%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP046^2 : 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 : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:07 AM UTC 2026
% Result : Theorem 91.49s 14.56s
% Output : Refutation 91.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP046^2 : 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
% 0.15/0.34 % Computer : n027.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:24:52 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : ITP046^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.46 % Domain : Interactive Theorem Proving
% 0.19/0.46 % Problem : Sledgehammer Determinacy problem prob_599__3354110_1
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Des21]
% 0.19/0.46 % Names : Determinacy/prob_599__3354110_1 [Des21]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.33 v8.1.0, 0.50 v7.5.0
% 0.19/0.46 % Syntax : Number of formulae : 346 ( 92 unt; 78 typ; 0 def)
% 0.19/0.46 % Number of atoms : 922 ( 390 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.19/0.46 % Number of connectives : 25058 ( 128 ~; 55 |; 78 &;24368 @)
% 0.19/0.46 % ( 0 <=>; 429 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 44 ( 14 avg)
% 0.19/0.46 % Number of types : 5 ( 4 usr)
% 0.19/0.46 % Number of type conns : 2786 (2786 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 77 ( 74 usr; 13 con; 0-7 aty)
% 0.19/0.46 % Number of variables : 1715 ( 59 ^;1467 !; 77 ?;1715 :)
% 0.19/0.46 % ( 112 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.46 % SPC : TH1_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:18:36.876
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % Could-be-implicit typings (11)
% 0.19/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.19/0.46 product_prod: $tType > $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Sum__Type_Osum,type,
% 0.19/0.46 sum_sum: $tType > $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Option_Ooption,type,
% 0.19/0.46 option: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Data_Oconst,type,
% 0.19/0.46 const: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Data_Ocntxt,type,
% 0.19/0.46 cntxt: $tType > $tType > $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Data_Oexpr,type,
% 0.19/0.46 expr: $tType > $tType > $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Data_Oval,type,
% 0.19/0.46 val: $tType > $tType > $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Set_Oset,type,
% 0.19/0.46 set: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_tf_v,type,
% 0.19/0.46 v: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_tf_r,type,
% 0.19/0.46 r: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_tf_l,type,
% 0.19/0.46 l: $tType ).
% 0.19/0.46
% 0.19/0.46 % Explicit typings (67)
% 0.19/0.46 thf(sy_cl_HOL_Otype,type,
% 0.19/0.46 type:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.46 order:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.19/0.46 finite_finite:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.19/0.46 semiring_char_0:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Ocombine,type,
% 0.19/0.46 combine:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( A > ( option @ B ) ) > A > ( option @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oconst_OF,type,
% 0.19/0.46 f: const ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oconst_OT,type,
% 0.19/0.46 t: const ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oconst_OUnit,type,
% 0.19/0.46 unit: const ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Odoms,type,
% 0.19/0.46 doms:
% 0.19/0.46 !>[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 ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oexpr_OAssign,type,
% 0.19/0.46 assign:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oexpr_OIte,type,
% 0.19/0.46 ite:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oexpr_ORead,type,
% 0.19/0.46 read:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oexpr_ORef,type,
% 0.19/0.46 ref:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oexpr_ORfork,type,
% 0.19/0.46 rfork:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oexpr_ORjoin,type,
% 0.19/0.46 rjoin:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oexpr_OVE,type,
% 0.19/0.46 ve:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( val @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oplug,type,
% 0.19/0.46 plug:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( cntxt @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oval_OCV,type,
% 0.19/0.46 cv:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( const > ( val @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oval_OLoc,type,
% 0.19/0.46 loc:
% 0.19/0.46 !>[L: $tType,R: $tType,V: $tType] : ( L > ( val @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Data_Oval_ORid,type,
% 0.19/0.46 rid:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( R > ( val @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Executions_Osubstitution_Oexecution,type,
% 0.19/0.46 execution:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Executions_Osubstitution_Oinductive__invariant,type,
% 0.19/0.46 inductive_invariant:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Executions_Osubstitution_Omaximal__execution,type,
% 0.19/0.46 maximal_execution:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Executions_Osubstitution_Oreachable,type,
% 0.19/0.46 reachable:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Executions_Osubstitution_Osteps,type,
% 0.19/0.46 steps:
% 0.19/0.46 !>[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 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Executions_Osubstitution_Oterminates__in,type,
% 0.19/0.46 terminates_in:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Finite__Set_Ofinite,type,
% 0.19/0.46 finite_finite2:
% 0.19/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Fun_Ofun__upd,type,
% 0.19/0.46 fun_upd:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_If,type,
% 0.19/0.46 if:
% 0.19/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Map_Odom,type,
% 0.19/0.46 dom:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Occurrences_OLID_092_060_094sub_062G,type,
% 0.19/0.46 lID_G:
% 0.19/0.46 !>[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 ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Occurrences_OLID_092_060_094sub_062L,type,
% 0.19/0.46 lID_L:
% 0.19/0.46 !>[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 ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Occurrences_ORID_092_060_094sub_062G,type,
% 0.19/0.46 rID_G:
% 0.19/0.46 !>[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 ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Occurrences_ORID_092_060_094sub_062L,type,
% 0.19/0.46 rID_L:
% 0.19/0.46 !>[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 ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume,type,
% 0.19/0.46 domains_subsume:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally,type,
% 0.19/0.46 domain398919503obally:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step,type,
% 0.19/0.46 revision_step:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed,type,
% 0.19/0.46 revisi1433015572elaxed:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible,type,
% 0.19/0.46 subsumes_accessible:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally,type,
% 0.19/0.46 subsum380726323obally:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Option_Ooption_ONone,type,
% 0.19/0.46 none:
% 0.19/0.46 !>[A: $tType] : ( option @ A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Option_Ooption_OSome,type,
% 0.19/0.46 some:
% 0.19/0.46 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Option_Ooption_Othe,type,
% 0.19/0.46 the:
% 0.19/0.46 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.46 ord_less_eq:
% 0.19/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.19/0.46 top_top:
% 0.19/0.46 !>[A: $tType] : A ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.19/0.46 product_Pair:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Renaming_Oeq__states,type,
% 0.19/0.46 eq_states:
% 0.19/0.46 !>[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 ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect,type,
% 0.19/0.46 collect:
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Substitution_Osubstitution,type,
% 0.19/0.46 substitution:
% 0.19/0.46 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Transitive__Closure_Ortrancl,type,
% 0.19/0.46 transitive_rtrancl:
% 0.19/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member,type,
% 0.19/0.46 member:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v__092_060E_062,type,
% 0.19/0.46 e: cntxt @ r @ l @ v ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v__092_060E_062_H____,type,
% 0.19/0.46 e2: cntxt @ r @ l @ v ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v__092_060sigma_062,type,
% 0.19/0.46 sigma: l > ( option @ ( val @ r @ l @ v ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v__092_060sigma_062_H____,type,
% 0.19/0.46 sigma2: l > ( option @ ( val @ r @ l @ v ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v__092_060tau_062,type,
% 0.19/0.46 tau: l > ( option @ ( val @ r @ l @ v ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v__092_060tau_062_H____,type,
% 0.19/0.46 tau2: l > ( option @ ( val @ r @ l @ v ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_e,type,
% 0.19/0.46 e3: expr @ r @ l @ v ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_e_H____,type,
% 0.19/0.46 e4: expr @ r @ l @ v ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_left__forkee,type,
% 0.19/0.46 left_forkee: r ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_r,type,
% 0.19/0.46 r2: r ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_r_H,type,
% 0.19/0.46 r3: r ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_right__forkee____,type,
% 0.19/0.46 right_forkee: r ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_s_092_060_094sub_0621,type,
% 0.19/0.46 s_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_s_092_060_094sub_0622,type,
% 0.19/0.46 s_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_s_092_060_094sub_0622_H,type,
% 0.19/0.46 s_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_subst,type,
% 0.19/0.46 subst: ( expr @ r @ l @ v ) > v > ( expr @ r @ l @ v ) > ( expr @ r @ l @ v ) ).
