @ L @ V] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.44/1.78 => ( ( member @ L @ L2 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau ) ) )
% 3.44/1.78 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau @ L2 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_233_revision__step_Oget,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( read @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( member @ l @ L2 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau ) ) )
% 3.44/1.78 => ( revision_step @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( the @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_234_revision__step__relaxed_Oget,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( read @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( the @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_235__092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r] :
% 3.44/1.78 ( ( domain398919503obally @ r @ l @ v @ S )
% 3.44/1.78 => ( ( member @ r @ R2 @ ( dom @ r @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ S ) )
% 3.44/1.78 => ( subsumes_accessible @ r @ l @ v @ R2 @ R2 @ S ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_236_subsumes__accessible__globally__def,axiom,
% 3.44/1.78 ( ( subsum380726323obally @ r @ l @ v )
% 3.44/1.78 = ( ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ! [R_12: r,R_22: r] :
% 3.44/1.78 ( ( member @ r @ R_12 @ ( dom @ r @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ S4 ) )
% 3.44/1.78 => ( ( member @ r @ R_22 @ ( dom @ r @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ S4 ) )
% 3.44/1.78 => ( subsumes_accessible @ r @ l @ v @ R_12 @ R_22 @ S4 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_237_expr_Oinject_I5_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X52: expr @ R @ L @ V,Y5: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ( read @ R @ L @ V @ X52 )
% 3.44/1.78 = ( read @ R @ L @ V @ Y5 ) )
% 3.44/1.78 = ( X52 = Y5 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_238_option_Ocollapse,axiom,
% 3.44/1.78 ! [A: $tType,Option: option @ A] :
% 3.44/1.78 ( ( Option
% 3.44/1.78 != ( none @ A ) )
% 3.44/1.78 => ( ( some @ A @ ( the @ A @ Option ) )
% 3.44/1.78 = Option ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_239_get__deterministic,axiom,
% 3.44/1.78 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ),R2: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,L2: l,S2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.44/1.78 ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( read @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L2 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( ( member @ l @ L2 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau ) ) )
% 3.44/1.78 & ( S2
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ ( plug @ r @ l @ v @ E @ ( ve @ r @ l @ v @ ( the @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_240_expr_Odistinct_I37_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X4: expr @ R @ L @ V,X52: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ref @ R @ L @ V @ X4 )
% 3.44/1.78 != ( read @ R @ L @ V @ X52 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_241_option_Oexpand,axiom,
% 3.44/1.78 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 3.44/1.78 ( ( ( Option
% 3.44/1.78 = ( none @ A ) )
% 3.44/1.78 = ( Option2
% 3.44/1.78 = ( none @ A ) ) )
% 3.44/1.78 => ( ( ( Option
% 3.44/1.78 != ( none @ A ) )
% 3.44/1.78 => ( ( Option2
% 3.44/1.78 != ( none @ A ) )
% 3.44/1.78 => ( ( the @ A @ Option )
% 3.44/1.78 = ( the @ A @ Option2 ) ) ) )
% 3.44/1.78 => ( Option = Option2 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_242_expr_Odistinct_I47_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X52: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 3.44/1.78 ( ( read @ R @ L @ V @ X52 )
% 3.44/1.78 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_243_expr_Odistinct_I49_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X52: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.44/1.78 ( ( read @ R @ L @ V @ X52 )
% 3.44/1.78 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_244_expr_Odistinct_I7_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X52: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ve @ R @ L @ V @ X1 )
% 3.44/1.78 != ( read @ R @ L @ V @ X52 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_245_expr_Odistinct_I29_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X31: expr @ R @ L @ V,X32: expr @ R @ L @ V,X33: expr @ R @ L @ V,X52: expr @ R @ L @ V] :
% 3.44/1.78 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 3.44/1.78 != ( read @ R @ L @ V @ X52 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_246_expr_Odistinct_I45_J,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,X52: expr @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 3.44/1.78 ( ( read @ R @ L @ V @ X52 )
% 3.44/1.78 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_247_option_Oexhaust__sel,axiom,
% 3.44/1.78 ! [A: $tType,Option: option @ A] :
% 3.44/1.78 ( ( Option
% 3.44/1.78 != ( none @ A ) )
% 3.44/1.78 => ( Option
% 3.44/1.78 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_248_option_Osel,axiom,
% 3.44/1.78 ! [A: $tType,X22: A] :
% 3.44/1.78 ( ( the @ A @ ( some @ A @ X22 ) )
% 3.44/1.78 = X22 ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_249_RID_092_060_094sub_062GE,axiom,
% 3.44/1.78 ! [C: $tType,A: $tType,B: $tType,R2: A,S: A > ( option @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) )] :
% 3.44/1.78 ( ( member @ A @ R2 @ ( rID_G @ A @ B @ C @ S ) )
% 3.44/1.78 => ( ~ ( member @ A @ R2 @ ( dom @ A @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) @ S ) )
% 3.44/1.78 => ~ ! [R9: A,Ls3: product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) )] :
% 3.44/1.78 ( ( ( S @ R9 )
% 3.44/1.78 = ( some @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( product_prod @ ( B > ( option @ ( val @ A @ B @ C ) ) ) @ ( expr @ A @ B @ C ) ) ) @ Ls3 ) )
% 3.44/1.78 => ~ ( member @ A @ R2 @ ( rID_L @ B @ A @ C @ Ls3 ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_250_substitution_O_092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( domain398919503obally @ R @ L @ V @ S )
% 3.44/1.78 => ( ( member @ R @ R2 @ ( dom @ R @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ S ) )
% 3.44/1.78 => ( subsumes_accessible @ R @ L @ V @ R2 @ R2 @ S ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_251_substitution_Osubsumes__accessible__globally__def,axiom,
% 3.44/1.78 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 3.44/1.78 = ( ! [R_12: R,R_22: R] :
% 3.44/1.78 ( ( member @ R @ R_12 @ ( dom @ R @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ S ) )
% 3.44/1.78 => ( ( member @ R @ R_22 @ ( dom @ R @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ S ) )
% 3.44/1.78 => ( subsumes_accessible @ R @ L @ V @ R_12 @ R_22 @ S ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_252_substitution_Orevision__step__relaxed_Oget,axiom,
% 3.44/1.78 ! [R: $tType,V: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( read @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( the @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_253_substitution_Oget__deterministic,axiom,
% 3.44/1.78 ! [R: $tType,V: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L,S2: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( read @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.44/1.78 = ( ( member @ L @ L2 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau ) ) )
% 3.44/1.78 & ( S2
% 3.44/1.78 = ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( the @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(fact_254_substitution_Orevision__step_Oget,axiom,
% 3.44/1.78 ! [R: $tType,V: $tType,L: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),S: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ),R2: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,L2: L] :
% 3.44/1.78 ( ( substitution @ R @ L @ V @ Subst )
% 3.44/1.78 => ( ( ( S @ R2 )
% 3.44/1.78 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( read @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L2 ) ) ) ) ) ) ) )
% 3.44/1.78 => ( ( member @ L @ L2 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau ) ) )
% 3.44/1.78 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) @ S @ R2 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ ( plug @ R @ L @ V @ E @ ( ve @ R @ L @ V @ ( the @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma @ Tau @ L2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.44/1.78 ! [A6: $tType,A7: $tType] :
% 3.44/1.78 ( ( order @ A7 )
% 3.44/1.78 => ( order @ ( A6 > A7 ) ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 3.44/1.78 ! [A6: $tType] : ( order @ ( set @ A6 ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 3.44/1.78 order @ $o ).
% 3.44/1.78
% 3.44/1.78 thf(help_If_3_1_T,axiom,
% 3.44/1.78 ! [P: $o] :
% 3.44/1.78 ( ( P = $true )
% 3.44/1.78 | ( P = $false ) ) ).
% 3.44/1.78
% 3.44/1.78 thf(help_If_2_1_T,axiom,
% 3.44/1.78 ! [A: $tType,X2: A,Y: A] :
% 3.44/1.78 ( ( if @ A @ $false @ X2 @ Y )
% 3.44/1.78 = Y ) ).
% 3.44/1.78
% 3.44/1.78 thf(help_If_1_1_T,axiom,
% 3.44/1.78 ! [A: $tType,X2: A,Y: A] :
% 3.44/1.78 ( ( if @ A @ $true @ X2 @ Y )
% 3.44/1.78 = X2 ) ).
% 3.44/1.78
% 3.44/1.78 thf(conj_0,conjecture,
% 3.44/1.78 ( ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r2 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ x ) ) @ r3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ r4 ) ) ) ) ) ) ) @ r4
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ sigma @ tau )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.44/1.78 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.44/1.78 @ e2 ) ) ) )
% 3.44/1.78 = ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )
% 3.44/1.78 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) @ s_1 @ r3 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ r4 ) ) ) ) ) ) ) @ r4
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ ( combine @ l @ ( val @ r @ l @ v ) @ sigma @ tau )
% 3.44/1.78 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.44/1.78 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.44/1.78 @ e2 ) ) ) )
% 3.44/1.78 @ r2
% 3.44/1.78 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ x ) ) ) ).
% 3.44/1.78 ------------------------
% 3.55/1.83 % (7472)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/183Mi)
% 3.55/1.84 % (7474)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/27Mi)
% 3.55/1.84 % (7473)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/4Mi)
% 3.55/1.84 % (7475)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/2Mi)
% 3.55/1.84 % (7477)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/275Mi)
% 3.55/1.84 % (7476)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/2Mi)
% 3.55/1.84 % (7478)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/18Mi)
% 3.55/1.84 % (7475)Instruction limit reached!
% 3.55/1.84 % (7475)------------------------------
% 3.55/1.84 % (7475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.84 % (7475)Termination reason: Unknown
% 3.55/1.84 % (7476)Instruction limit reached!
% 3.55/1.84 % (7476)------------------------------
% 3.55/1.84 % (7476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.84 % (7475)Termination phase: shuffling
% 3.55/1.84
% 3.55/1.84 % (7475)Memory used [KB]: 1407
% 3.55/1.84 % (7475)Time elapsed: 0.003 s
% 3.55/1.84 % (7475)Instructions burned: 3 (million)
% 3.55/1.84 % (7475)------------------------------
% 3.55/1.84 % (7475)------------------------------
% 3.55/1.84 % (7476)Termination reason: Unknown
% 3.55/1.84 % (7476)Termination phase: shuffling
% 3.55/1.84
% 3.55/1.84 % (7476)Memory used [KB]: 1407
% 3.55/1.84 % (7476)Time elapsed: 0.003 s
% 3.55/1.84 % (7476)Instructions burned: 3 (million)
% 3.55/1.84 % (7476)------------------------------
% 3.55/1.84 % (7476)------------------------------
% 3.55/1.84 % (7473)Instruction limit reached!
% 3.55/1.84 % (7473)------------------------------
% 3.55/1.84 % (7473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.84 % (7473)Termination reason: Unknown
% 3.55/1.84 % (7473)Termination phase: shuffling
% 3.55/1.84
% 3.55/1.84 % (7473)Memory used [KB]: 1535
% 3.55/1.84 % (7473)Time elapsed: 0.004 s
% 3.55/1.84 % (7473)Instructions burned: 5 (million)
% 3.55/1.84 % (7473)------------------------------
% 3.55/1.84 % (7473)------------------------------
% 3.55/1.85 % (7478)Instruction limit reached!
% 3.55/1.85 % (7478)------------------------------
% 3.55/1.85 % (7478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.85 % (7478)Termination reason: Unknown
% 3.55/1.85 % (7478)Termination phase: shuffling
% 3.55/1.85
% 3.55/1.85 % (7478)Memory used [KB]: 1663
% 3.55/1.85 % (7478)Time elapsed: 0.010 s
% 3.55/1.85 % (7478)Instructions burned: 18 (million)
% 3.55/1.85 % (7478)------------------------------
% 3.55/1.85 % (7478)------------------------------
% 3.55/1.85 % (7474)Instruction limit reached!
% 3.55/1.85 % (7474)------------------------------
% 3.55/1.85 % (7474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.85 % (7474)Termination reason: Unknown
% 3.55/1.85 % (7474)Termination phase: shuffling
% 3.55/1.85
% 3.55/1.85 % (7474)Memory used [KB]: 1791
% 3.55/1.85 % (7474)Time elapsed: 0.014 s
% 3.55/1.85 % (7474)Instructions burned: 27 (million)
% 3.55/1.85 % (7474)------------------------------
% 3.55/1.85 % (7474)------------------------------
% 3.55/1.86 % (7480)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/3Mi)
% 3.55/1.86 % (7482)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/15Mi)
% 3.55/1.86 % (7480)Instruction limit reached!
% 3.55/1.86 % (7480)------------------------------
% 3.55/1.86 % (7480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.86 % (7480)Termination reason: Unknown
% 3.55/1.86 % (7481)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/37Mi)
% 3.55/1.86 % (7480)Termination phase: shuffling
% 3.55/1.86
% 3.55/1.86 % (7480)Memory used [KB]: 1407
% 3.55/1.86 % (7480)Time elapsed: 0.003 s
% 3.55/1.86 % (7480)Instructions burned: 3 (million)
% 3.55/1.86 % (7480)------------------------------
% 3.55/1.86 % (7480)------------------------------
% 3.55/1.86 % (7482)Instruction limit reached!
% 3.55/1.86 % (7482)------------------------------
% 3.55/1.86 % (7482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.86 % (7482)Termination reason: Unknown
% 3.55/1.86 % (7482)Termination phase: shuffling
% 3.55/1.86
% 3.55/1.86 % (7482)Memory used [KB]: 1535
% 3.55/1.86 % (7482)Time elapsed: 0.008 s
% 3.55/1.86 % (7482)Instructions burned: 15 (million)
% 3.55/1.86 % (7482)------------------------------
% 3.55/1.86 % (7482)------------------------------
% 3.55/1.87 % (7484)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/1041Mi)
% 3.55/1.87 % (7485)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/7Mi)
% 3.55/1.88 % (7481)Instruction limit reached!
% 3.55/1.88 % (7481)------------------------------
% 3.55/1.88 % (7481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.88 % (7481)Termination reason: Unknown
% 3.55/1.88 % (7481)Termination phase: shuffling
% 3.55/1.88
% 3.55/1.88 % (7483)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/3Mi)
% 3.55/1.88 % (7481)Memory used [KB]: 2046
% 3.55/1.88 % (7481)Time elapsed: 0.020 s
% 3.55/1.88 % (7481)Instructions burned: 37 (million)
% 3.55/1.88 % (7481)------------------------------
% 3.55/1.88 % (7481)------------------------------
% 3.55/1.88 % (7485)Instruction limit reached!