% 0.19/0.46
% 0.19/0.46 % Relevant facts (255)
% 0.19/0.46 thf(fact_0_local_Ofork_I3_J,axiom,
% 0.19/0.46 ~ ( member @ r @ right_forkee @ ( rID_G @ r @ l @ v @ s_1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.fork(3)
% 0.19/0.46 thf(fact_1_side,axiom,
% 0.19/0.46 ~ ( member @ r @ left_forkee @ ( rID_G @ r @ l @ v @ s_1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % side
% 0.19/0.46 thf(fact_2_neq,axiom,
% 0.19/0.46 r2 != r3 ).
% 0.19/0.46
% 0.19/0.46 % neq
% 0.19/0.46 thf(fact_3__092_060open_062r_H_A_092_060noteq_062_Aleft__forkee_092_060close_062,axiom,
% 0.19/0.46 r3 != left_forkee ).
% 0.19/0.46
% 0.19/0.46 % \<open>r' \<noteq> left_forkee\<close>
% 0.19/0.46 thf(fact_4_r_H__unchanged__left,axiom,
% 0.19/0.46 ( ( s_2 @ r3 )
% 0.19/0.46 = ( s_1 @ r3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % r'_unchanged_left
% 0.19/0.46 thf(fact_5__092_060open_062r_A_092_060noteq_062_Aright__forkee_092_060close_062,axiom,
% 0.19/0.46 r2 != right_forkee ).
% 0.19/0.46
% 0.19/0.46 % \<open>r \<noteq> right_forkee\<close>
% 0.19/0.46 thf(fact_6_local_Ofork_I2_J,axiom,
% 0.19/0.46 ( ( s_1 @ r3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ e2 @ ( rfork @ r @ l @ v @ e4 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.fork(2)
% 0.19/0.46 thf(fact_7_right,axiom,
% 0.19/0.46 revision_step @ r @ l @ v @ subst @ r3 @ s_1 @ s_22 ).
% 0.19/0.46
% 0.19/0.46 % right
% 0.19/0.46 thf(fact_8_local_Ofork_I1_J,axiom,
% 0.19/0.46 ( s_22
% 0.19/0.46 = ( 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 ) ) @ sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau2 @ ( plug @ r @ l @ v @ e2 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ right_forkee ) ) ) ) ) ) ) @ right_forkee
% 0.19/0.46 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.19/0.46 @ ( 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 ) @ sigma2 @ tau2 )
% 0.19/0.46 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.19/0.46 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.19/0.46 @ e4 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.fork(1)
% 0.19/0.46 thf(fact_9__092_060open_062r_A_092_060noteq_062_Aleft__forkee_092_060close_062,axiom,
% 0.19/0.46 r2 != left_forkee ).
% 0.19/0.46
% 0.19/0.46 % \<open>r \<noteq> left_forkee\<close>
% 0.19/0.46 thf(fact_10_r__unchanged__right,axiom,
% 0.19/0.46 ( ( s_22 @ r2 )
% 0.19/0.46 = ( s_1 @ r2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % r_unchanged_right
% 0.19/0.46 thf(fact_11_reach,axiom,
% 0.19/0.46 reachable @ r @ l @ v @ subst @ s_1 ).
% 0.19/0.46
% 0.19/0.46 % reach
% 0.19/0.46 thf(fact_12_left__step,axiom,
% 0.19/0.46 revision_step @ r @ l @ v @ subst @ r2 @ s_1 @ s_2 ).
% 0.19/0.46
% 0.19/0.46 % left_step
% 0.19/0.46 thf(fact_13_only__fork__introduces__rids_H,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ! [Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v] :
% 0.19/0.46 ( ( S @ R2 )
% 0.19/0.46 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 0.19/0.46 => ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % only_fork_introduces_rids'
% 0.19/0.46 thf(fact_14_revision__step_Ofork,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: expr @ r @ l @ v,R3: r] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 0.19/0.46 => ( revision_step @ r @ l @ v @ subst @ R2 @ S
% 0.19/0.46 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) @ R3
% 0.19/0.46 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.19/0.46 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.19/0.46 @ E4 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step.fork
% 0.19/0.46 thf(fact_15_fork__pseudodeterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( ? [R4: r] :
% 0.19/0.46 ( ~ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( rfork @ r @ l @ v @ E4 ) ) ) ) ) ) ) )
% 0.19/0.46 & ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R4 ) ) ) ) ) ) ) @ R4
% 0.19/0.46 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.19/0.46 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.19/0.46 @ E4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fork_pseudodeterministic
% 0.19/0.46 thf(fact_16_substitution__axioms,axiom,
% 0.19/0.46 substitution @ r @ l @ v @ subst ).
% 0.19/0.46
% 0.19/0.46 % substitution_axioms
% 0.19/0.46 thf(fact_17_revision__step__relaxed_Ofork,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: expr @ r @ l @ v,R3: r] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 0.19/0.46 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S
% 0.19/0.46 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) @ R3
% 0.19/0.46 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.19/0.46 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.19/0.46 @ E4 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step_relaxed.fork
% 0.19/0.46 thf(fact_18_local__and__fork__commute,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,R5: r,E4: expr @ r @ l @ v] :
% 0.19/0.46 ( ( S_2
% 0.19/0.46 = ( 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 ) ) )
% 0.19/0.46 => ( ( S_22
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) @ R5
% 0.19/0.46 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.19/0.46 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.19/0.46 @ E4 ) ) ) ) )
% 0.19/0.46 => ( ( ( S_2 @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ r @ R5 @ ( rID_G @ r @ l @ v @ S_2 ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22
% 0.19/0.46 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )
% 0.19/0.46 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) @ R5
% 0.19/0.46 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.19/0.46 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.19/0.46 @ E4 ) ) ) )
% 0.19/0.46 @ R2
% 0.19/0.46 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( ( R2 != R5 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local_and_fork_commute
% 0.19/0.46 thf(fact_19_s_092_060_094sub_0622,axiom,
% 0.19/0.46 ( s_2
% 0.19/0.46 = ( 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 ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ left_forkee ) ) ) ) ) ) ) @ left_forkee
% 0.19/0.46 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 0.19/0.46 @ ( 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 )
% 0.19/0.46 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 0.19/0.46 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 0.19/0.46 @ e3 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % s\<^sub>2
% 0.19/0.46 thf(fact_20_restrictions__inwards,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,X2: A,X3: A,F: A > ( option @ B ),Y: B] :
% 0.19/0.46 ( ( X2 != X3 )
% 0.19/0.46 => ( ( fun_upd @ A @ ( option @ B ) @ ( fun_upd @ A @ ( option @ B ) @ F @ X2 @ ( some @ B @ Y ) ) @ X3 @ ( none @ B ) )
% 0.19/0.46 = ( fun_upd @ A @ ( option @ B ) @ ( fun_upd @ A @ ( option @ B ) @ F @ X3 @ ( none @ B ) ) @ X2 @ ( some @ B @ Y ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % restrictions_inwards
% 0.19/0.46 thf(fact_21_empty__upd__none,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,X2: A] :
% 0.19/0.46 ( ( fun_upd @ A @ ( option @ B )
% 0.19/0.46 @ ^ [X: A] : ( none @ B )
% 0.19/0.46 @ X2
% 0.19/0.46 @ ( none @ B ) )
% 0.19/0.46 = ( ^ [X: A] : ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % empty_upd_none
% 0.19/0.46 thf(fact_22_RID_092_060_094sub_062GI_I1_J,axiom,
% 0.19/0.46 ! [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 ) )] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ V2 ) )
% 0.19/0.46 => ( member @ B @ R2 @ ( rID_G @ B @ A @ C @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % RID\<^sub>GI(1)
% 0.19/0.46 thf(fact_23_not__None__eq,axiom,
% 0.19/0.46 ! [A: $tType,X2: option @ A] :
% 0.19/0.46 ( ( X2
% 0.19/0.46 != ( none @ A ) )
% 0.19/0.46 = ( ? [Y2: A] :
% 0.19/0.46 ( X2
% 0.19/0.46 = ( some @ A @ Y2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_None_eq
% 0.19/0.46 thf(fact_24_not__Some__eq,axiom,
% 0.19/0.46 ! [A: $tType,X2: option @ A] :
% 0.19/0.46 ( ( ! [Y2: A] :
% 0.19/0.46 ( X2
% 0.19/0.46 != ( some @ A @ Y2 ) ) )
% 0.19/0.46 = ( X2
% 0.19/0.46 = ( none @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_Some_eq
% 0.19/0.46 thf(fact_25_s_092_060_094sub_0621__r,axiom,
% 0.19/0.46 ( ( s_1 @ r2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 @ e3 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % s\<^sub>1_r
% 0.19/0.46 thf(fact_26_local__steps__commute,axiom,
% 0.19/0.46 ! [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 ) )] :
% 0.19/0.46 ( ( S_2
% 0.19/0.46 = ( 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 ) ) )
% 0.19/0.46 => ( ( S_22
% 0.19/0.46 = ( 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 ) ) )
% 0.19/0.46 => ( ( 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 ) ) )
% 0.19/0.46 => ( ( 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 ) ) )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local_steps_commute
% 0.19/0.46 thf(fact_27_only__fork__introduces__rids,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ! [Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v] :
% 0.19/0.46 ( ( S @ R2 )
% 0.19/0.46 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 ) ) ) ) ) )
% 0.19/0.46 => ( ord_less_eq @ ( set @ r ) @ ( rID_G @ r @ l @ v @ S2 ) @ ( rID_G @ r @ l @ v @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % only_fork_introduces_rids
% 0.19/0.46 thf(fact_28_local__determinism,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_1 @ S_2 )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_1 @ S_22 )
% 0.19/0.46 => ( eq_states @ r @ l @ v @ S_2 @ S_22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local_determinism
% 0.19/0.46 thf(fact_29_SLC__sym,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_33 @ S_34 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_33 )
% 0.19/0.46 | ( S_2 = S_33 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_34 )
% 0.19/0.46 | ( S_22 = S_34 ) ) )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_3 )
% 0.19/0.46 | ( S_22 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_32 )
% 0.19/0.46 | ( S_2 = S_32 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_sym
% 0.19/0.46 thf(fact_30_SLC__commute,axiom,
% 0.19/0.46 ! [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 ) ) ) ),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 ) ) ) )] :
% 0.19/0.46 ( ( S_35 = S_36 )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_35 )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_36 )
% 0.19/0.46 => ( ( eq_states @ r @ l @ v @ S_35 @ S_36 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_35 )
% 0.19/0.46 | ( S_2 = S_35 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_36 )
% 0.19/0.46 | ( S_22 = S_36 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_commute
% 0.19/0.46 thf(fact_31_reachability__closed__under__execution__step,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( reachable @ r @ l @ v @ subst @ S2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % reachability_closed_under_execution_step
% 0.19/0.46 thf(fact_32_option_Oinject,axiom,
% 0.19/0.46 ! [A: $tType,X22: A,Y22: A] :
% 0.19/0.46 ( ( ( some @ A @ X22 )
% 0.19/0.46 = ( some @ A @ Y22 ) )
% 0.19/0.46 = ( X22 = Y22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % option.inject
% 0.19/0.46 thf(fact_33_transition__relations__equivalent,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ S2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transition_relations_equivalent
% 0.19/0.46 thf(fact_34_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( 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 ) ) ) ) ) ) )
% 0.19/0.46 => ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_restricted_global_in_unrestricted_global(1)
% 0.19/0.46 thf(fact_35_in__restricted__global__in__updated__global_I1_J,axiom,
% 0.19/0.46 ! [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 ) )] :
% 0.19/0.46 ( ( 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 ) ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_restricted_global_in_updated_global(1)
% 0.19/0.46 thf(fact_36_reachable__def,axiom,
% 0.19/0.46 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 = ( ? [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 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % reachable_def
% 0.19/0.46 thf(fact_37_substitution_Olocal__determinism,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_1 @ S_2 )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_1 @ S_22 )
% 0.19/0.46 => ( eq_states @ R @ L @ V @ S_2 @ S_22 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.local_determinism
% 0.19/0.46 thf(fact_38_substitution_OSLC__commute,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ 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 ) ) ) ),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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( S_35 = S_36 )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_35 )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_36 )
% 0.19/0.46 => ( ( eq_states @ R @ L @ V @ S_35 @ S_36 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_35 )
% 0.19/0.46 | ( S_2 = S_35 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_36 )
% 0.19/0.46 | ( S_22 = S_36 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.SLC_commute
% 0.19/0.46 thf(fact_39_substitution_OSLC__sym,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_33 @ S_34 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_33 )
% 0.19/0.46 | ( S_2 = S_33 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_34 )
% 0.19/0.46 | ( S_22 = S_34 ) ) )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_3 )
% 0.19/0.46 | ( S_22 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_32 )
% 0.19/0.46 | ( S_2 = S_32 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.SLC_sym
% 0.19/0.46 thf(fact_40_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 0.19/0.46 ! [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 ) ) ).