% 3.55/1.88 % (7485)------------------------------
% 3.55/1.88 % (7485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.88 % (7483)Instruction limit reached!
% 3.55/1.88 % (7483)------------------------------
% 3.55/1.88 % (7483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.88 % (7483)Termination reason: Unknown
% 3.55/1.88 % (7483)Termination phase: shuffling
% 3.55/1.88
% 3.55/1.88 % (7483)Memory used [KB]: 1407
% 3.55/1.88 % (7483)Time elapsed: 0.003 s
% 3.55/1.88 % (7483)Instructions burned: 3 (million)
% 3.55/1.88 % (7483)------------------------------
% 3.55/1.88 % (7483)------------------------------
% 3.55/1.88 % (7485)Termination reason: Unknown
% 3.55/1.88 % (7485)Termination phase: shuffling
% 3.55/1.88
% 3.55/1.88 % (7485)Memory used [KB]: 1407
% 3.55/1.88 % (7485)Time elapsed: 0.005 s
% 3.55/1.88 % (7485)Instructions burned: 8 (million)
% 3.55/1.88 % (7485)------------------------------
% 3.55/1.88 % (7485)------------------------------
% 3.55/1.88 % (7486)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/16Mi)
% 3.55/1.89 % (7486)Instruction limit reached!
% 3.55/1.89 % (7486)------------------------------
% 3.55/1.89 % (7486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.89 % (7486)Termination reason: Unknown
% 3.55/1.89 % (7486)Termination phase: shuffling
% 3.55/1.89
% 3.55/1.89 % (7486)Memory used [KB]: 1535
% 3.55/1.89 % (7486)Time elapsed: 0.009 s
% 3.55/1.89 % (7486)Instructions burned: 17 (million)
% 3.55/1.89 % (7486)------------------------------
% 3.55/1.89 % (7486)------------------------------
% 3.55/1.89 % (7472)Instruction limit reached!
% 3.55/1.89 % (7472)------------------------------
% 3.55/1.89 % (7472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.89 % (7472)Termination reason: Unknown
% 3.55/1.89 % (7472)Termination phase: Property scanning
% 3.55/1.89
% 3.55/1.89 % (7472)Memory used [KB]: 3070
% 3.55/1.89 % (7472)Time elapsed: 0.057 s
% 3.55/1.89 % (7472)Instructions burned: 184 (million)
% 3.55/1.89 % (7472)------------------------------
% 3.55/1.89 % (7472)------------------------------
% 3.55/1.89 % (7488)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/3Mi)
% 3.55/1.89 % (7487)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/3Mi)
% 3.55/1.89 % (7488)Instruction limit reached!
% 3.55/1.89 % (7488)------------------------------
% 3.55/1.89 % (7488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.89 % (7488)Termination reason: Unknown
% 3.55/1.89 % (7488)Termination phase: shuffling
% 3.55/1.89
% 3.55/1.89 % (7488)Memory used [KB]: 1407
% 3.55/1.89 % (7488)Time elapsed: 0.003 s
% 3.55/1.89 % (7488)Instructions burned: 3 (million)
% 3.55/1.89 % (7488)------------------------------
% 3.55/1.89 % (7488)------------------------------
% 3.55/1.89 % (7487)Instruction limit reached!
% 3.55/1.89 % (7487)------------------------------
% 3.55/1.89 % (7487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.90 % (7487)Termination reason: Unknown
% 3.55/1.90 % (7487)Termination phase: shuffling
% 3.55/1.90
% 3.55/1.90 % (7487)Memory used [KB]: 1407
% 3.55/1.90 % (7487)Time elapsed: 0.004 s
% 3.55/1.90 % (7487)Instructions burned: 4 (million)
% 3.55/1.90 % (7487)------------------------------
% 3.55/1.90 % (7487)------------------------------
% 3.55/1.90 % (7489)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/7Mi)
% 3.55/1.90 % (7491)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/4Mi)
% 3.55/1.90 % (7491)Instruction limit reached!
% 3.55/1.90 % (7491)------------------------------
% 3.55/1.90 % (7491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.90 % (7491)Termination reason: Unknown
% 3.55/1.90 % (7491)Termination phase: shuffling
% 3.55/1.90
% 3.55/1.90 % (7491)Memory used [KB]: 1535
% 3.55/1.90 % (7491)Time elapsed: 0.003 s
% 3.55/1.90 % (7491)Instructions burned: 6 (million)
% 3.55/1.90 % (7491)------------------------------
% 3.55/1.90 % (7491)------------------------------
% 3.55/1.90 % (7489)Instruction limit reached!
% 3.55/1.90 % (7489)------------------------------
% 3.55/1.90 % (7489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.90 % (7489)Termination reason: Unknown
% 3.55/1.90 % (7489)Termination phase: shuffling
% 3.55/1.90
% 3.55/1.90 % (7489)Memory used [KB]: 1535
% 3.55/1.90 % (7489)Time elapsed: 0.006 s
% 3.55/1.90 % (7489)Instructions burned: 9 (million)
% 3.55/1.90 % (7489)------------------------------
% 3.55/1.90 % (7489)------------------------------
% 3.55/1.90 % (7490)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7240 for (2999ds/3Mi)
% 3.55/1.90 % (7490)Instruction limit reached!
% 3.55/1.90 % (7490)------------------------------
% 3.55/1.90 % (7490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.90 % (7490)Termination reason: Unknown
% 3.55/1.90 % (7490)Termination phase: shuffling
% 3.55/1.90
% 3.55/1.90 % (7490)Memory used [KB]: 1407
% 3.55/1.90 % (7490)Time elapsed: 0.003 s
% 3.55/1.90 % (7490)Instructions burned: 3 (million)
% 3.55/1.90 % (7490)------------------------------
% 3.55/1.90 % (7490)------------------------------
% 3.55/1.91 % (7494)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/710Mi)
% 3.55/1.91 % (7493)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/18Mi)
% 3.55/1.91 % (7495)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/6Mi)
% 3.55/1.91 % (7495)Instruction limit reached!
% 3.55/1.91 % (7495)------------------------------
% 3.55/1.91 % (7495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.91 % (7495)Termination reason: Unknown
% 3.55/1.91 % (7495)Termination phase: shuffling
% 3.55/1.91
% 3.55/1.91 % (7495)Memory used [KB]: 1535
% 3.55/1.91 % (7495)Time elapsed: 0.005 s
% 3.55/1.91 % (7495)Instructions burned: 7 (million)
% 3.55/1.91 % (7495)------------------------------
% 3.55/1.91 % (7495)------------------------------
% 3.55/1.92 % (7496)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/902Mi)
% 3.55/1.92 % (7493)Instruction limit reached!
% 3.55/1.92 % (7493)------------------------------
% 3.55/1.92 % (7493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.92 % (7493)Termination reason: Unknown
% 3.55/1.92 % (7493)Termination phase: shuffling
% 3.55/1.92
% 3.55/1.92 % (7493)Memory used [KB]: 1663
% 3.55/1.92 % (7493)Time elapsed: 0.010 s
% 3.55/1.92 % (7493)Instructions burned: 19 (million)
% 3.55/1.92 % (7493)------------------------------
% 3.55/1.92 % (7493)------------------------------
% 3.55/1.92 % (7498)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/21Mi)
% 3.55/1.93 % (7499)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/5Mi)
% 3.55/1.93 % (7499)Instruction limit reached!
% 3.55/1.93 % (7499)------------------------------
% 3.55/1.93 % (7499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.93 % (7499)Termination reason: Unknown
% 3.55/1.93 % (7499)Termination phase: shuffling
% 3.55/1.93
% 3.55/1.93 % (7499)Memory used [KB]: 1535
% 3.55/1.93 % (7499)Time elapsed: 0.003 s
% 3.55/1.93 % (7499)Instructions burned: 5 (million)
% 3.55/1.93 % (7499)------------------------------
% 3.55/1.93 % (7499)------------------------------
% 3.55/1.93 % (7498)Instruction limit reached!
% 3.55/1.93 % (7498)------------------------------
% 3.55/1.93 % (7498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.93 % (7498)Termination reason: Unknown
% 3.55/1.93 % (7498)Termination phase: shuffling
% 3.55/1.93
% 3.55/1.93 % (7498)Memory used [KB]: 1535
% 3.55/1.93 % (7498)Time elapsed: 0.011 s
% 3.55/1.93 % (7498)Instructions burned: 21 (million)
% 3.55/1.93 % (7498)------------------------------
% 3.55/1.93 % (7498)------------------------------
% 3.55/1.93 % (7500)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/6Mi)
% 3.55/1.94 % (7500)Instruction limit reached!
% 3.55/1.94 % (7500)------------------------------
% 3.55/1.94 % (7500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.94 % (7503)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/377Mi)
% 3.55/1.94 % (7500)Termination reason: Unknown
% 3.55/1.94 % (7500)Termination phase: shuffling
% 3.55/1.94
% 3.55/1.94 % (7500)Memory used [KB]: 1535
% 3.55/1.94 % (7500)Time elapsed: 0.005 s
% 3.55/1.94 % (7500)Instructions burned: 8 (million)
% 3.55/1.94 % (7500)------------------------------
% 3.55/1.94 % (7500)------------------------------
% 3.55/1.95 % (7504)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/779Mi)
% 3.55/1.95 % (7505)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/19Mi)
% 3.55/1.96 % (7477)Instruction limit reached!
% 3.55/1.96 % (7477)------------------------------
% 3.55/1.96 % (7477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.96 % (7477)Termination reason: Unknown
% 3.55/1.96 % (7477)Termination phase: Saturation
% 3.55/1.96
% 3.55/1.96 % (7477)Memory used [KB]: 7931
% 3.55/1.96 % (7477)Time elapsed: 0.125 s
% 3.55/1.96 % (7477)Instructions burned: 275 (million)
% 3.55/1.96 % (7477)------------------------------
% 3.55/1.96 % (7477)------------------------------
% 3.55/1.96 % (7505)Instruction limit reached!
% 3.55/1.96 % (7505)------------------------------
% 3.55/1.96 % (7505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.96 % (7505)Termination reason: Unknown
% 3.55/1.96 % (7505)Termination phase: shuffling
% 3.55/1.96
% 3.55/1.96 % (7505)Memory used [KB]: 1663
% 3.55/1.96 % (7505)Time elapsed: 0.010 s
% 3.55/1.96 % (7505)Instructions burned: 20 (million)
% 3.55/1.96 % (7505)------------------------------
% 3.55/1.96 % (7505)------------------------------
% 3.55/1.98 % (7507)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/879Mi)
% 3.55/1.98 % (7508)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/17Mi)
% 3.55/1.99 % (7508)Instruction limit reached!
% 3.55/1.99 % (7508)------------------------------
% 3.55/1.99 % (7508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/1.99 % (7508)Termination reason: Unknown
% 3.55/1.99 % (7508)Termination phase: shuffling
% 3.55/1.99
% 3.55/1.99 % (7508)Memory used [KB]: 1535
% 3.55/1.99 % (7508)Time elapsed: 0.009 s
% 3.55/1.99 % (7508)Instructions burned: 18 (million)
% 3.55/1.99 % (7508)------------------------------
% 3.55/1.99 % (7508)------------------------------
% 3.55/2.00 % (7511)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7240 for (2998ds/3Mi)
% 3.55/2.00 % (7511)Instruction limit reached!
% 3.55/2.00 % (7511)------------------------------
% 3.55/2.00 % (7511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.55/2.00 % (7511)Termination reason: Unknown
% 3.55/2.00 % (7511)Termination phase: shuffling
% 3.55/2.00
% 3.55/2.00 % (7511)Memory used [KB]: 1407
% 3.55/2.00 % (7511)Time elapsed: 0.003 s
% 3.55/2.00 % (7511)Instructions burned: 3 (million)
% 3.55/2.00 % (7511)------------------------------
% 3.55/2.00 % (7511)------------------------------
% 3.55/2.02 % (7513)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7240 for (2997ds/30Mi)
% 4.89/2.03 % (7513)Instruction limit reached!
% 4.89/2.03 % (7513)------------------------------
% 4.89/2.03 % (7513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.03 % (7513)Termination reason: Unknown
% 4.89/2.03 % (7513)Termination phase: shuffling
% 4.89/2.03
% 4.89/2.03 % (7513)Memory used [KB]: 1791
% 4.89/2.03 % (7513)Time elapsed: 0.016 s
% 4.89/2.03 % (7513)Instructions burned: 30 (million)
% 4.89/2.03 % (7513)------------------------------
% 4.89/2.03 % (7513)------------------------------
% 4.89/2.05 % (7516)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7240 for (2997ds/127Mi)
% 4.89/2.06 % (7503)Instruction limit reached!
% 4.89/2.06 % (7503)------------------------------
% 4.89/2.06 % (7503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.06 % (7503)Termination reason: Unknown
% 4.89/2.06 % (7503)Termination phase: Property scanning
% 4.89/2.06
% 4.89/2.06 % (7503)Memory used [KB]: 3709
% 4.89/2.06 % (7503)Time elapsed: 0.122 s
% 4.89/2.06 % (7503)Instructions burned: 377 (million)
% 4.89/2.06 % (7503)------------------------------
% 4.89/2.06 % (7503)------------------------------
% 4.89/2.08 % (7517)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7240 for (2997ds/100Mi)
% 4.89/2.11 % (7516)Instruction limit reached!
% 4.89/2.11 % (7516)------------------------------
% 4.89/2.11 % (7516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.11 % (7516)Termination reason: Unknown
% 4.89/2.11 % (7516)Termination phase: shuffling
% 4.89/2.11
% 4.89/2.11 % (7516)Memory used [KB]: 2558
% 4.89/2.11 % (7516)Time elapsed: 0.060 s
% 4.89/2.11 % (7516)Instructions burned: 127 (million)
% 4.89/2.11 % (7516)------------------------------
% 4.89/2.11 % (7516)------------------------------
% 4.89/2.12 % (7517)Instruction limit reached!
% 4.89/2.12 % (7517)------------------------------
% 4.89/2.12 % (7517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.12 % (7517)Termination reason: Unknown
% 4.89/2.12 % (7517)Termination phase: Property scanning
% 4.89/2.12
% 4.89/2.12 % (7517)Memory used [KB]: 2686
% 4.89/2.12 % (7517)Time elapsed: 0.042 s
% 4.89/2.12 % (7517)Instructions burned: 100 (million)
% 4.89/2.12 % (7517)------------------------------
% 4.89/2.12 % (7517)------------------------------
% 5.63/2.13 % (7522)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_7240 for (2996ds/3Mi)
% 5.63/2.13 % (7522)Instruction limit reached!