% 0.19/0.46
% 0.19/0.46 % ID_restricted_global_subset_unrestricted(2)
% 0.19/0.46 thf(fact_41_substitution_Olocal__steps__commute,axiom,
% 0.19/0.46 ! [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 ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) )
% 0.19/0.46 => ( ( S_22
% 0.19/0.46 = ( 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 ) ) )
% 0.19/0.46 => ( ( 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 ) ) )
% 0.19/0.46 => ( ( 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 ) ) )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.local_steps_commute
% 0.19/0.46 thf(fact_42_substitution_Olocal__and__fork__commute,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,R5: R,E4: expr @ R @ L @ V] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) )
% 0.19/0.46 => ( ( S_22
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) @ R5
% 0.19/0.46 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 0.19/0.46 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 0.19/0.46 @ E4 ) ) ) ) )
% 0.19/0.46 => ( ( ( S_2 @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ R @ R5 @ ( rID_G @ R @ L @ V @ S_2 ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22
% 0.19/0.46 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )
% 0.19/0.46 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) @ R5
% 0.19/0.46 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 0.19/0.46 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 0.19/0.46 @ E4 ) ) ) )
% 0.19/0.46 @ R2
% 0.19/0.46 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( ( R2 != R5 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.local_and_fork_commute
% 0.19/0.46 thf(fact_43_combine__options__cases,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,X2: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 0.19/0.46 ( ( ( X2
% 0.19/0.46 = ( none @ A ) )
% 0.19/0.46 => ( P @ X2 @ Y ) )
% 0.19/0.46 => ( ( ( Y
% 0.19/0.46 = ( none @ B ) )
% 0.19/0.46 => ( P @ X2 @ Y ) )
% 0.19/0.46 => ( ! [A2: A,B2: B] :
% 0.19/0.46 ( ( X2
% 0.19/0.46 = ( some @ A @ A2 ) )
% 0.19/0.46 => ( ( Y
% 0.19/0.46 = ( some @ B @ B2 ) )
% 0.19/0.46 => ( P @ X2 @ Y ) ) )
% 0.19/0.46 => ( P @ X2 @ Y ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % combine_options_cases
% 0.19/0.46 thf(fact_44_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: $tType,A3: A,P: A > $o] :
% 0.19/0.46 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.19/0.46 = ( P @ A3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_45_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A: $tType,A4: set @ A] :
% 0.19/0.46 ( ( collect @ A
% 0.19/0.46 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.19/0.46 = A4 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_46_Collect__cong,axiom,
% 0.19/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.46 ( ! [X4: A] :
% 0.19/0.46 ( ( P @ X4 )
% 0.19/0.46 = ( Q @ X4 ) )
% 0.19/0.46 => ( ( collect @ A @ P )
% 0.19/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_cong
% 0.19/0.46 thf(fact_47_ext,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.19/0.46 ( ! [X4: A] :
% 0.19/0.46 ( ( F @ X4 )
% 0.19/0.46 = ( G @ X4 ) )
% 0.19/0.46 => ( F = G ) ) ).
% 0.19/0.46
% 0.19/0.46 % ext
% 0.19/0.46 thf(fact_48_split__option__all,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.19/0.46 ! [X5: option @ A] : ( P2 @ X5 ) )
% 0.19/0.46 = ( ^ [P3: ( option @ A ) > $o] :
% 0.19/0.46 ( ( P3 @ ( none @ A ) )
% 0.19/0.46 & ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % split_option_all
% 0.19/0.46 thf(fact_49_split__option__ex,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.19/0.46 ? [X5: option @ A] : ( P2 @ X5 ) )
% 0.19/0.46 = ( ^ [P3: ( option @ A ) > $o] :
% 0.19/0.46 ( ( P3 @ ( none @ A ) )
% 0.19/0.46 | ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % split_option_ex
% 0.19/0.46 thf(fact_50_option_Oinducts,axiom,
% 0.19/0.46 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.19/0.46 ( ( P @ ( none @ A ) )
% 0.19/0.46 => ( ! [X4: A] : ( P @ ( some @ A @ X4 ) )
% 0.19/0.46 => ( P @ Option ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % option.inducts
% 0.19/0.46 thf(fact_51_option_Oexhaust,axiom,
% 0.19/0.46 ! [A: $tType,Y: option @ A] :
% 0.19/0.46 ( ( Y
% 0.19/0.46 != ( none @ A ) )
% 0.19/0.46 => ~ ! [X23: A] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( some @ A @ X23 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % option.exhaust
% 0.19/0.46 thf(fact_52_option_OdiscI,axiom,
% 0.19/0.46 ! [A: $tType,Option: option @ A,X22: A] :
% 0.19/0.46 ( ( Option
% 0.19/0.46 = ( some @ A @ X22 ) )
% 0.19/0.46 => ( Option
% 0.19/0.46 != ( none @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % option.discI
% 0.19/0.46 thf(fact_53_option_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,X22: A] :
% 0.19/0.46 ( ( none @ A )
% 0.19/0.46 != ( some @ A @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % option.distinct(1)
% 0.19/0.46 thf(fact_54_map__upd__Some__unfold,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,M: B > ( option @ A ),A3: B,B3: A,X2: B,Y: A] :
% 0.19/0.46 ( ( ( fun_upd @ B @ ( option @ A ) @ M @ A3 @ ( some @ A @ B3 ) @ X2 )
% 0.19/0.46 = ( some @ A @ Y ) )
% 0.19/0.46 = ( ( ( X2 = A3 )
% 0.19/0.46 & ( B3 = Y ) )
% 0.19/0.46 | ( ( X2 != A3 )
% 0.19/0.46 & ( ( M @ X2 )
% 0.19/0.46 = ( some @ A @ Y ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % map_upd_Some_unfold
% 0.19/0.46 thf(fact_55_map__upd__triv,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,T: B > ( option @ A ),K: B,X2: A] :
% 0.19/0.46 ( ( ( T @ K )
% 0.19/0.46 = ( some @ A @ X2 ) )
% 0.19/0.46 => ( ( fun_upd @ B @ ( option @ A ) @ T @ K @ ( some @ A @ X2 ) )
% 0.19/0.46 = T ) ) ).