% 5.63/2.13 % (7522)------------------------------
% 5.63/2.13 % (7522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.13 % (7522)Termination reason: Unknown
% 5.63/2.13 % (7522)Termination phase: shuffling
% 5.63/2.13
% 5.63/2.13 % (7522)Memory used [KB]: 1535
% 5.63/2.13 % (7522)Time elapsed: 0.004 s
% 5.63/2.13 % (7522)Instructions burned: 5 (million)
% 5.63/2.13 % (7522)------------------------------
% 5.63/2.13 % (7522)------------------------------
% 5.63/2.13 % (7524)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_7240 for (2996ds/20Mi)
% 5.63/2.14 % (7524)Instruction limit reached!
% 5.63/2.14 % (7524)------------------------------
% 5.63/2.14 % (7524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.14 % (7524)Termination reason: Unknown
% 5.63/2.14 % (7524)Termination phase: shuffling
% 5.63/2.14
% 5.63/2.14 % (7524)Memory used [KB]: 1535
% 5.63/2.14 % (7524)Time elapsed: 0.011 s
% 5.63/2.14 % (7524)Instructions burned: 21 (million)
% 5.63/2.14 % (7524)------------------------------
% 5.63/2.14 % (7524)------------------------------
% 5.63/2.15 % (7526)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_7240 for (2996ds/86Mi)
% 5.63/2.16 % (7527)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_7240 for (2996ds/107Mi)
% 5.63/2.19 % (7526)Instruction limit reached!
% 5.63/2.19 % (7526)------------------------------
% 5.63/2.19 % (7526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.19 % (7526)Termination reason: Unknown
% 5.63/2.19 % (7526)Termination phase: shuffling
% 5.63/2.19
% 5.63/2.19 % (7526)Memory used [KB]: 2174
% 5.63/2.19 % (7526)Time elapsed: 0.028 s
% 5.63/2.19 % (7526)Instructions burned: 86 (million)
% 5.63/2.19 % (7526)------------------------------
% 5.63/2.19 % (7526)------------------------------
% 5.63/2.20 % (7494)Instruction limit reached!
% 5.63/2.20 % (7494)------------------------------
% 5.63/2.20 % (7494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.20 % (7494)Termination reason: Unknown
% 5.63/2.20 % (7494)Termination phase: Saturation
% 5.63/2.20
% 5.63/2.20 % (7494)Memory used [KB]: 9083
% 5.63/2.20 % (7494)Time elapsed: 0.290 s
% 5.63/2.20 % (7494)Instructions burned: 710 (million)
% 5.63/2.20 % (7494)------------------------------
% 5.63/2.20 % (7494)------------------------------
% 5.73/2.20 % (7532)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_7240 for (2995ds/39Mi)
% 5.73/2.21 % (7527)Instruction limit reached!
% 5.73/2.21 % (7527)------------------------------
% 5.73/2.21 % (7527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.21 % (7527)Termination reason: Unknown
% 5.73/2.21 % (7527)Termination phase: shuffling
% 5.73/2.21
% 5.73/2.21 % (7527)Memory used [KB]: 2558
% 5.73/2.21 % (7527)Time elapsed: 0.050 s
% 5.73/2.21 % (7527)Instructions burned: 107 (million)
% 5.73/2.21 % (7527)------------------------------
% 5.73/2.21 % (7527)------------------------------
% 5.73/2.21 % (7533)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_7240 for (2995ds/448Mi)
% 5.73/2.22 % (7532)Instruction limit reached!
% 5.73/2.22 % (7532)------------------------------
% 5.73/2.22 % (7532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.22 % (7532)Termination reason: Unknown
% 5.73/2.22 % (7532)Termination phase: shuffling
% 5.73/2.22
% 5.73/2.22 % (7532)Memory used [KB]: 2046
% 5.73/2.22 % (7532)Time elapsed: 0.019 s
% 5.73/2.22 % (7532)Instructions burned: 39 (million)
% 5.73/2.22 % (7532)------------------------------
% 5.73/2.22 % (7532)------------------------------
% 5.73/2.22 % (7536)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_7240 for (2995ds/46Mi)
% 5.73/2.24 % (7538)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_7240 for (2995ds/98Mi)
% 5.73/2.25 % (7536)Instruction limit reached!
% 5.73/2.25 % (7536)------------------------------
% 5.73/2.25 % (7536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.25 % (7536)Termination reason: Unknown
% 5.73/2.25 % (7536)Termination phase: shuffling
% 5.73/2.25
% 5.73/2.25 % (7536)Memory used [KB]: 1918
% 5.73/2.25 % (7536)Time elapsed: 0.023 s
% 5.73/2.25 % (7536)Instructions burned: 46 (million)
% 5.73/2.25 % (7536)------------------------------
% 5.73/2.25 % (7536)------------------------------
% 5.73/2.26 % (7541)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_7240 for (2995ds/507Mi)
% 5.73/2.28 % (7504)Instruction limit reached!
% 5.73/2.28 % (7504)------------------------------
% 5.73/2.28 % (7504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.28 % (7504)Termination reason: Unknown
% 5.73/2.28 % (7504)Termination phase: Saturation
% 5.73/2.28
% 5.73/2.28 % (7504)Memory used [KB]: 9083
% 5.73/2.28 % (7504)Time elapsed: 0.310 s
% 5.73/2.28 % (7504)Instructions burned: 780 (million)
% 5.73/2.28 % (7504)------------------------------
% 5.73/2.28 % (7504)------------------------------
% 5.73/2.28 % (7538)Instruction limit reached!
% 5.73/2.28 % (7538)------------------------------
% 5.73/2.28 % (7538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.73/2.28 % (7538)Termination reason: Unknown
% 5.73/2.28 % (7538)Termination phase: Property scanning
% 5.73/2.28
% 5.73/2.28 % (7538)Memory used [KB]: 2686
% 5.73/2.28 % (7538)Time elapsed: 0.044 s
% 5.73/2.28 % (7538)Instructions burned: 99 (million)
% 5.73/2.28 % (7538)------------------------------
% 5.73/2.28 % (7538)------------------------------
% 5.73/2.29 % (7547)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_7240 for (2995ds/149Mi)
% 5.73/2.29 % (7548)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7240 for (2995ds/39Mi)
% 6.60/2.30 % (7496)Instruction limit reached!
% 6.60/2.30 % (7496)------------------------------
% 6.60/2.30 % (7496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.30 % (7496)Termination reason: Unknown
% 6.60/2.30 % (7496)Termination phase: Saturation
% 6.60/2.30
% 6.60/2.30 % (7496)Memory used [KB]: 10362
% 6.60/2.30 % (7496)Time elapsed: 0.387 s
% 6.60/2.30 % (7496)Instructions burned: 902 (million)
% 6.60/2.30 % (7496)------------------------------
% 6.60/2.30 % (7496)------------------------------
% 6.60/2.30 % (7484)Instruction limit reached!
% 6.60/2.30 % (7484)------------------------------
% 6.60/2.30 % (7484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.30 % (7484)Termination reason: Unknown
% 6.60/2.30 % (7484)Termination phase: Saturation
% 6.60/2.30
% 6.60/2.30 % (7484)Memory used [KB]: 10106
% 6.60/2.30 % (7484)Time elapsed: 0.439 s
% 6.60/2.30 % (7484)Instructions burned: 1042 (million)
% 6.60/2.30 % (7484)------------------------------
% 6.60/2.30 % (7484)------------------------------
% 6.60/2.31 % (7548)Instruction limit reached!
% 6.60/2.31 % (7548)------------------------------
% 6.60/2.31 % (7548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.31 % (7548)Termination reason: Unknown
% 6.60/2.31 % (7548)Termination phase: shuffling
% 6.60/2.31
% 6.60/2.31 % (7548)Memory used [KB]: 1918
% 6.60/2.31 % (7548)Time elapsed: 0.019 s
% 6.60/2.31 % (7548)Instructions burned: 39 (million)
% 6.60/2.31 % (7548)------------------------------
% 6.60/2.31 % (7548)------------------------------
% 6.60/2.32 % (7549)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/6Mi)
% 6.60/2.32 % (7550)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/1087Mi)
% 6.60/2.32 % (7549)Instruction limit reached!
% 6.60/2.32 % (7549)------------------------------
% 6.60/2.32 % (7549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.32 % (7549)Termination reason: Unknown
% 6.60/2.32 % (7549)Termination phase: shuffling
% 6.60/2.32
% 6.60/2.32 % (7549)Memory used [KB]: 1535
% 6.60/2.32 % (7549)Time elapsed: 0.005 s
% 6.60/2.32 % (7549)Instructions burned: 7 (million)
% 6.60/2.32 % (7549)------------------------------
% 6.60/2.32 % (7549)------------------------------
% 6.60/2.34 % (7551)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/47Mi)
% 6.60/2.34 % (7552)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/44Mi)
% 6.60/2.34 % (7507)Instruction limit reached!
% 6.60/2.34 % (7507)------------------------------
% 6.60/2.34 % (7507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.34 % (7507)Termination reason: Unknown
% 6.60/2.34 % (7507)Termination phase: Saturation
% 6.60/2.34
% 6.60/2.34 % (7507)Memory used [KB]: 9978
% 6.60/2.34 % (7507)Time elapsed: 0.365 s
% 6.60/2.34 % (7507)Instructions burned: 880 (million)
% 6.60/2.34 % (7507)------------------------------
% 6.60/2.34 % (7507)------------------------------
% 6.60/2.36 % (7552)Instruction limit reached!
% 6.60/2.36 % (7552)------------------------------
% 6.60/2.36 % (7552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.36 % (7552)Termination reason: Unknown
% 6.60/2.36 % (7553)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/432Mi)
% 6.60/2.36 % (7552)Termination phase: shuffling
% 6.60/2.36
% 6.60/2.36 % (7552)Memory used [KB]: 2046
% 6.60/2.36 % (7552)Time elapsed: 0.021 s
% 6.60/2.36 % (7552)Instructions burned: 45 (million)
% 6.60/2.36 % (7552)------------------------------
% 6.60/2.36 % (7552)------------------------------
% 6.60/2.36 % (7547)Instruction limit reached!
% 6.60/2.36 % (7547)------------------------------
% 6.60/2.36 % (7547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.36 % (7547)Termination reason: Unknown
% 6.60/2.36 % (7547)Termination phase: shuffling
% 6.60/2.36
% 6.60/2.36 % (7547)Memory used [KB]: 2814
% 6.60/2.36 % (7547)Time elapsed: 0.067 s
% 6.60/2.36 % (7547)Instructions burned: 149 (million)
% 6.60/2.36 % (7547)------------------------------
% 6.60/2.36 % (7547)------------------------------
% 6.60/2.36 % (7533)Instruction limit reached!
% 6.60/2.36 % (7533)------------------------------
% 6.60/2.36 % (7533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.36 % (7533)Termination reason: Unknown
% 6.60/2.36 % (7533)Termination phase: Saturation
% 6.60/2.36
% 6.60/2.36 % (7533)Memory used [KB]: 7803
% 6.60/2.36 % (7533)Time elapsed: 0.138 s
% 6.60/2.36 % (7533)Instructions burned: 449 (million)
% 6.60/2.36 % (7533)------------------------------
% 6.60/2.36 % (7533)------------------------------
% 6.60/2.37 % (7558)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/31Mi)
% 6.60/2.37 % (7551)Instruction limit reached!
% 6.60/2.37 % (7551)------------------------------
% 6.60/2.37 % (7551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.37 % (7551)Termination reason: Unknown
% 6.60/2.37 % (7551)Termination phase: shuffling
% 6.60/2.37
% 6.60/2.37 % (7551)Memory used [KB]: 2046
% 6.60/2.37 % (7551)Time elapsed: 0.021 s
% 6.60/2.37 % (7551)Instructions burned: 47 (million)
% 6.60/2.37 % (7551)------------------------------
% 6.60/2.37 % (7551)------------------------------
% 6.60/2.37 % (7557)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/62Mi)
% 6.60/2.38 % (7558)Instruction limit reached!
% 6.60/2.38 % (7558)------------------------------
% 6.60/2.38 % (7558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.38 % (7558)Termination reason: Unknown
% 6.60/2.38 % (7558)Termination phase: shuffling
% 6.60/2.38
% 6.60/2.38 % (7558)Memory used [KB]: 1791
% 6.60/2.38 % (7558)Time elapsed: 0.011 s
% 6.60/2.38 % (7558)Instructions burned: 34 (million)
% 6.60/2.38 % (7558)------------------------------
% 6.60/2.38 % (7558)------------------------------
% 6.60/2.39 % (7559)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/96Mi)
% 6.60/2.39 % (7561)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/71Mi)
% 7.07/2.40 % (7560)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_7240 for (2994ds/453Mi)
% 7.07/2.40 % (7557)Instruction limit reached!
% 7.07/2.40 % (7557)------------------------------
% 7.07/2.40 % (7557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.40 % (7557)Termination reason: Unknown
% 7.07/2.40 % (7557)Termination phase: shuffling
% 7.07/2.40
% 7.07/2.40 % (7557)Memory used [KB]: 2302
% 7.07/2.40 % (7557)Time elapsed: 0.029 s
% 7.07/2.40 % (7557)Instructions burned: 64 (million)
% 7.07/2.40 % (7557)------------------------------
% 7.07/2.40 % (7557)------------------------------
% 7.07/2.42 % (7562)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7240 for (2993ds/83Mi)
% 7.07/2.43 % (7561)Instruction limit reached!
% 7.07/2.43 % (7561)------------------------------
% 7.07/2.43 % (7561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.43 % (7561)Termination reason: Unknown
% 7.07/2.43 % (7561)Termination phase: shuffling
% 7.07/2.43
% 7.07/2.43 % (7561)Memory used [KB]: 2174
% 7.07/2.43 % (7561)Time elapsed: 0.034 s
% 7.07/2.43 % (7561)Instructions burned: 72 (million)
% 7.07/2.43 % (7561)------------------------------
% 7.07/2.43 % (7561)------------------------------
% 7.07/2.43 % (7559)Instruction limit reached!