% 0.19/0.46
% 0.19/0.46 % map_upd_triv
% 0.19/0.46 thf(fact_56_map__upd__eqD1,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,M: A > ( option @ B ),A3: A,X2: B,N: A > ( option @ B ),Y: B] :
% 0.19/0.46 ( ( ( fun_upd @ A @ ( option @ B ) @ M @ A3 @ ( some @ B @ X2 ) )
% 0.19/0.46 = ( fun_upd @ A @ ( option @ B ) @ N @ A3 @ ( some @ B @ Y ) ) )
% 0.19/0.46 => ( X2 = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % map_upd_eqD1
% 0.19/0.46 thf(fact_57_map__upd__nonempty,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,T: A > ( option @ B ),K: A,X2: B] :
% 0.19/0.46 ( ( fun_upd @ A @ ( option @ B ) @ T @ K @ ( some @ B @ X2 ) )
% 0.19/0.46 != ( ^ [X: A] : ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % map_upd_nonempty
% 0.19/0.46 thf(fact_58_substitution_Ofork__pseudodeterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( ? [R4: R] :
% 0.19/0.46 ( ~ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( rfork @ R @ L @ V @ E4 ) ) ) ) ) ) ) )
% 0.19/0.46 & ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R4 ) ) ) ) ) ) ) @ R4
% 0.19/0.46 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 0.19/0.46 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 0.19/0.46 @ E4 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.fork_pseudodeterministic
% 0.19/0.46 thf(fact_59_inductive__invariant__is__execution__invariant,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( ( inductive_invariant @ r @ l @ v @ subst @ P )
% 0.19/0.46 => ( P @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % inductive_invariant_is_execution_invariant
% 0.19/0.46 thf(fact_60_substitution_Orevision__step__relaxed_Ofork,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: expr @ R @ L @ V,R3: R] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 0.19/0.46 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S
% 0.19/0.46 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) @ R3
% 0.19/0.46 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 0.19/0.46 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 0.19/0.46 @ E4 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step_relaxed.fork
% 0.19/0.46 thf(fact_61_substitution_Orevision__step_Ofork,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: expr @ R @ L @ V,R3: R] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 0.19/0.46 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S
% 0.19/0.46 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) @ R3
% 0.19/0.46 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 0.19/0.46 @ ( 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 ) @ Sigma2 @ Tau2 )
% 0.19/0.46 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 0.19/0.46 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 0.19/0.46 @ E4 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step.fork
% 0.19/0.46 thf(fact_62_substitution_Oonly__fork__introduces__rids,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V] :
% 0.19/0.46 ( ( S @ R2 )
% 0.19/0.46 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ 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 ) ) ) ) ) )
% 0.19/0.46 => ( ord_less_eq @ ( set @ R ) @ ( rID_G @ R @ L @ V @ S2 ) @ ( rID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.only_fork_introduces_rids
% 0.19/0.46 thf(fact_63_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.19/0.46 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( domain398919503obally @ r @ l @ v @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % reachable_imp_\<S>\<^sub>G
% 0.19/0.46 thf(fact_64_substitution_Oonly__fork__introduces__rids_H,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V] :
% 0.19/0.46 ( ( S @ R2 )
% 0.19/0.46 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ 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 ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 0.19/0.46 => ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.only_fork_introduces_rids'
% 0.19/0.46 thf(fact_65_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S_1 @ R5 )
% 0.19/0.46 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_join\<^sub>\<epsilon>
% 0.19/0.46 thf(fact_66_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,R3: r] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 0.19/0.46 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S
% 0.19/0.46 @ ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step_relaxed.join\<^sub>\<epsilon>
% 0.19/0.46 thf(fact_67_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,R3: r] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 0.19/0.46 => ( revision_step @ r @ l @ v @ subst @ R2 @ S
% 0.19/0.46 @ ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step.join\<^sub>\<epsilon>
% 0.19/0.46 thf(fact_68_domains__subsume__globally__def,axiom,
% 0.19/0.46 ( ( domain398919503obally @ r @ l @ v )
% 0.19/0.46 = ( ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ! [R6: r,Ls2: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) )] :
% 0.19/0.46 ( ( ( S4 @ R6 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Ls2 ) )
% 0.19/0.46 => ( domains_subsume @ l @ r @ v @ Ls2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % domains_subsume_globally_def
% 0.19/0.46 thf(fact_69_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( S2
% 0.19/0.46 = ( ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rjoin\<^sub>\<epsilon>_deterministic
% 0.19/0.46 thf(fact_70_substitution_Orevision__step_Ocong,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType] :
% 0.19/0.46 ( ( revision_step @ R @ L @ V )
% 0.19/0.46 = ( revision_step @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step.cong
% 0.19/0.46 thf(fact_71_substitution_Orevision__step__relaxed_Ocong,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType] :
% 0.19/0.46 ( ( revisi1433015572elaxed @ R @ L @ V )
% 0.19/0.46 = ( revisi1433015572elaxed @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step_relaxed.cong
% 0.19/0.46 thf(fact_72_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,R3: R] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 0.19/0.46 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S
% 0.19/0.46 @ ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step.join\<^sub>\<epsilon>
% 0.19/0.46 thf(fact_73_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,R3: R] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 0.19/0.46 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S
% 0.19/0.46 @ ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step_relaxed.join\<^sub>\<epsilon>
% 0.19/0.46 thf(fact_74_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( S2
% 0.19/0.46 = ( ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.rjoin\<^sub>\<epsilon>_deterministic
% 0.19/0.46 thf(fact_75_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S_1 @ R5 )
% 0.19/0.46 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.SLC_join\<^sub>\<epsilon>
% 0.19/0.46 thf(fact_76_nice__ind__inv__is__inductive__invariant,axiom,
% 0.19/0.46 ( inductive_invariant @ r @ l @ v @ subst
% 0.19/0.46 @ ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ( domain398919503obally @ r @ l @ v @ S4 )
% 0.19/0.46 & ( subsum380726323obally @ r @ l @ v @ S4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nice_ind_inv_is_inductive_invariant
% 0.19/0.46 thf(fact_77_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ( domain398919503obally @ r @ l @ v @ S )
% 0.19/0.46 => ( ( subsum380726323obally @ r @ l @ v @ S )
% 0.19/0.46 => ( subsum380726323obally @ r @ l @ v @ S2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.19/0.46 thf(fact_78_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ( domain398919503obally @ r @ l @ v @ S )
% 0.19/0.46 => ( ( subsum380726323obally @ r @ l @ v @ S )
% 0.19/0.46 => ( domain398919503obally @ r @ l @ v @ S2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.19/0.46 thf(fact_79_substitution_Odomains__subsume__globallyI,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ! [R7: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E2: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ( S @ R7 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ E2 ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ E2 ) ) ) )