% 7.07/2.43 % (7559)------------------------------
% 7.07/2.43 % (7559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.43 % (7559)Termination reason: Unknown
% 7.07/2.43 % (7559)Termination phase: shuffling
% 7.07/2.43
% 7.07/2.43 % (7559)Memory used [KB]: 2302
% 7.07/2.43 % (7559)Time elapsed: 0.032 s
% 7.07/2.43 % (7559)Instructions burned: 97 (million)
% 7.07/2.43 % (7559)------------------------------
% 7.07/2.43 % (7559)------------------------------
% 7.07/2.44 % (7567)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7240 for (2993ds/11Mi)
% 7.07/2.44 % (7568)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_7240 for (2993ds/41Mi)
% 7.07/2.45 % (7567)Instruction limit reached!
% 7.07/2.45 % (7567)------------------------------
% 7.07/2.45 % (7567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.45 % (7567)Termination reason: Unknown
% 7.07/2.45 % (7567)Termination phase: shuffling
% 7.07/2.45
% 7.07/2.45 % (7567)Memory used [KB]: 1663
% 7.07/2.45 % (7567)Time elapsed: 0.007 s
% 7.07/2.45 % (7567)Instructions burned: 12 (million)
% 7.07/2.45 % (7567)------------------------------
% 7.07/2.45 % (7567)------------------------------
% 7.07/2.45 % (7562)Instruction limit reached!
% 7.07/2.45 % (7562)------------------------------
% 7.07/2.45 % (7562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.45 % (7562)Termination reason: Unknown
% 7.07/2.45 % (7562)Termination phase: shuffling
% 7.07/2.45
% 7.07/2.45 % (7562)Memory used [KB]: 2430
% 7.07/2.45 % (7562)Time elapsed: 0.027 s
% 7.07/2.45 % (7562)Instructions burned: 85 (million)
% 7.07/2.45 % (7562)------------------------------
% 7.07/2.45 % (7562)------------------------------
% 7.07/2.46 % (7569)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7240 for (2993ds/6Mi)
% 7.07/2.46 % (7569)Instruction limit reached!
% 7.07/2.46 % (7569)------------------------------
% 7.07/2.46 % (7569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.46 % (7569)Termination reason: Unknown
% 7.07/2.46 % (7569)Termination phase: shuffling
% 7.07/2.46
% 7.07/2.46 % (7569)Memory used [KB]: 1535
% 7.07/2.46 % (7569)Time elapsed: 0.003 s
% 7.07/2.46 % (7569)Instructions burned: 7 (million)
% 7.07/2.46 % (7569)------------------------------
% 7.07/2.46 % (7569)------------------------------
% 7.07/2.46 % (7568)Instruction limit reached!
% 7.07/2.46 % (7568)------------------------------
% 7.07/2.46 % (7568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.46 % (7568)Termination reason: Unknown
% 7.07/2.46 % (7568)Termination phase: shuffling
% 7.07/2.46
% 7.07/2.46 % (7568)Memory used [KB]: 2046
% 7.07/2.46 % (7568)Time elapsed: 0.020 s
% 7.07/2.46 % (7568)Instructions burned: 42 (million)
% 7.07/2.46 % (7568)------------------------------
% 7.07/2.46 % (7568)------------------------------
% 7.07/2.47 % (7570)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_7240 for (2993ds/150Mi)
% 7.07/2.47 % (7571)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_7240 for (2993ds/343Mi)
% 7.07/2.49 % (7541)Instruction limit reached!
% 7.07/2.49 % (7541)------------------------------
% 7.07/2.49 % (7541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.49 % (7541)Termination reason: Unknown
% 7.07/2.49 % (7541)Termination phase: Saturation
% 7.07/2.49
% 7.07/2.49 % (7541)Memory used [KB]: 5117
% 7.07/2.49 % (7541)Time elapsed: 0.224 s
% 7.07/2.49 % (7541)Instructions burned: 508 (million)
% 7.07/2.49 % (7541)------------------------------
% 7.07/2.49 % (7541)------------------------------
% 7.07/2.49 % (7572)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_7240 for (2993ds/109Mi)
% 7.54/2.51 % (7574)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_7240 for (2993ds/253Mi)
% 7.54/2.54 % (7570)Instruction limit reached!
% 7.54/2.54 % (7570)------------------------------
% 7.54/2.54 % (7570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.54 % (7570)Termination reason: Unknown
% 7.54/2.54 % (7570)Termination phase: shuffling
% 7.54/2.54
% 7.54/2.54 % (7570)Memory used [KB]: 2942
% 7.54/2.54 % (7570)Time elapsed: 0.070 s
% 7.54/2.54 % (7570)Instructions burned: 151 (million)
% 7.54/2.54 % (7570)------------------------------
% 7.54/2.54 % (7570)------------------------------
% 7.54/2.54 % (7572)Instruction limit reached!
% 7.54/2.54 % (7572)------------------------------
% 7.54/2.54 % (7572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.54 % (7572)Termination reason: Unknown
% 7.54/2.54 % (7572)Termination phase: shuffling
% 7.54/2.54
% 7.54/2.54 % (7572)Memory used [KB]: 2430
% 7.54/2.54 % (7572)Time elapsed: 0.051 s
% 7.54/2.54 % (7572)Instructions burned: 109 (million)
% 7.54/2.54 % (7572)------------------------------
% 7.54/2.54 % (7572)------------------------------
% 7.54/2.54 % (7553)Instruction limit reached!
% 7.54/2.54 % (7553)------------------------------
% 7.54/2.54 % (7553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.54 % (7553)Termination reason: Unknown
% 7.54/2.54 % (7553)Termination phase: Saturation
% 7.54/2.54
% 7.54/2.54 % (7553)Memory used [KB]: 3454
% 7.54/2.54 % (7553)Time elapsed: 0.187 s
% 7.54/2.54 % (7553)Instructions burned: 433 (million)
% 7.54/2.54 % (7553)------------------------------
% 7.54/2.54 % (7553)------------------------------
% 7.54/2.55 % (7577)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_7240 for (2992ds/614Mi)
% 7.54/2.56 % (7576)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_7240 for (2992ds/140Mi)
% 7.54/2.57 % (7579)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_7240 for (2992ds/202Mi)
% 7.54/2.57 % (7560)Instruction limit reached!
% 7.54/2.57 % (7560)------------------------------
% 7.54/2.57 % (7560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.57 % (7560)Termination reason: Unknown
% 7.54/2.57 % (7560)Termination phase: Saturation
% 7.54/2.57
% 7.54/2.57 % (7560)Memory used [KB]: 7803
% 7.54/2.57 % (7560)Time elapsed: 0.176 s
% 7.54/2.57 % (7560)Instructions burned: 456 (million)
% 7.54/2.57 % (7560)------------------------------
% 7.54/2.57 % (7560)------------------------------
% 7.54/2.58 % (7581)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_7240 for (2992ds/339Mi)
% 8.07/2.61 % (7571)Instruction limit reached!
% 8.07/2.61 % (7571)------------------------------
% 8.07/2.61 % (7571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.61 % (7571)Termination reason: Unknown
% 8.07/2.61 % (7571)Termination phase: Equality resolution with deletion
% 8.07/2.61
% 8.07/2.61 % (7571)Memory used [KB]: 3454
% 8.07/2.61 % (7571)Time elapsed: 0.129 s
% 8.07/2.61 % (7571)Instructions burned: 345 (million)
% 8.07/2.61 % (7571)------------------------------
% 8.07/2.61 % (7571)------------------------------
% 8.07/2.62 % (7576)Instruction limit reached!
% 8.07/2.62 % (7576)------------------------------
% 8.07/2.62 % (7576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.62 % (7576)Termination reason: Unknown
% 8.07/2.62 % (7576)Termination phase: shuffling
% 8.07/2.62
% 8.07/2.62 % (7576)Memory used [KB]: 2814
% 8.07/2.62 % (7576)Time elapsed: 0.063 s
% 8.07/2.62 % (7576)Instructions burned: 140 (million)
% 8.07/2.62 % (7576)------------------------------
% 8.07/2.62 % (7576)------------------------------
% 8.07/2.62 % (7574)Instruction limit reached!
% 8.07/2.62 % (7574)------------------------------
% 8.07/2.62 % (7574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.62 % (7574)Termination reason: Unknown
% 8.07/2.62 % (7574)Termination phase: Property scanning
% 8.07/2.62
% 8.07/2.62 % (7574)Memory used [KB]: 3326
% 8.07/2.62 % (7574)Time elapsed: 0.100 s
% 8.07/2.62 % (7574)Instructions burned: 253 (million)
% 8.07/2.62 % (7574)------------------------------
% 8.07/2.62 % (7574)------------------------------
% 8.07/2.63 % (7587)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_7240 for (2991ds/283Mi)
% 8.07/2.63 % (7588)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_7240 for (2991ds/134Mi)
% 8.07/2.64 % (7590)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_7240 for (2991ds/298Mi)
% 8.07/2.67 % (7579)Instruction limit reached!
% 8.07/2.67 % (7579)------------------------------
% 8.07/2.67 % (7579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.67 % (7579)Termination reason: Unknown
% 8.07/2.67 % (7579)Termination phase: Property scanning
% 8.07/2.67
% 8.07/2.67 % (7579)Memory used [KB]: 3198
% 8.07/2.67 % (7579)Time elapsed: 0.091 s
% 8.07/2.67 % (7579)Instructions burned: 202 (million)
% 8.07/2.67 % (7579)------------------------------
% 8.07/2.67 % (7579)------------------------------
% 8.07/2.69 % (7593)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_7240 for (2991ds/192Mi)
% 8.07/2.69 % (7588)Instruction limit reached!
% 8.07/2.69 % (7588)------------------------------
% 8.07/2.69 % (7588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.69 % (7588)Termination reason: Unknown
% 8.07/2.69 % (7588)Termination phase: shuffling
% 8.07/2.69
% 8.07/2.69 % (7588)Memory used [KB]: 2686
% 8.07/2.69 % (7588)Time elapsed: 0.062 s
% 8.07/2.69 % (7588)Instructions burned: 134 (million)
% 8.07/2.69 % (7588)------------------------------
% 8.07/2.69 % (7588)------------------------------
% 8.57/2.72 % (7594)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_7240 for (2990ds/258Mi)
% 8.57/2.73 % (7581)Instruction limit reached!
% 8.57/2.73 % (7581)------------------------------
% 8.57/2.73 % (7581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.73 % (7581)Termination reason: Unknown
% 8.57/2.73 % (7581)Termination phase: Function definition elimination
% 8.57/2.73
% 8.57/2.73 % (7581)Memory used [KB]: 3582
% 8.57/2.73 % (7581)Time elapsed: 0.146 s
% 8.57/2.73 % (7581)Instructions burned: 339 (million)
% 8.57/2.73 % (7581)------------------------------
% 8.57/2.73 % (7581)------------------------------
% 8.57/2.74 % (7590)Instruction limit reached!
% 8.57/2.74 % (7590)------------------------------
% 8.57/2.74 % (7590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.74 % (7590)Termination reason: Unknown
% 8.57/2.74 % (7590)Termination phase: Function definition elimination
% 8.57/2.74
% 8.57/2.74 % (7590)Memory used [KB]: 3198
% 8.57/2.74 % (7590)Time elapsed: 0.104 s
% 8.57/2.74 % (7590)Instructions burned: 298 (million)
% 8.57/2.74 % (7590)------------------------------
% 8.57/2.74 % (7590)------------------------------
% 8.57/2.74 % (7600)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_7240 for (2990ds/90Mi)
% 8.57/2.75 % (7587)Instruction limit reached!
% 8.57/2.75 % (7587)------------------------------
% 8.57/2.75 % (7587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.75 % (7587)Termination reason: Unknown
% 8.57/2.75 % (7587)Termination phase: Property scanning
% 8.57/2.75
% 8.57/2.75 % (7587)Memory used [KB]: 3198
% 8.57/2.75 % (7587)Time elapsed: 0.122 s
% 8.57/2.75 % (7587)Instructions burned: 284 (million)
% 8.57/2.75 % (7587)------------------------------
% 8.57/2.75 % (7587)------------------------------
% 8.57/2.76 % (7601)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_7240 for (2990ds/231Mi)
% 8.57/2.77 % (7602)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_7240 for (2990ds/458Mi)
% 8.57/2.77 % (7593)Instruction limit reached!
% 8.57/2.77 % (7593)------------------------------
% 8.57/2.77 % (7593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.77 % (7593)Termination reason: Unknown
% 8.57/2.77 % (7593)Termination phase: Property scanning
% 8.57/2.77
% 8.57/2.77 % (7593)Memory used [KB]: 3070
% 8.57/2.77 % (7593)Time elapsed: 0.083 s
% 8.57/2.77 % (7593)Instructions burned: 193 (million)
% 8.57/2.77 % (7593)------------------------------
% 8.57/2.77 % (7593)------------------------------
% 8.57/2.79 % (7603)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_7240 for (2990ds/31Mi)
% 8.57/2.79 % (7600)Instruction limit reached!
% 8.57/2.79 % (7600)------------------------------
% 8.57/2.79 % (7600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.79 % (7600)Termination reason: Unknown
% 8.57/2.79 % (7600)Termination phase: shuffling
% 8.57/2.79
% 8.57/2.79 % (7600)Memory used [KB]: 2430
% 8.57/2.79 % (7600)Time elapsed: 0.043 s
% 8.57/2.79 % (7600)Instructions burned: 91 (million)
% 8.57/2.79 % (7600)------------------------------
% 8.57/2.79 % (7600)------------------------------
% 8.57/2.79 % (7550)Instruction limit reached!
% 8.57/2.79 % (7550)------------------------------
% 8.57/2.79 % (7550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.79 % (7550)Termination reason: Unknown
% 8.57/2.79 % (7550)Termination phase: Saturation
% 8.57/2.79
% 8.57/2.79 % (7550)Memory used [KB]: 8955
% 8.57/2.79 % (7550)Time elapsed: 0.480 s
% 8.57/2.79 % (7550)Instructions burned: 1087 (million)
% 8.57/2.79 % (7550)------------------------------
% 8.57/2.79 % (7550)------------------------------
% 8.57/2.79 % (7577)Instruction limit reached!
% 8.57/2.79 % (7577)------------------------------
% 8.57/2.79 % (7577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.79 % (7577)Termination reason: Unknown
% 8.57/2.79 % (7577)Termination phase: Saturation
% 8.57/2.79
% 8.57/2.79 % (7577)Memory used [KB]: 9722
% 8.57/2.79 % (7577)Time elapsed: 0.260 s
% 8.57/2.79 % (7577)Instructions burned: 615 (million)
% 8.57/2.79 % (7577)------------------------------
% 8.57/2.79 % (7577)------------------------------
% 8.57/2.79 % (7594)Instruction limit reached!
% 8.57/2.79 % (7594)------------------------------
% 8.57/2.79 % (7594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.79 % (7594)Termination reason: Unknown
% 8.57/2.79 % (7594)Termination phase: Preprocessing 3
% 8.57/2.79
% 8.57/2.79 % (7594)Memory used [KB]: 3326
% 8.57/2.79 % (7594)Time elapsed: 0.079 s
% 8.57/2.79 % (7594)Instructions burned: 258 (million)
% 8.57/2.79 % (7594)------------------------------
% 8.57/2.79 % (7594)------------------------------
% 9.93/2.80 % (7603)Instruction limit reached!
% 9.93/2.80 % (7603)------------------------------
% 9.93/2.80 % (7603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.80 % (7603)Termination reason: Unknown
% 9.93/2.80 % (7603)Termination phase: shuffling
% 9.93/2.80
% 9.93/2.80 % (7603)Memory used [KB]: 1791
% 9.93/2.80 % (7603)Time elapsed: 0.016 s
% 9.93/2.80 % (7603)Instructions burned: 32 (million)
% 9.93/2.80 % (7603)------------------------------
% 9.93/2.80 % (7603)------------------------------
% 9.93/2.80 % (7605)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_7240 for (2989ds/297Mi)
% 9.93/2.80 % (7607)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_7240 for (2989ds/987Mi)
% 9.93/2.81 % (7608)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_7240 for (2989ds/182Mi)
% 9.93/2.81 % (7609)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_7240 for (2989ds/182Mi)
% 9.93/2.82 % (7610)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_7240 for (2989ds/154Mi)
% 9.93/2.86 % (7601)Instruction limit reached!
% 9.93/2.86 % (7601)------------------------------
% 9.93/2.86 % (7601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.86 % (7601)Termination reason: Unknown
% 9.93/2.86 % (7601)Termination phase: Preprocessing 3
% 9.93/2.86
% 9.93/2.86 % (7601)Memory used [KB]: 3070
% 9.93/2.86 % (7601)Time elapsed: 0.101 s
% 9.93/2.86 % (7601)Instructions burned: 232 (million)
% 9.93/2.86 % (7601)------------------------------
% 9.93/2.86 % (7601)------------------------------
% 9.93/2.87 % (7615)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_7240 for (2989ds/79Mi)
% 9.93/2.88 % (7609)Instruction limit reached!
% 9.93/2.88 % (7609)------------------------------
% 9.93/2.88 % (7609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.88 % (7609)Termination reason: Unknown
% 9.93/2.88 % (7609)Termination phase: Property scanning
% 9.93/2.88
% 9.93/2.88 % (7609)Memory used [KB]: 3198
% 9.93/2.88 % (7609)Time elapsed: 0.074 s
% 9.93/2.88 % (7609)Instructions burned: 184 (million)
% 9.93/2.88 % (7609)------------------------------
% 9.93/2.88 % (7609)------------------------------
% 9.93/2.89 % (7610)Instruction limit reached!
% 9.93/2.89 % (7610)------------------------------
% 9.93/2.89 % (7610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.89 % (7610)Termination reason: Unknown
% 9.93/2.89 % (7610)Termination phase: Preprocessing 1
% 9.93/2.89
% 9.93/2.89 % (7610)Memory used [KB]: 2686
% 9.93/2.89 % (7610)Time elapsed: 0.069 s
% 9.93/2.89 % (7610)Instructions burned: 155 (million)
% 9.93/2.89 % (7610)------------------------------
% 9.93/2.89 % (7610)------------------------------
% 9.93/2.89 % (7608)Instruction limit reached!
% 9.93/2.89 % (7608)------------------------------
% 9.93/2.89 % (7608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.89 % (7608)Termination reason: Unknown
% 9.93/2.89 % (7608)Termination phase: Property scanning
% 9.93/2.89
% 9.93/2.89 % (7608)Memory used [KB]: 3070
% 9.93/2.89 % (7608)Time elapsed: 0.084 s
% 9.93/2.89 % (7608)Instructions burned: 183 (million)
% 9.93/2.89 % (7608)------------------------------
% 9.93/2.89 % (7608)------------------------------
% 9.93/2.89 % (7617)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_7240 for (2989ds/216Mi)
% 9.93/2.90 % (7615)Instruction limit reached!
% 9.93/2.90 % (7615)------------------------------
% 9.93/2.90 % (7615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.90 % (7615)Termination reason: Unknown
% 9.93/2.90 % (7615)Termination phase: shuffling
% 9.93/2.90
% 9.93/2.90 % (7615)Memory used [KB]: 2174
% 9.93/2.90 % (7615)Time elapsed: 0.029 s
% 9.93/2.90 % (7615)Instructions burned: 80 (million)
% 9.93/2.90 % (7615)------------------------------
% 9.93/2.90 % (7615)------------------------------
% 10.39/2.90 % (7605)Instruction limit reached!
% 10.39/2.90 % (7605)------------------------------
% 10.39/2.90 % (7605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.90 % (7605)Termination reason: Unknown
% 10.39/2.90 % (7605)Termination phase: Saturation
% 10.39/2.90
% 10.39/2.90 % (7605)Memory used [KB]: 7419
% 10.39/2.90 % (7605)Time elapsed: 0.105 s
% 10.39/2.90 % (7605)Instructions burned: 298 (million)
% 10.39/2.90 % (7605)------------------------------
% 10.39/2.90 % (7605)------------------------------
% 10.39/2.91 % (7619)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_7240 for (2988ds/922Mi)
% 10.39/2.91 % (7618)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_7240 for (2989ds/114Mi)
% 10.39/2.92 % (7620)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_7240 for (2988ds/182Mi)
% 10.39/2.92 % (7621)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_7240 for (2988ds/164Mi)
% 10.39/2.96 % (7618)Instruction limit reached!
% 10.39/2.96 % (7618)------------------------------
% 10.39/2.96 % (7618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.96 % (7618)Termination reason: Unknown
% 10.39/2.96 % (7618)Termination phase: shuffling
% 10.39/2.96
% 10.39/2.96 % (7618)Memory used [KB]: 2558
% 10.39/2.96 % (7618)Time elapsed: 0.054 s
% 10.39/2.96 % (7618)Instructions burned: 115 (million)
% 10.39/2.96 % (7618)------------------------------
% 10.39/2.96 % (7618)------------------------------
% 10.39/2.96 % (7602)Instruction limit reached!
% 10.39/2.96 % (7602)------------------------------
% 10.39/2.96 % (7602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.96 % (7602)Termination reason: Unknown
% 10.39/2.96 % (7602)Termination phase: Saturation
% 10.39/2.96
% 10.39/2.96 % (7602)Memory used [KB]: 8187
% 10.39/2.96 % (7602)Time elapsed: 0.196 s
% 10.39/2.96 % (7602)Instructions burned: 458 (million)
% 10.39/2.96 % (7602)------------------------------
% 10.39/2.96 % (7602)------------------------------
% 10.39/2.96 % (7617)Instruction limit reached!
% 10.39/2.96 % (7617)------------------------------
% 10.39/2.96 % (7617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.96 % (7617)Termination reason: Unknown
% 10.39/2.96 % (7617)Termination phase: SInE selection
% 10.39/2.96
% 10.39/2.96 % (7617)Memory used [KB]: 2686
% 10.39/2.96 % (7617)Time elapsed: 0.069 s
% 10.39/2.96 % (7617)Instructions burned: 216 (million)
% 10.39/2.96 % (7617)------------------------------
% 10.39/2.96 % (7617)------------------------------
% 10.39/2.97 % (7620)Instruction limit reached!
% 10.39/2.97 % (7620)------------------------------
% 10.39/2.97 % (7620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.97 % (7620)Termination reason: Unknown
% 10.39/2.97 % (7620)Termination phase: Preprocessing 1
% 10.39/2.97
% 10.39/2.97 % (7620)Memory used [KB]: 2942
% 10.39/2.97 % (7620)Time elapsed: 0.049 s
% 10.39/2.97 % (7620)Instructions burned: 183 (million)
% 10.39/2.97 % (7620)------------------------------
% 10.39/2.97 % (7620)------------------------------
% 10.39/2.98 % (7625)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_7240 for (2988ds/50Mi)
% 10.39/2.98 % (7626)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_7240 for (2988ds/368Mi)
% 10.39/2.98 % (7627)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_7240 for (2988ds/1021Mi)
% 10.39/2.98 % (7628)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_7240 for (2988ds/267Mi)
% 10.39/2.99 % (7625)Instruction limit reached!
% 10.39/2.99 % (7625)------------------------------
% 10.39/2.99 % (7625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.99 % (7625)Termination reason: Unknown
% 10.39/2.99 % (7625)Termination phase: shuffling
% 10.39/2.99
% 10.39/2.99 % (7625)Memory used [KB]: 2174
% 10.39/2.99 % (7625)Time elapsed: 0.015 s
% 10.39/2.99 % (7625)Instructions burned: 52 (million)
% 10.39/2.99 % (7625)------------------------------
% 10.39/2.99 % (7625)------------------------------
% 10.39/2.99 % (7621)Instruction limit reached!
% 10.39/2.99 % (7621)------------------------------
% 10.39/2.99 % (7621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.99 % (7621)Termination reason: Unknown
% 10.39/2.99 % (7621)Termination phase: SInE selection
% 10.39/2.99
% 10.39/2.99 % (7621)Memory used [KB]: 2686
% 10.39/2.99 % (7621)Time elapsed: 0.072 s
% 10.39/2.99 % (7621)Instructions burned: 166 (million)
% 10.39/2.99 % (7621)------------------------------
% 10.39/2.99 % (7621)------------------------------
% 10.39/3.00 % (7630)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_7240 for (2988ds/204Mi)
% 10.39/3.01 % (7631)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_7240 for (2987ds/26Mi)
% 10.39/3.02 % (7631)Instruction limit reached!
% 10.39/3.02 % (7631)------------------------------
% 10.39/3.02 % (7631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/3.02 % (7631)Termination reason: Unknown
% 10.39/3.02 % (7631)Termination phase: shuffling
% 10.39/3.02
% 10.39/3.02 % (7631)Memory used [KB]: 1918
% 10.39/3.02 % (7631)Time elapsed: 0.013 s
% 10.39/3.02 % (7631)Instructions burned: 26 (million)
% 10.39/3.02 % (7631)------------------------------
% 10.39/3.02 % (7631)------------------------------
% 11.58/3.04 % (7632)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_7240 for (2987ds/53Mi)
% 11.58/3.06 % (7630)Instruction limit reached!
% 11.58/3.06 % (7630)------------------------------
% 11.58/3.06 % (7630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.58/3.06 % (7630)Termination reason: Unknown
% 11.58/3.06 % (7630)Termination phase: SInE selection
% 11.58/3.06
% 11.58/3.06 % (7630)Memory used [KB]: 3070
% 11.58/3.06 % (7630)Time elapsed: 0.061 s
% 11.58/3.06 % (7630)Instructions burned: 204 (million)
% 11.58/3.06 % (7630)------------------------------
% 11.58/3.06 % (7630)------------------------------
% 11.58/3.06 % (7632)Instruction limit reached!
% 11.58/3.06 % (7632)------------------------------
% 11.58/3.06 % (7632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.58/3.06 % (7632)Termination reason: Unknown
% 11.58/3.06 % (7632)Termination phase: shuffling
% 11.58/3.06
% 11.58/3.06 % (7632)Memory used [KB]: 2174
% 11.58/3.06 % (7632)Time elapsed: 0.026 s
% 11.58/3.06 % (7632)Instructions burned: 54 (million)
% 11.58/3.06 % (7632)------------------------------
% 11.58/3.06 % (7632)------------------------------
% 11.58/3.07 % (7633)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_7240 for (2987ds/4436Mi)
% 11.58/3.08 % (7634)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_7240 for (2987ds/1539Mi)
% 11.58/3.09 % (7628)Instruction limit reached!
% 11.58/3.09 % (7628)------------------------------
% 11.58/3.09 % (7628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.58/3.09 % (7628)Termination reason: Unknown
% 11.58/3.09 % (7628)Termination phase: Property scanning
% 11.58/3.09
% 11.58/3.09 % (7628)Memory used [KB]: 3198
% 11.58/3.09 % (7628)Time elapsed: 0.114 s
% 11.58/3.09 % (7628)Instructions burned: 267 (million)
% 11.58/3.09 % (7628)------------------------------
% 11.58/3.09 % (7628)------------------------------
% 11.58/3.11 % (7635)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_7240 for (2986ds/408Mi)
% 11.58/3.12 % (7626)Instruction limit reached!
% 11.58/3.12 % (7626)------------------------------
% 11.58/3.12 % (7626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.58/3.12 % (7626)Termination reason: Unknown
% 11.58/3.12 % (7626)Termination phase: Property scanning
% 11.58/3.12
% 11.58/3.12 % (7626)Memory used [KB]: 3582
% 11.58/3.12 % (7626)Time elapsed: 0.148 s
% 11.58/3.12 % (7626)Instructions burned: 369 (million)
% 11.58/3.12 % (7626)------------------------------
% 11.58/3.12 % (7626)------------------------------
% 12.19/3.13 % (7638)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_7240 for (2986ds/5205Mi)
% 12.40/3.25 % (7607)Instruction limit reached!
% 12.40/3.25 % (7607)------------------------------
% 12.40/3.25 % (7607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.40/3.25 % (7607)Termination reason: Unknown
% 12.40/3.25 % (7607)Termination phase: Saturation
% 12.40/3.25
% 12.40/3.25 % (7607)Memory used [KB]: 9978
% 12.40/3.25 % (7607)Time elapsed: 0.450 s
% 12.40/3.25 % (7607)Instructions burned: 989 (million)
% 12.40/3.25 % (7607)------------------------------
% 12.40/3.25 % (7607)------------------------------
% 12.40/3.27 % (7641)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_7240 for (2985ds/1913Mi)
% 12.40/3.29 % (7635)Instruction limit reached!
% 12.40/3.29 % (7635)------------------------------
% 12.40/3.29 % (7635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.40/3.29 % (7635)Termination reason: Unknown
% 12.40/3.29 % (7635)Termination phase: Saturation
% 12.40/3.29
% 12.40/3.29 % (7635)Memory used [KB]: 4349
% 12.40/3.29 % (7635)Time elapsed: 0.179 s
% 12.40/3.29 % (7635)Instructions burned: 409 (million)
% 12.40/3.29 % (7635)------------------------------
% 12.40/3.29 % (7635)------------------------------
% 12.83/3.31 % (7642)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_7240 for (2985ds/4350Mi)
% 12.83/3.33 % (7619)Instruction limit reached!