% 0.19/0.46 => ( domain398919503obally @ R @ L @ V @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.domains_subsume_globallyI
% 0.19/0.46 thf(fact_80_substitution_Otransition__relations__equivalent,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ S2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.transition_relations_equivalent
% 0.19/0.46 thf(fact_81_domains__subsume__globallyI,axiom,
% 0.19/0.46 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ! [R7: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E2: expr @ r @ l @ v] :
% 0.19/0.46 ( ( ( S @ R7 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ E2 ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ E2 ) ) ) )
% 0.19/0.46 => ( domain398919503obally @ r @ l @ v @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % domains_subsume_globallyI
% 0.19/0.46 thf(fact_82_substitution_Oreachable__def,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 = ( ? [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 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.reachable_def
% 0.19/0.46 thf(fact_83_substitution_Oreachable_Ocong,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType] :
% 0.19/0.46 ( ( reachable @ R @ L @ V )
% 0.19/0.46 = ( reachable @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.reachable.cong
% 0.19/0.46 thf(fact_84_substitution_Oinductive__invariant_Ocong,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType] :
% 0.19/0.46 ( ( inductive_invariant @ R @ L @ V )
% 0.19/0.46 = ( inductive_invariant @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.inductive_invariant.cong
% 0.19/0.46 thf(fact_85_substitution_Oexecution_Ocong,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType] :
% 0.19/0.46 ( ( execution @ R @ L @ V )
% 0.19/0.46 = ( execution @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.execution.cong
% 0.19/0.46 thf(fact_86_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( inductive_invariant @ R @ L @ V @ Subst
% 0.19/0.46 @ ^ [S4: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 0.19/0.46 ( ( domain398919503obally @ R @ L @ V @ S4 )
% 0.19/0.46 & ( subsum380726323obally @ R @ L @ V @ S4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.nice_ind_inv_is_inductive_invariant
% 0.19/0.46 thf(fact_87_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ( domain398919503obally @ R @ L @ V @ S )
% 0.19/0.46 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 0.19/0.46 => ( subsum380726323obally @ R @ L @ V @ S2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.19/0.46 thf(fact_88_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ( domain398919503obally @ R @ L @ V @ S )
% 0.19/0.46 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 0.19/0.46 => ( domain398919503obally @ R @ L @ V @ S2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.19/0.46 thf(fact_89_substitution_Odomains__subsume__globally__def,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( domain398919503obally @ R @ L @ V @ S )
% 0.19/0.46 = ( ! [R6: R,Ls2: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 0.19/0.46 ( ( ( S @ R6 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Ls2 ) )
% 0.19/0.46 => ( domains_subsume @ L @ R @ V @ Ls2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.domains_subsume_globally_def
% 0.19/0.46 thf(fact_90_substitution_Oreachability__closed__under__execution__step,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( reachable @ R @ L @ V @ Subst @ S2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.reachability_closed_under_execution_step
% 0.19/0.46 thf(fact_91_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 => ( domain398919503obally @ R @ L @ V @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.reachable_imp_\<S>\<^sub>G
% 0.19/0.46 thf(fact_92_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 => ( ( inductive_invariant @ R @ L @ V @ Subst @ P )
% 0.19/0.46 => ( P @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.inductive_invariant_is_execution_invariant
% 0.19/0.46 thf(fact_93_substitution_Osubsumes__accessible__globallyI,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ! [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] :
% 0.19/0.46 ( ( ( S @ R_1 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ 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 ) ) ) )
% 0.19/0.46 => ( ( ( S @ R_2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ 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 ) ) ) )
% 0.19/0.46 => ( subsumes_accessible @ R @ L @ V @ R_1 @ R_2 @ S ) ) )
% 0.19/0.46 => ( subsum380726323obally @ R @ L @ V @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.subsumes_accessible_globallyI
% 0.19/0.46 thf(fact_94_join__and__local__commute,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),E3: 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] :
% 0.19/0.46 ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ( S_22
% 0.19/0.46 = ( 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 ) ) )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( ( R3 != R5 )
% 0.19/0.46 => ( ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) )
% 0.19/0.46 => ( ( ( S_22 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S_22 @ R5 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % join_and_local_commute
% 0.19/0.46 thf(fact_95_SLC__join,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S_1 @ R5 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_join
% 0.19/0.46 thf(fact_96_revision__step__relaxed_Ojoin,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step_relaxed.join
% 0.19/0.46 thf(fact_97_reachable__imp__identifiers__finite_I1_J,axiom,
% 0.19/0.46 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( finite_finite2 @ r @ ( rID_G @ r @ l @ v @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % reachable_imp_identifiers_finite(1)
% 0.19/0.46 thf(fact_98_revision__step_Ojoin,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step.join
% 0.19/0.46 thf(fact_99_empty__map__finite_I3_J,axiom,
% 0.19/0.46 ! [H: $tType,I: $tType,G2: $tType] :
% 0.19/0.46 ( finite_finite2 @ G2
% 0.19/0.46 @ ( rID_G @ G2 @ H @ I
% 0.19/0.46 @ ^ [X: G2] : ( none @ ( product_prod @ ( H > ( option @ ( val @ G2 @ H @ I ) ) ) @ ( product_prod @ ( H > ( option @ ( val @ G2 @ H @ I ) ) ) @ ( expr @ G2 @ H @ I ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % empty_map_finite(3)
% 0.19/0.46 thf(fact_100_rid__inf,axiom,
% 0.19/0.46 ~ ( finite_finite2 @ r @ ( top_top @ ( set @ r ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rid_inf
% 0.19/0.46 thf(fact_101_RID_092_060_094sub_062G__finite__invariant,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ( finite_finite2 @ r @ ( rID_G @ r @ l @ v @ S ) )
% 0.19/0.46 => ( finite_finite2 @ r @ ( rID_G @ r @ l @ v @ S2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % RID\<^sub>G_finite_invariant
% 0.19/0.46 thf(fact_102_finite__state__imp__restriction__finite_I1_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( finite_finite2 @ A @ ( rID_G @ A @ B @ C @ S ) )
% 0.19/0.46 => ( finite_finite2 @ 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 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_state_imp_restriction_finite(1)
% 0.19/0.46 thf(fact_103_subsumes__accessible__globallyI,axiom,
% 0.19/0.46 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ! [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] :
% 0.19/0.46 ( ( ( S @ R_1 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ 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 ) ) ) )
% 0.19/0.46 => ( ( ( S @ R_2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ 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 ) ) ) )
% 0.19/0.46 => ( subsumes_accessible @ r @ l @ v @ R_1 @ R_2 @ S ) ) )
% 0.19/0.46 => ( subsum380726323obally @ r @ l @ v @ S ) ) ).