% 12.83/3.33 % (7619)------------------------------
% 12.83/3.33 % (7619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.83/3.33 % (7619)Termination reason: Unknown
% 12.83/3.33 % (7619)Termination phase: Saturation
% 12.83/3.33
% 12.83/3.33 % (7619)Memory used [KB]: 8827
% 12.83/3.33 % (7619)Time elapsed: 0.424 s
% 12.83/3.33 % (7619)Instructions burned: 922 (million)
% 12.83/3.33 % (7619)------------------------------
% 12.83/3.33 % (7619)------------------------------
% 12.83/3.35 % (7645)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_7240 for (2984ds/68Mi)
% 12.83/3.38 % (7645)Instruction limit reached!
% 12.83/3.38 % (7645)------------------------------
% 12.83/3.38 % (7645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.83/3.38 % (7645)Termination reason: Unknown
% 12.83/3.38 % (7645)Termination phase: shuffling
% 12.83/3.38
% 12.83/3.38 % (7645)Memory used [KB]: 2174
% 12.83/3.38 % (7645)Time elapsed: 0.023 s
% 12.83/3.38 % (7645)Instructions burned: 71 (million)
% 12.83/3.38 % (7645)------------------------------
% 12.83/3.38 % (7645)------------------------------
% 12.83/3.39 % (7646)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_7240 for (2984ds/358Mi)
% 13.02/3.45 % (7627)Instruction limit reached!
% 13.02/3.45 % (7627)------------------------------
% 13.02/3.45 % (7627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.02/3.45 % (7627)Termination reason: Unknown
% 13.02/3.45 % (7627)Termination phase: Saturation
% 13.02/3.45
% 13.02/3.45 % (7627)Memory used [KB]: 9850
% 13.02/3.45 % (7627)Time elapsed: 0.470 s
% 13.02/3.45 % (7627)Instructions burned: 1021 (million)
% 13.02/3.45 % (7627)------------------------------
% 13.02/3.45 % (7627)------------------------------
% 13.02/3.47 % (7648)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_7240 for (2983ds/31Mi)
% 13.02/3.49 % (7648)Instruction limit reached!
% 13.02/3.49 % (7648)------------------------------
% 13.02/3.49 % (7648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.02/3.49 % (7648)Termination reason: Unknown
% 13.02/3.49 % (7648)Termination phase: shuffling
% 13.02/3.49
% 13.02/3.49 % (7648)Memory used [KB]: 1791
% 13.02/3.49 % (7648)Time elapsed: 0.012 s
% 13.02/3.49 % (7648)Instructions burned: 32 (million)
% 13.02/3.49 % (7648)------------------------------
% 13.02/3.49 % (7648)------------------------------
% 13.02/3.50 % (7646)Instruction limit reached!
% 13.02/3.50 % (7646)------------------------------
% 13.02/3.50 % (7646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.02/3.50 % (7646)Termination reason: Unknown
% 13.02/3.50 % (7646)Termination phase: Property scanning
% 13.09/3.50
% 13.09/3.50 % (7646)Memory used [KB]: 3454
% 13.09/3.50 % (7646)Time elapsed: 0.112 s
% 13.09/3.50 % (7646)Instructions burned: 358 (million)
% 13.09/3.50 % (7646)------------------------------
% 13.09/3.50 % (7646)------------------------------
% 13.09/3.51 % (7649)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_7240 for (2983ds/279Mi)
% 13.09/3.51 % (7650)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_7240 for (2983ds/258Mi)
% 13.22/3.63 % (7650)Instruction limit reached!
% 13.22/3.63 % (7650)------------------------------
% 13.22/3.63 % (7650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.63 % (7650)Termination reason: Unknown
% 13.22/3.63 % (7650)Termination phase: Preprocessing 3
% 13.22/3.63
% 13.22/3.63 % (7650)Memory used [KB]: 3454
% 13.22/3.63 % (7650)Time elapsed: 0.116 s
% 13.22/3.63 % (7650)Instructions burned: 258 (million)
% 13.22/3.63 % (7650)------------------------------
% 13.22/3.63 % (7650)------------------------------
% 13.22/3.63 % (7649)Instruction limit reached!
% 13.22/3.63 % (7649)------------------------------
% 13.22/3.63 % (7649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.63 % (7649)Termination reason: Unknown
% 13.22/3.63 % (7649)Termination phase: Saturation
% 13.22/3.63
% 13.22/3.63 % (7649)Memory used [KB]: 7547
% 13.22/3.63 % (7649)Time elapsed: 0.120 s
% 13.22/3.63 % (7649)Instructions burned: 279 (million)
% 13.22/3.63 % (7649)------------------------------
% 13.22/3.63 % (7649)------------------------------
% 13.22/3.64 % (7654)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_7240 for (2981ds/26Mi)
% 13.22/3.65 % (7655)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_7240 for (2981ds/995Mi)
% 13.22/3.66 % (7654)Instruction limit reached!
% 13.22/3.66 % (7654)------------------------------
% 13.22/3.66 % (7654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.66 % (7654)Termination reason: Unknown
% 13.22/3.66 % (7654)Termination phase: shuffling
% 13.22/3.66
% 13.22/3.66 % (7654)Memory used [KB]: 1918
% 13.22/3.66 % (7654)Time elapsed: 0.014 s
% 13.22/3.66 % (7654)Instructions burned: 28 (million)
% 13.22/3.66 % (7654)------------------------------
% 13.22/3.66 % (7654)------------------------------
% 13.22/3.67 % (7656)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_7240 for (2981ds/373Mi)
% 13.51/3.77 % (7634)Instruction limit reached!
% 13.51/3.77 % (7634)------------------------------
% 13.51/3.77 % (7634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.51/3.77 % (7634)Termination reason: Unknown
% 13.51/3.77 % (7634)Termination phase: Saturation
% 13.51/3.77
% 13.51/3.77 % (7634)Memory used [KB]: 9850
% 13.51/3.77 % (7634)Time elapsed: 0.712 s
% 13.51/3.77 % (7634)Instructions burned: 1539 (million)
% 13.51/3.77 % (7634)------------------------------
% 13.51/3.77 % (7634)------------------------------
% 13.51/3.80 % (7659)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_7240 for (2980ds/253Mi)
% 14.19/3.83 % (7656)Instruction limit reached!
% 14.19/3.83 % (7656)------------------------------
% 14.19/3.83 % (7656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.19/3.83 % (7656)Termination reason: Unknown
% 14.19/3.83 % (7656)Termination phase: Saturation
% 14.19/3.83
% 14.19/3.83 % (7656)Memory used [KB]: 8315
% 14.19/3.83 % (7656)Time elapsed: 0.164 s
% 14.19/3.83 % (7656)Instructions burned: 374 (million)
% 14.19/3.83 % (7656)------------------------------
% 14.19/3.83 % (7656)------------------------------
% 14.19/3.85 % (7661)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_7240 for (2979ds/832Mi)
% 14.19/3.87 % (7659)Instruction limit reached!
% 14.19/3.87 % (7659)------------------------------
% 14.19/3.87 % (7659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.19/3.87 % (7659)Termination reason: Unknown
% 14.19/3.87 % (7659)Termination phase: Property scanning
% 14.19/3.87
% 14.19/3.87 % (7659)Memory used [KB]: 3198
% 14.19/3.87 % (7659)Time elapsed: 0.069 s
% 14.19/3.87 % (7659)Instructions burned: 257 (million)
% 14.19/3.87 % (7659)------------------------------
% 14.19/3.87 % (7659)------------------------------
% 14.19/3.88 % (7662)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_7240 for (2979ds/668Mi)
% 18.40/4.07 % (7655)Instruction limit reached!
% 18.40/4.07 % (7655)------------------------------
% 18.40/4.07 % (7655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/4.07 % (7655)Termination reason: Unknown
% 18.40/4.07 % (7655)Termination phase: Saturation
% 18.40/4.07
% 18.40/4.07 % (7655)Memory used [KB]: 9338
% 18.40/4.07 % (7655)Time elapsed: 0.424 s
% 18.40/4.07 % (7655)Instructions burned: 995 (million)
% 18.40/4.07 % (7655)------------------------------
% 18.40/4.07 % (7655)------------------------------
% 18.40/4.09 % (7667)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_7240 for (2977ds/40Mi)
% 18.40/4.09 % (7641)Instruction limit reached!
% 18.40/4.09 % (7641)------------------------------
% 18.40/4.09 % (7641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/4.09 % (7641)Termination reason: Unknown
% 18.40/4.09 % (7641)Termination phase: Saturation
% 18.40/4.09
% 18.40/4.09 % (7641)Memory used [KB]: 5117
% 18.40/4.09 % (7641)Time elapsed: 0.842 s
% 18.40/4.09 % (7641)Instructions burned: 1913 (million)
% 18.40/4.09 % (7641)------------------------------
% 18.40/4.09 % (7641)------------------------------
% 18.40/4.10 % (7667)Instruction limit reached!
% 18.40/4.10 % (7667)------------------------------
% 18.40/4.10 % (7667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/4.10 % (7667)Termination reason: Unknown
% 18.40/4.10 % (7667)Termination phase: shuffling
% 18.40/4.10
% 18.40/4.10 % (7667)Memory used [KB]: 2046
% 18.40/4.10 % (7667)Time elapsed: 0.020 s
% 18.40/4.10 % (7667)Instructions burned: 41 (million)
% 18.40/4.10 % (7667)------------------------------
% 18.40/4.10 % (7667)------------------------------
% 18.40/4.11 % (7669)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_7240 for (2977ds/294Mi)
% 18.40/4.12 % (7662)Instruction limit reached!
% 18.40/4.12 % (7662)------------------------------
% 18.40/4.12 % (7662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/4.12 % (7662)Termination reason: Unknown
% 18.40/4.12 % (7662)Termination phase: Saturation
% 18.40/4.12
% 18.40/4.12 % (7662)Memory used [KB]: 13688
% 18.40/4.12 % (7662)Time elapsed: 0.235 s
% 18.40/4.12 % (7662)Instructions burned: 670 (million)
% 18.40/4.12 % (7662)------------------------------
% 18.40/4.12 % (7662)------------------------------
% 18.40/4.12 % (7670)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_7240 for (2976ds/187Mi)
% 19.10/4.13 % (7672)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_7240 for (2976ds/371Mi)
% 19.38/4.20 % (7670)Instruction limit reached!
% 19.38/4.20 % (7670)------------------------------
% 19.38/4.20 % (7670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.38/4.20 % (7670)Termination reason: Unknown
% 19.38/4.20 % (7670)Termination phase: Property scanning
% 19.38/4.20
% 19.38/4.20 % (7670)Memory used [KB]: 3070
% 19.38/4.20 % (7670)Time elapsed: 0.085 s
% 19.38/4.20 % (7670)Instructions burned: 188 (million)
% 19.38/4.20 % (7670)------------------------------
% 19.38/4.20 % (7670)------------------------------
% 19.38/4.22 % (7669)Instruction limit reached!
% 19.38/4.22 % (7669)------------------------------
% 19.38/4.22 % (7669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.38/4.22 % (7669)Termination reason: Unknown
% 19.38/4.22 % (7669)Termination phase: Saturation
% 19.38/4.22
% 19.38/4.22 % (7669)Memory used [KB]: 2942
% 19.38/4.22 % (7669)Time elapsed: 0.106 s
% 19.38/4.22 % (7669)Instructions burned: 297 (million)
% 19.38/4.22 % (7669)------------------------------
% 19.38/4.22 % (7669)------------------------------
% 19.38/4.22 % (7661)Instruction limit reached!
% 19.38/4.22 % (7661)------------------------------
% 19.38/4.22 % (7661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.38/4.22 % (7661)Termination reason: Unknown
% 19.38/4.22 % (7661)Termination phase: Saturation
% 19.38/4.22
% 19.38/4.22 % (7661)Memory used [KB]: 11129
% 19.38/4.22 % (7661)Time elapsed: 0.390 s
% 19.38/4.22 % (7661)Instructions burned: 834 (million)
% 19.38/4.22 % (7661)------------------------------
% 19.38/4.22 % (7661)------------------------------
% 19.38/4.22 % (7675)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_7240 for (2976ds/1827Mi)
% 19.38/4.23 % (7676)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_7240 for (2975ds/70Mi)
% 19.38/4.24 % (7677)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_7240 for (2975ds/316Mi)
% 19.38/4.24 % (7676)Instruction limit reached!
% 19.38/4.24 % (7676)------------------------------
% 19.38/4.24 % (7676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.38/4.24 % (7676)Termination reason: Unknown
% 19.38/4.24 % (7676)Termination phase: shuffling
% 19.38/4.24
% 19.38/4.24 % (7676)Memory used [KB]: 2302
% 19.38/4.24 % (7676)Time elapsed: 0.020 s
% 19.38/4.24 % (7676)Instructions burned: 70 (million)
% 19.38/4.24 % (7676)------------------------------
% 19.38/4.24 % (7676)------------------------------
% 19.38/4.26 % (7678)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_7240 for (2975ds/932Mi)
% 19.38/4.29 % (7672)Instruction limit reached!
% 19.38/4.29 % (7672)------------------------------
% 19.38/4.29 % (7672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.38/4.29 % (7672)Termination reason: Unknown
% 19.38/4.29 % (7672)Termination phase: Saturation
% 19.38/4.29
% 19.38/4.29 % (7672)Memory used [KB]: 7931
% 19.38/4.29 % (7672)Time elapsed: 0.159 s
% 19.38/4.29 % (7672)Instructions burned: 371 (million)
% 19.38/4.29 % (7672)------------------------------
% 19.38/4.29 % (7672)------------------------------
% 20.13/4.31 % (7681)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_7240 for (2974ds/4714Mi)
% 20.13/4.37 % (7677)Instruction limit reached!
% 20.13/4.37 % (7677)------------------------------
% 20.13/4.37 % (7677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.13/4.37 % (7677)Termination reason: Unknown
% 20.13/4.37 % (7677)Termination phase: Property scanning
% 20.13/4.37
% 20.13/4.37 % (7677)Memory used [KB]: 3198
% 20.13/4.37 % (7677)Time elapsed: 0.135 s
% 20.13/4.37 % (7677)Instructions burned: 317 (million)
% 20.13/4.37 % (7677)------------------------------
% 20.13/4.37 % (7677)------------------------------
% 20.13/4.39 % (7682)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_7240 for (2974ds/8250Mi)
% 20.84/4.57 % (7681)Refutation not found, incomplete strategy
% 20.84/4.57 % (7681)------------------------------
% 20.84/4.57 % (7681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.84/4.57 % (7681)Termination reason: Refutation not found, incomplete strategy
% 20.84/4.57
% 20.84/4.57
% 20.84/4.57 % (7681)Memory used [KB]: 8955
% 20.84/4.57 % (7681)Time elapsed: 0.262 s
% 20.84/4.57 % (7681)Instructions burned: 610 (million)
% 20.84/4.57 % (7681)------------------------------
% 20.84/4.57 % (7681)------------------------------
% 20.84/4.59 % (7685)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_7240 for (2972ds/770Mi)
% 21.42/4.66 % (7678)Instruction limit reached!
% 21.42/4.66 % (7678)------------------------------
% 21.42/4.66 % (7678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.42/4.66 % (7678)Termination reason: Unknown
% 21.42/4.66 % (7678)Termination phase: Saturation
% 21.42/4.66
% 21.42/4.66 % (7678)Memory used [KB]: 9210
% 21.42/4.66 % (7678)Time elapsed: 0.401 s
% 21.42/4.66 % (7678)Instructions burned: 932 (million)
% 21.42/4.66 % (7678)------------------------------
% 21.42/4.66 % (7678)------------------------------
% 21.42/4.68 % (7686)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_7240 for (2971ds/794Mi)
% 22.75/4.90 % (7633)Instruction limit reached!
% 22.75/4.90 % (7633)------------------------------
% 22.75/4.90 % (7633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.75/4.90 % (7633)Termination reason: Unknown
% 22.75/4.90 % (7633)Termination phase: Saturation
% 22.75/4.90
% 22.75/4.90 % (7633)Memory used [KB]: 10618
% 22.75/4.90 % (7633)Time elapsed: 1.846 s
% 22.75/4.90 % (7633)Instructions burned: 4437 (million)
% 22.75/4.90 % (7633)------------------------------
% 22.75/4.90 % (7633)------------------------------
% 22.75/4.91 % (7687)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_7240 for (2968ds/464Mi)
% 22.75/4.92 % (7685)Instruction limit reached!
% 22.75/4.92 % (7685)------------------------------
% 22.75/4.92 % (7685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.75/4.92 % (7685)Termination reason: Unknown
% 22.75/4.92 % (7685)Termination phase: Saturation
% 22.75/4.92
% 22.75/4.92 % (7685)Memory used [KB]: 8699
% 22.75/4.92 % (7685)Time elapsed: 0.340 s
% 22.75/4.92 % (7685)Instructions burned: 770 (million)
% 22.75/4.92 % (7685)------------------------------
% 22.75/4.92 % (7685)------------------------------
% 22.75/4.94 % (7689)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_7240 for (2968ds/1376Mi)
% 25.22/5.03 % (7686)Instruction limit reached!
% 25.22/5.03 % (7686)------------------------------
% 25.22/5.03 % (7686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.22/5.03 % (7686)Termination reason: Unknown
% 25.22/5.03 % (7686)Termination phase: Saturation
% 25.22/5.03
% 25.22/5.03 % (7686)Memory used [KB]: 5500
% 25.22/5.03 % (7686)Time elapsed: 0.354 s
% 25.22/5.03 % (7686)Instructions burned: 795 (million)
% 25.22/5.03 % (7686)------------------------------
% 25.22/5.03 % (7686)------------------------------
% 25.22/5.05 % (7691)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_7240 for (2967ds/906Mi)
% 25.22/5.08 % (7687)Instruction limit reached!
% 25.22/5.08 % (7687)------------------------------
% 25.22/5.08 % (7687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.22/5.08 % (7687)Termination reason: Unknown
% 25.22/5.08 % (7687)Termination phase: Saturation
% 25.22/5.08
% 25.22/5.08 % (7687)Memory used [KB]: 8571
% 25.22/5.08 % (7687)Time elapsed: 0.159 s
% 25.22/5.08 % (7687)Instructions burned: 464 (million)
% 25.22/5.08 % (7687)------------------------------
% 25.22/5.08 % (7687)------------------------------
% 25.22/5.10 % (7694)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_7240 for (2967ds/434Mi)
% 25.22/5.10 % (7675)Instruction limit reached!
% 25.22/5.10 % (7675)------------------------------
% 25.22/5.10 % (7675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.22/5.10 % (7675)Termination reason: Unknown
% 25.22/5.10 % (7675)Termination phase: Saturation
% 25.22/5.10
% 25.22/5.10 % (7675)Memory used [KB]: 10362
% 25.22/5.10 % (7675)Time elapsed: 0.906 s
% 25.22/5.10 % (7675)Instructions burned: 1828 (million)
% 25.22/5.10 % (7675)------------------------------
% 25.22/5.10 % (7675)------------------------------
% 25.85/5.12 % (7695)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_7240 for (2966ds/865Mi)
% 25.85/5.15 % (7642)Instruction limit reached!
% 25.85/5.15 % (7642)------------------------------
% 25.85/5.15 % (7642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.85/5.15 % (7642)Termination reason: Unknown
% 25.85/5.15 % (7642)Termination phase: Saturation
% 25.85/5.15
% 25.85/5.15 % (7642)Memory used [KB]: 10362
% 25.85/5.15 % (7642)Time elapsed: 1.860 s
% 25.85/5.15 % (7642)Instructions burned: 4352 (million)
% 25.85/5.15 % (7642)------------------------------
% 25.85/5.15 % (7642)------------------------------
% 25.85/5.17 % (7696)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_7240 for (2966ds/593Mi)
% 26.15/5.20 % (7638)Instruction limit reached!
% 26.15/5.20 % (7638)------------------------------
% 26.15/5.20 % (7638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.15/5.20 % (7638)Termination reason: Unknown
% 26.15/5.20 % (7638)Termination phase: Saturation
% 26.15/5.20
% 26.15/5.20 % (7638)Memory used [KB]: 15095
% 26.15/5.20 % (7638)Time elapsed: 2.069 s
% 26.15/5.20 % (7638)Instructions burned: 5205 (million)
% 26.15/5.20 % (7638)------------------------------
% 26.15/5.20 % (7638)------------------------------
% 26.15/5.22 % (7698)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_7240 for (2965ds/443Mi)
% 26.15/5.28 % (7694)Instruction limit reached!
% 26.15/5.28 % (7694)------------------------------
% 26.15/5.28 % (7694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.15/5.28 % (7694)Termination reason: Unknown
% 26.15/5.28 % (7694)Termination phase: Saturation
% 26.15/5.28
% 26.15/5.28 % (7694)Memory used [KB]: 8699
% 26.15/5.28 % (7694)Time elapsed: 0.182 s
% 26.15/5.28 % (7694)Instructions burned: 437 (million)
% 26.15/5.28 % (7694)------------------------------
% 26.15/5.28 % (7694)------------------------------
% 26.15/5.29 % (7700)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_7240 for (2965ds/594Mi)
% 26.76/5.41 % (7698)Instruction limit reached!
% 26.76/5.41 % (7698)------------------------------
% 26.76/5.41 % (7698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.76/5.41 % (7698)Termination reason: Unknown
% 26.76/5.41 % (7698)Termination phase: Property scanning
% 26.76/5.41
% 26.76/5.41 % (7698)Memory used [KB]: 3582
% 26.76/5.41 % (7698)Time elapsed: 0.191 s
% 26.76/5.41 % (7698)Instructions burned: 445 (million)
% 26.76/5.41 % (7698)------------------------------
% 26.76/5.41 % (7698)------------------------------
% 26.76/5.42 % (7696)Instruction limit reached!
% 26.76/5.42 % (7696)------------------------------
% 26.76/5.42 % (7696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.76/5.42 % (7696)Termination reason: Unknown
% 26.76/5.42 % (7696)Termination phase: Saturation
% 26.76/5.42
% 26.76/5.42 % (7696)Memory used [KB]: 8699
% 26.76/5.42 % (7696)Time elapsed: 0.253 s
% 26.76/5.42 % (7696)Instructions burned: 593 (million)
% 26.76/5.42 % (7696)------------------------------
% 26.76/5.42 % (7696)------------------------------
% 26.76/5.43 % (7702)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_7240 for (2963ds/327Mi)
% 26.76/5.44 % (7703)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_7240 for (2963ds/5411Mi)
% 26.76/5.45 % (7695)Instruction limit reached!
% 26.76/5.45 % (7695)------------------------------
% 26.76/5.45 % (7695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.76/5.45 % (7695)Termination reason: Unknown
% 26.76/5.45 % (7695)Termination phase: Saturation
% 26.76/5.45
% 26.76/5.45 % (7695)Memory used [KB]: 9338
% 26.76/5.45 % (7695)Time elapsed: 0.332 s
% 26.76/5.45 % (7695)Instructions burned: 865 (million)
% 26.76/5.45 % (7695)------------------------------
% 26.76/5.45 % (7695)------------------------------
% 26.76/5.46 % (7704)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_7240 for (2963ds/1762Mi)
% 26.76/5.49 % (7691)Instruction limit reached!
% 26.76/5.49 % (7691)------------------------------
% 26.76/5.49 % (7691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.76/5.49 % (7691)Termination reason: Unknown
% 26.76/5.49 % (7691)Termination phase: Saturation
% 26.76/5.49
% 26.76/5.49 % (7691)Memory used [KB]: 13432
% 26.76/5.49 % (7691)Time elapsed: 0.441 s
% 26.76/5.49 % (7691)Instructions burned: 907 (million)
% 26.76/5.49 % (7691)------------------------------
% 26.76/5.49 % (7691)------------------------------
% 28.24/5.50 % (7705)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_7240 for (2963ds/96Mi)
% 28.24/5.51 % (7689)Instruction limit reached!
% 28.24/5.51 % (7689)------------------------------
% 28.24/5.51 % (7689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.51 % (7689)Termination reason: Unknown
% 28.24/5.51 % (7689)Termination phase: Saturation
% 28.24/5.51
% 28.24/5.51 % (7689)Memory used [KB]: 13560
% 28.24/5.51 % (7689)Time elapsed: 0.566 s
% 28.24/5.51 % (7689)Instructions burned: 1377 (million)
% 28.24/5.51 % (7689)------------------------------
% 28.24/5.51 % (7689)------------------------------
% 28.24/5.51 % (7700)Instruction limit reached!
% 28.24/5.51 % (7700)------------------------------
% 28.24/5.51 % (7700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.51 % (7700)Termination reason: Unknown
% 28.24/5.51 % (7700)Termination phase: Saturation
% 28.24/5.51
% 28.24/5.51 % (7700)Memory used [KB]: 8315
% 28.24/5.51 % (7700)Time elapsed: 0.224 s
% 28.24/5.51 % (7700)Instructions burned: 595 (million)
% 28.24/5.51 % (7700)------------------------------
% 28.24/5.51 % (7700)------------------------------
% 28.24/5.52 % (7707)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_7240 for (2962ds/503Mi)
% 28.24/5.53 % (7708)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_7240 for (2962ds/90Mi)
% 28.24/5.54 % (7705)Instruction limit reached!
% 28.24/5.54 % (7705)------------------------------
% 28.24/5.54 % (7705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.54 % (7705)Termination reason: Unknown
% 28.24/5.54 % (7705)Termination phase: Property scanning
% 28.24/5.54
% 28.24/5.54 % (7705)Memory used [KB]: 2686
% 28.24/5.54 % (7705)Time elapsed: 0.044 s
% 28.24/5.54 % (7705)Instructions burned: 97 (million)
% 28.24/5.54 % (7705)------------------------------
% 28.24/5.54 % (7705)------------------------------
% 28.24/5.56 % (7708)Instruction limit reached!
% 28.24/5.56 % (7708)------------------------------
% 28.24/5.56 % (7708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.56 % (7708)Termination reason: Unknown
% 28.24/5.56 % (7708)Termination phase: shuffling
% 28.24/5.56
% 28.24/5.56 % (7708)Memory used [KB]: 2302
% 28.24/5.56 % (7708)Time elapsed: 0.036 s
% 28.24/5.56 % (7708)Instructions burned: 93 (million)
% 28.24/5.56 % (7708)------------------------------
% 28.24/5.56 % (7708)------------------------------
% 28.24/5.56 % (7711)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_7240 for (2962ds/593Mi)
% 28.24/5.57 % (7702)Instruction limit reached!
% 28.24/5.57 % (7702)------------------------------
% 28.24/5.57 % (7702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.57 % (7702)Termination reason: Unknown
% 28.24/5.57 % (7702)Termination phase: Property scanning
% 28.24/5.57
% 28.24/5.57 % (7702)Memory used [KB]: 3837
% 28.24/5.57 % (7702)Time elapsed: 0.145 s
% 28.24/5.57 % (7702)Instructions burned: 327 (million)
% 28.24/5.57 % (7702)------------------------------
% 28.24/5.57 % (7702)------------------------------
% 28.24/5.57 % (7714)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_7240 for (2962ds/1512Mi)
% 28.24/5.59 % (7715)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_7240 for (2962ds/569Mi)
% 28.24/5.59 % (7703)First to succeed.
% 28.24/5.60 % (7703)Refutation found. Thanks to Tanya!
% 28.24/5.60 % SZS status Theorem for DTF2THF_7240
% 28.24/5.60 % SZS output start Proof for DTF2THF_7240
% 28.24/5.60 thf(type_def_5, type, option: ($tType) > $tType).
% 28.24/5.60 thf(type_def_7, type, const: $tType).
% 28.24/5.60 thf(type_def_8, type, val: ($tType * $tType * $tType) > $tType).
% 28.24/5.60 thf(type_def_9, type, expr: ($tType * $tType * $tType) > $tType).
% 28.24/5.60 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 28.24/5.60 thf(type_def_11, type, set: ($tType) > $tType).
% 28.24/5.60 thf(type_def_12, type, cntxt: ($tType * $tType * $tType) > $tType).
% 28.24/5.60 thf(type_def_13, type, r: $tType).
% 28.24/5.60 thf(type_def_14, type, l: $tType).
% 28.24/5.60 thf(type_def_15, type, v: $tType).
% 28.24/5.60 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 28.24/5.60 thf(func_def_1, type, option: ($tType) > $tType).
% 28.24/5.60 thf(func_def_2, type, const: $tType).
% 28.24/5.60 thf(func_def_3, type, cntxt: ($tType * $tType * $tType) > $tType).
% 28.24/5.60 thf(func_def_4, type, expr: ($tType * $tType * $tType) > $tType).
% 28.24/5.60 thf(func_def_5, type, val: ($tType * $tType * $tType) > $tType).
% 28.24/5.60 thf(func_def_6, type, set: ($tType) > $tType).