% 0.19/0.46
% 0.19/0.46 % subsumes_accessible_globallyI
% 0.19/0.46 thf(fact_104_rjoin__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rjoin_deterministic
% 0.19/0.46 thf(fact_105_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ( finite_finite2 @ R @ ( rID_G @ R @ L @ V @ S ) )
% 0.19/0.46 => ( finite_finite2 @ R @ ( rID_G @ R @ L @ V @ S2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.RID\<^sub>G_finite_invariant
% 0.19/0.46 thf(fact_106_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 => ( finite_finite2 @ R @ ( rID_G @ R @ L @ V @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.reachable_imp_identifiers_finite(1)
% 0.19/0.46 thf(fact_107_substitution_Oempty__map__finite_I3_J,axiom,
% 0.19/0.46 ! [R: $tType,L: $tType,V: $tType,H: $tType,I: $tType,G2: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( finite_finite2 @ G2
% 0.19/0.46 @ ( rID_G @ G2 @ H @ I
% 0.19/0.46 @ ^ [X: G2] : ( none @ ( product_prod @ ( H > ( option @ ( val @ G2 @ H @ I ) ) ) @ ( product_prod @ ( H > ( option @ ( val @ G2 @ H @ I ) ) ) @ ( expr @ G2 @ H @ I ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.empty_map_finite(3)
% 0.19/0.46 thf(fact_108_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( finite_finite2 @ A @ ( rID_G @ A @ B @ C @ S ) )
% 0.19/0.46 => ( finite_finite2 @ 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 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.finite_state_imp_restriction_finite(1)
% 0.19/0.46 thf(fact_109_substitution_Orevision__step_Ojoin,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step.join
% 0.19/0.46 thf(fact_110_substitution_Orjoin__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.rjoin_deterministic
% 0.19/0.46 thf(fact_111_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step_relaxed.join
% 0.19/0.46 thf(fact_112_substitution_OSLC__join,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S_1 @ R5 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.SLC_join
% 0.19/0.46 thf(fact_113_substitution_Ojoin__and__local__commute,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),E3: 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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) )
% 0.19/0.46 => ( ( S_22
% 0.19/0.46 = ( 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 ) ) )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( ( R3 != R5 )
% 0.19/0.46 => ( ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) )
% 0.19/0.46 => ( ( ( S_22 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( ( S_22 @ R5 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.join_and_local_commute
% 0.19/0.46 thf(fact_114_finite__Collect__subsets,axiom,
% 0.19/0.46 ! [A: $tType,A4: set @ A] :
% 0.19/0.46 ( ( finite_finite2 @ A @ A4 )
% 0.19/0.46 => ( finite_finite2 @ ( set @ A )
% 0.19/0.46 @ ( collect @ ( set @ A )
% 0.19/0.46 @ ^ [B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_Collect_subsets
% 0.19/0.46 thf(fact_115_reachable__imp__identifiers__available_I1_J,axiom,
% 0.19/0.46 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( ~ ( finite_finite2 @ r @ ( top_top @ ( set @ r ) ) )
% 0.19/0.46 => ? [R7: r] :
% 0.19/0.46 ~ ( member @ r @ R7 @ ( rID_G @ r @ l @ v @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % reachable_imp_identifiers_available(1)
% 0.19/0.46 thf(fact_116_finite__Collect__conjI,axiom,
% 0.19/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.46 ( ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 0.19/0.46 | ( finite_finite2 @ A @ ( collect @ A @ Q ) ) )
% 0.19/0.46 => ( finite_finite2 @ A
% 0.19/0.46 @ ( collect @ A
% 0.19/0.46 @ ^ [X: A] :
% 0.19/0.46 ( ( P @ X )
% 0.19/0.46 & ( Q @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_Collect_conjI
% 0.19/0.46 thf(fact_117_finite__Collect__disjI,axiom,
% 0.19/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.46 ( ( finite_finite2 @ A
% 0.19/0.46 @ ( collect @ A
% 0.19/0.46 @ ^ [X: A] :
% 0.19/0.46 ( ( P @ X )
% 0.19/0.46 | ( Q @ X ) ) ) )
% 0.19/0.46 = ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 0.19/0.46 & ( finite_finite2 @ A @ ( collect @ A @ Q ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_Collect_disjI
% 0.19/0.46 thf(fact_118_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.19/0.46 => ( ( finite_finite2 @ 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 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( finite_finite2 @ B @ ( rID_L @ A @ B @ C @ Ls ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local_state_of_finite_restricted_global_state_is_finite(1)
% 0.19/0.46 thf(fact_119_finite__code,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( finite_finite @ A )
% 0.19/0.46 => ( ( finite_finite2 @ A )
% 0.19/0.46 = ( ^ [A5: set @ A] : $true ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_code
% 0.19/0.46 thf(fact_120_finite__option__UNIV,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( finite_finite2 @ ( option @ A ) @ ( top_top @ ( set @ ( option @ A ) ) ) )
% 0.19/0.46 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_option_UNIV
% 0.19/0.46 thf(fact_121_finite__Plus__UNIV__iff,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType] :
% 0.19/0.46 ( ( finite_finite2 @ ( sum_sum @ A @ B ) @ ( top_top @ ( set @ ( sum_sum @ A @ B ) ) ) )
% 0.19/0.46 = ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.19/0.46 & ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_Plus_UNIV_iff
% 0.19/0.46 thf(fact_122_finite__Collect__not,axiom,
% 0.19/0.46 ! [A: $tType,P: A > $o] :
% 0.19/0.46 ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 0.19/0.46 => ( ( finite_finite2 @ A
% 0.19/0.46 @ ( collect @ A
% 0.19/0.46 @ ^ [X: A] :
% 0.19/0.46 ~ ( P @ X ) ) )
% 0.19/0.46 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_Collect_not
% 0.19/0.46 thf(fact_123_RID_092_060_094sub_062GI_I2_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.19/0.46 => ( ( member @ B @ R2 @ ( rID_L @ A @ B @ C @ Ls ) )
% 0.19/0.46 => ( member @ B @ R2 @ ( rID_G @ B @ A @ C @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % RID\<^sub>GI(2)