% 28.24/5.60 thf(func_def_7, type, v: $tType).
% 28.24/5.60 thf(func_def_8, type, r: $tType).
% 28.24/5.60 thf(func_def_9, type, l: $tType).
% 28.24/5.60 thf(func_def_10, type, type: !>[X0: $tType]:($o)).
% 28.24/5.60 thf(func_def_11, type, order: !>[X0: $tType]:($o)).
% 28.24/5.60 thf(func_def_12, type, combine: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > (X0 > option @ X1) > X0 > option @ X1)).
% 28.24/5.60 thf(func_def_13, type, f: const).
% 28.24/5.60 thf(func_def_14, type, t: const).
% 28.24/5.60 thf(func_def_15, type, unit: const).
% 28.24/5.60 thf(func_def_16, type, doms: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X0 > option @ val @ X1 @ X0 @ X2) @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X2) @ expr @ X1 @ X0 @ X2 > set @ X0)).
% 28.24/5.60 thf(func_def_17, type, assign: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_18, type, ite: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_19, type, read: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_20, type, ref: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_21, type, rfork: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_22, type, rjoin: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_23, type, ve: !>[X0: $tType, X1: $tType, X2: $tType]:(val @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_24, type, plug: !>[X0: $tType, X1: $tType, X2: $tType]:(cntxt @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_25, type, cv: !>[X0: $tType, X1: $tType, X2: $tType]:(const > val @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_26, type, loc: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > val @ X1 @ X0 @ X2)).
% 28.24/5.60 thf(func_def_27, type, rid: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > val @ X0 @ X1 @ X2)).
% 28.24/5.60 thf(func_def_28, type, execution: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > expr @ X0 @ X1 @ X2 > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_29, type, inductive_invariant: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > ((X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o) > $o)).
% 28.24/5.60 thf(func_def_30, type, maximal_execution: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > expr @ X0 @ X1 @ X2 > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_31, type, reachable: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_32, type, steps: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > set @ product_prod @ (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) @ (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2))).
% 28.24/5.60 thf(func_def_33, type, terminates_in: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > expr @ X0 @ X1 @ X2 > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_34, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 28.24/5.60 thf(func_def_35, type, fun_upd: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0 > X1 > X0 > X1)).
% 28.24/5.60 thf(func_def_36, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 28.24/5.60 thf(func_def_37, type, dom: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > set @ X0)).
% 28.24/5.60 thf(func_def_38, type, lID_G: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > set @ X1)).
% 28.24/5.60 thf(func_def_39, type, lID_L: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X0 > option @ val @ X1 @ X0 @ X2) @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X2) @ expr @ X1 @ X0 @ X2 > set @ X0)).
% 28.24/5.60 thf(func_def_40, type, rID_G: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > set @ X0)).
% 28.24/5.60 thf(func_def_41, type, rID_L: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X0 > option @ val @ X1 @ X0 @ X2) @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X2) @ expr @ X1 @ X0 @ X2 > set @ X1)).
% 28.24/5.60 thf(func_def_42, type, domains_subsume: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X0 > option @ val @ X1 @ X0 @ X2) @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X2) @ expr @ X1 @ X0 @ X2 > $o)).
% 28.24/5.60 thf(func_def_43, type, domain398919503obally: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_44, type, revision_step: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > X0 > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_45, type, revisi1433015572elaxed: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > X0 > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_46, type, subsumes_accessible: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > X0 > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_47, type, subsum380726323obally: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_48, type, none: !>[X0: $tType]:(option @ X0)).
% 28.24/5.60 thf(func_def_49, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 28.24/5.60 thf(func_def_50, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 28.24/5.60 thf(func_def_51, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 28.24/5.60 thf(func_def_52, type, top_top: !>[X0: $tType]:(X0)).
% 28.24/5.60 thf(func_def_53, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 28.24/5.60 thf(func_def_54, type, eq_states: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > (X0 > option @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ product_prod @ (X1 > option @ val @ X0 @ X1 @ X2) @ expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_55, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 28.24/5.60 thf(func_def_56, type, substitution: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > $o)).
% 28.24/5.60 thf(func_def_57, type, transitive_rtrancl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0)).
% 28.24/5.60 thf(func_def_58, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 28.24/5.60 thf(func_def_59, type, e: cntxt @ r @ l @ v).
% 28.24/5.60 thf(func_def_60, type, sigma: l > option @ val @ r @ l @ v).
% 28.24/5.60 thf(func_def_61, type, tau: l > option @ val @ r @ l @ v).
% 28.24/5.60 thf(func_def_62, type, e2: expr @ r @ l @ v).
% 28.24/5.60 thf(func_def_63, type, r2: r).
% 28.24/5.60 thf(func_def_64, type, r3: r).
% 28.24/5.60 thf(func_def_65, type, r4: r).
% 28.24/5.60 thf(func_def_66, type, s_1: r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 28.24/5.60 thf(func_def_67, type, s_2: r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 28.24/5.60 thf(func_def_68, type, s_22: r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 28.24/5.60 thf(func_def_69, type, subst: expr @ r @ l @ v > v > expr @ r @ l @ v > expr @ r @ l @ v).
% 28.24/5.60 thf(func_def_70, type, x: product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 28.24/5.60 thf(func_def_86, type, sP0: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > $o)).
% 28.24/5.60 thf(func_def_87, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ expr @ X1 @ X2 @ X0 > $o) > X2 > option @ val @ X1 @ X2 @ X0)).
% 28.24/5.60 thf(func_def_88, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ expr @ X1 @ X2 @ X0 > $o) > X2 > option @ val @ X1 @ X2 @ X0)).
% 28.24/5.60 thf(func_def_89, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ expr @ X1 @ X2 @ X0 > $o) > expr @ X1 @ X2 @ X0)).
% 28.24/5.60 thf(func_def_90, type, sK4: !>[X0: $tType]:(option @ X0 > X0)).
% 28.24/5.60 thf(func_def_91, type, sK5: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X1)).
% 28.24/5.60 thf(func_def_92, type, sK6: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X0)).
% 28.24/5.60 thf(func_def_93, type, sK7: !>[X0: $tType]:(option @ X0 > X0)).
% 28.24/5.60 thf(func_def_94, type, sK8: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > option @ X0) @ product_prod @ (X1 > option @ X0) @ X1 > X1 > option @ X0)).
% 28.24/5.60 thf(func_def_95, type, sK9: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > option @ X0) @ product_prod @ (X1 > option @ X0) @ X1 > X1 > option @ X0)).
% 28.24/5.60 thf(func_def_96, type, sK10: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > option @ X0) @ product_prod @ (X1 > option @ X0) @ X1 > X1)).
% 28.24/5.60 thf(func_def_97, type, sK11: !>[X0: $tType]:((option @ X0 > $o) > X0)).
% 28.24/5.60 thf(func_def_98, type, sK12: !>[X0: $tType]:(option @ X0 > X0)).
% 28.24/5.60 thf(func_def_99, type, sK13: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 28.24/5.60 thf(func_def_100, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0 > X1 > option @ val @ X2 @ X1 @ X0)).
% 28.24/5.60 thf(func_def_101, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0 > X1 > option @ val @ X2 @ X1 @ X0)).
% 28.24/5.60 thf(func_def_102, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0)).
% 28.24/5.60 thf(func_def_104, type, ph18: !>[X0: $tType]:(X0)).
% 28.24/5.60 thf(func_def_105, type, sK19: r).
% 28.24/5.60 thf(func_def_106, type, sK20: r).
% 28.24/5.60 thf(func_def_107, type, sK21: r).
% 28.24/5.60 thf(func_def_108, type, sK22: r).
% 28.24/5.60 thf(func_def_109, type, sK23: r).
% 28.24/5.60 thf(f982,plain,(
% 28.24/5.60 $false),
% 28.24/5.60 inference(subsumption_resolution,[status(thm)],[f979,f785])).
% 28.24/5.60 thf(f785,plain,(
% 28.24/5.60 (r2 != r3)),
% 28.24/5.60 inference(cnf_transformation,[status(thm)],[f3])).
% 28.24/5.60 thf(f3,axiom,(
% 28.24/5.60 (r2 != r3)),
% 28.24/5.60 file('/export/starexec/sandbox/tmp/tmp.qbB1WGygH8/DTF2THF_7240.p',fact_2_assms_I6_J)).
% 28.24/5.60 thf(f979,plain,(
% 28.24/5.60 (r2 = r3)),
% 28.24/5.60 inference(trivial_inequality_removal,[status(thm)],[f976])).
% 28.24/5.60 thf(f976,plain,(
% 28.24/5.60 (r2 = r3) | ((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) != (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))))),
% 28.24/5.60 inference(superposition,[status(thm)],[f840,f744])).
% 28.24/5.60 thf(f744,plain,(
% 28.24/5.60 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X6 : X1,X4 : X0 > X1,X5 : X1] : (((fun_upd @ X0 @ X1 @ (fun_upd @ X0 @ X1 @ X4 @ X3 @ X6) @ X2 @ X5) = (fun_upd @ X0 @ X1 @ (fun_upd @ X0 @ X1 @ X4 @ X2 @ X5) @ X3 @ X6)) | (X2 = X3)) )),
% 28.24/5.60 inference(cnf_transformation,[status(thm)],[f688])).
% 28.24/5.60 thf(f688,plain,(
% 28.24/5.60 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1,X6 : X1] : ((X2 = X3) | ((fun_upd @ X0 @ X1 @ (fun_upd @ X0 @ X1 @ X4 @ X3 @ X6) @ X2 @ X5) = (fun_upd @ X0 @ X1 @ (fun_upd @ X0 @ X1 @ X4 @ X2 @ X5) @ X3 @ X6)))),
% 28.24/5.60 inference(ennf_transformation,[status(thm)],[f670])).
% 28.24/5.60 thf(f670,plain,(
% 28.24/5.60 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1,X6 : X1] : ((X2 != X3) => ((fun_upd @ X0 @ X1 @ (fun_upd @ X0 @ X1 @ X4 @ X3 @ X6) @ X2 @ X5) = (fun_upd @ X0 @ X1 @ (fun_upd @ X0 @ X1 @ X4 @ X2 @ X5) @ X3 @ X6)))),
% 28.24/5.60 inference(rectify,[status(thm)],[f31])).
% 28.24/5.60 thf(f31,axiom,(
% 28.24/5.60 ! [X0 : $tType,X1 : $tType,X42 : X0,X43 : X0,X44 : X0 > X1,X45 : X1,X46 : X1] : ((X42 != X43) => ((fun_upd @ X0 @ X1 @ (fun_upd @ X0 @ X1 @ X44 @ X42 @ X45) @ X43 @ X46) = (fun_upd @ X0 @ X1 @ (fun_upd @ X0 @ X1 @ X44 @ X43 @ X46) @ X42 @ X45)))),
% 28.24/5.60 file('/export/starexec/sandbox/tmp/tmp.qbB1WGygH8/DTF2THF_7240.p',fact_30_fun__upd__twist)).
% 28.24/5.60 thf(f840,plain,(
% 28.24/5.60 ((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) != (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))))),
% 28.24/5.60 inference(subsumption_resolution,[status(thm)],[f821,f784])).
% 28.24/5.60 thf(f784,plain,(
% 28.24/5.60 (r4 != r2)),
% 28.24/5.60 inference(cnf_transformation,[status(thm)],[f2])).
% 28.24/5.60 thf(f2,axiom,(
% 28.24/5.60 (r4 != r2)),
% 28.24/5.60 file('/export/starexec/sandbox/tmp/tmp.qbB1WGygH8/DTF2THF_7240.p',fact_1_assms_I7_J)).
% 28.24/5.60 thf(f821,plain,(
% 28.24/5.60 (r4 = r2) | ((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) != (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))))),
% 28.24/5.60 inference(superposition,[status(thm)],[f778,f744])).
% 28.24/5.60 thf(f778,plain,(
% 28.24/5.60 ((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) != (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)))),
% 28.24/5.60 inference(cnf_transformation,[status(thm)],[f663])).
% 28.24/5.60 thf(f663,plain,(
% 28.24/5.60 ((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) != (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)))),
% 28.24/5.60 inference(flattening,[status(thm)],[f288])).
% 28.24/5.60 thf(f288,plain,(
% 28.24/5.60 ~((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) = (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[Y0 : l]: (none @ val @ r @ l @ v)) @ e2)))) @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)))),
% 28.24/5.60 inference(fool_elimination,[status(thm)],[f287])).
% 28.24/5.60 thf(f287,plain,(
% 28.24/5.60 ~((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[X0 : l] : (none @ val @ r @ l @ v)) @ e2)))) @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) = (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[X1 : l] : (none @ val @ r @ l @ v)) @ e2)))))),
% 28.24/5.60 inference(rectify,[status(thm)],[f263])).
% 28.24/5.60 thf(f263,negated_conjecture,(
% 28.24/5.60 ~((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[X5 : l] : (none @ val @ r @ l @ v)) @ e2)))) @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) = (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[X5 : l] : (none @ val @ r @ l @ v)) @ e2)))))),
% 28.24/5.60 inference(negated_conjecture,[status(cth)],[f262])).
% 28.24/5.60 thf(f262,conjecture,(
% 28.24/5.60 ((fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[X5 : l] : (none @ val @ r @ l @ v)) @ e2)))) @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) = (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (fun_upd @ r @ option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ s_1 @ r2 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ x)) @ r3 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ sigma @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau @ (plug @ r @ l @ v @ e @ (ve @ r @ l @ v @ (rid @ r @ l @ v @ r4))))))) @ r4 @ (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (product_Pair @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (combine @ l @ val @ r @ l @ v @ sigma @ tau) @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ (^[X5 : l] : (none @ val @ r @ l @ v)) @ e2)))))),
% 28.24/5.60 file('/export/starexec/sandbox/tmp/tmp.qbB1WGygH8/DTF2THF_7240.p',conj_0)).
% 28.24/5.60 % SZS output end Proof for DTF2THF_7240
% 28.24/5.60 % (7703)------------------------------
% 28.24/5.60 % (7703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.60 % (7703)Termination reason: Refutation
% 28.24/5.60
% 28.24/5.60 % (7703)Memory used [KB]: 8315
% 28.24/5.60 % (7703)Time elapsed: 0.160 s
% 28.24/5.60 % (7703)Instructions burned: 427 (million)
% 28.24/5.60 % (7703)------------------------------
% 28.24/5.60 % (7703)------------------------------
% 28.24/5.60 % (7469)Success in time 3.799 s
%------------------------------------------------------------------------------