% 0.19/0.46 thf(fact_124_Finite__Set_Ofinite__set,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( finite_finite2 @ ( set @ A ) @ ( top_top @ ( set @ ( set @ A ) ) ) )
% 0.19/0.46 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Finite_Set.finite_set
% 0.19/0.46 thf(fact_125_finite__prod,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType] :
% 0.19/0.46 ( ( finite_finite2 @ ( product_prod @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 0.19/0.46 = ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.19/0.46 & ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_prod
% 0.19/0.46 thf(fact_126_ex__new__if__finite,axiom,
% 0.19/0.46 ! [A: $tType,A4: set @ A] :
% 0.19/0.46 ( ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.19/0.46 => ( ( finite_finite2 @ A @ A4 )
% 0.19/0.46 => ? [A2: A] :
% 0.19/0.46 ~ ( member @ A @ A2 @ A4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ex_new_if_finite
% 0.19/0.46 thf(fact_127_finite__Prod__UNIV,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.19/0.46 => ( ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) )
% 0.19/0.46 => ( finite_finite2 @ ( product_prod @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_Prod_UNIV
% 0.19/0.46 thf(fact_128_finite__fun__UNIVD2,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType] :
% 0.19/0.46 ( ( finite_finite2 @ ( A > B ) @ ( top_top @ ( set @ ( A > B ) ) ) )
% 0.19/0.46 => ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_fun_UNIVD2
% 0.19/0.46 thf(fact_129_infinite__UNIV__char__0,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( semiring_char_0 @ A )
% 0.19/0.46 => ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % infinite_UNIV_char_0
% 0.19/0.46 thf(fact_130_finite__UNIV,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( finite_finite @ A )
% 0.19/0.46 => ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_UNIV
% 0.19/0.46 thf(fact_131_finite,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( finite_finite @ A )
% 0.19/0.46 => ! [A4: set @ A] : ( finite_finite2 @ A @ A4 ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite
% 0.19/0.46 thf(fact_132_finite__set__choice,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A4: set @ A,P: A > B > $o] :
% 0.19/0.46 ( ( finite_finite2 @ A @ A4 )
% 0.19/0.46 => ( ! [X4: A] :
% 0.19/0.46 ( ( member @ A @ X4 @ A4 )
% 0.19/0.46 => ? [X_1: B] : ( P @ X4 @ X_1 ) )
% 0.19/0.46 => ? [F2: A > B] :
% 0.19/0.46 ! [X6: A] :
% 0.19/0.46 ( ( member @ A @ X6 @ A4 )
% 0.19/0.46 => ( P @ X6 @ ( F2 @ X6 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_set_choice
% 0.19/0.46 thf(fact_133_pigeonhole__infinite__rel,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A4: set @ A,B5: set @ B,R8: A > B > $o] :
% 0.19/0.46 ( ~ ( finite_finite2 @ A @ A4 )
% 0.19/0.46 => ( ( finite_finite2 @ B @ B5 )
% 0.19/0.46 => ( ! [X4: A] :
% 0.19/0.46 ( ( member @ A @ X4 @ A4 )
% 0.19/0.46 => ? [Xa: B] :
% 0.19/0.46 ( ( member @ B @ Xa @ B5 )
% 0.19/0.46 & ( R8 @ X4 @ Xa ) ) )
% 0.19/0.46 => ? [X4: B] :
% 0.19/0.46 ( ( member @ B @ X4 @ B5 )
% 0.19/0.46 & ~ ( finite_finite2 @ A
% 0.19/0.46 @ ( collect @ A
% 0.19/0.46 @ ^ [A6: A] :
% 0.19/0.46 ( ( member @ A @ A6 @ A4 )
% 0.19/0.46 & ( R8 @ A6 @ X4 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pigeonhole_infinite_rel
% 0.19/0.46 thf(fact_134_not__finite__existsD,axiom,
% 0.19/0.46 ! [A: $tType,P: A > $o] :
% 0.19/0.46 ( ~ ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 0.19/0.46 => ? [X_12: A] : ( P @ X_12 ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_finite_existsD
% 0.19/0.46 thf(fact_135_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 => ( ~ ( finite_finite2 @ R @ ( top_top @ ( set @ R ) ) )
% 0.19/0.46 => ? [R7: R] :
% 0.19/0.46 ~ ( member @ R @ R7 @ ( rID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.reachable_imp_identifiers_available(1)
% 0.19/0.46 thf(fact_136_finite__has__minimal2,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [A4: set @ A,A3: A] :
% 0.19/0.46 ( ( finite_finite2 @ A @ A4 )
% 0.19/0.46 => ( ( member @ A @ A3 @ A4 )
% 0.19/0.46 => ? [X4: A] :
% 0.19/0.46 ( ( member @ A @ X4 @ A4 )
% 0.19/0.46 & ( ord_less_eq @ A @ X4 @ A3 )
% 0.19/0.46 & ! [Xa: A] :
% 0.19/0.46 ( ( member @ A @ Xa @ A4 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ Xa @ X4 )
% 0.19/0.46 => ( X4 = Xa ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_has_minimal2
% 0.19/0.46 thf(fact_137_finite__has__maximal2,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [A4: set @ A,A3: A] :
% 0.19/0.46 ( ( finite_finite2 @ A @ A4 )
% 0.19/0.46 => ( ( member @ A @ A3 @ A4 )
% 0.19/0.46 => ? [X4: A] :
% 0.19/0.46 ( ( member @ A @ X4 @ A4 )
% 0.19/0.46 & ( ord_less_eq @ A @ A3 @ X4 )
% 0.19/0.46 & ! [Xa: A] :
% 0.19/0.46 ( ( member @ A @ Xa @ A4 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ X4 @ Xa )
% 0.19/0.46 => ( X4 = Xa ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_has_maximal2
% 0.19/0.46 thf(fact_138_finite__subset,axiom,
% 0.19/0.46 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.19/0.46 => ( ( finite_finite2 @ A @ B5 )
% 0.19/0.46 => ( finite_finite2 @ A @ A4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_subset
% 0.19/0.46 thf(fact_139_infinite__super,axiom,
% 0.19/0.46 ! [A: $tType,S5: set @ A,T2: set @ A] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ S5 @ T2 )
% 0.19/0.46 => ( ~ ( finite_finite2 @ A @ S5 )
% 0.19/0.46 => ~ ( finite_finite2 @ A @ T2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % infinite_super
% 0.19/0.46 thf(fact_140_rev__finite__subset,axiom,
% 0.19/0.46 ! [A: $tType,B5: set @ A,A4: set @ A] :
% 0.19/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.19/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.19/0.46 => ( finite_finite2 @ A @ A4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rev_finite_subset
% 0.19/0.46 thf(fact_141_finite__update__induct,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,C2: B,P: ( A > B ) > $o] :
% 0.19/0.46 ( ( finite_finite2 @ A
% 0.19/0.46 @ ( collect @ A
% 0.19/0.46 @ ^ [A6: A] :
% 0.19/0.46 ( ( F @ A6 )
% 0.19/0.46 != C2 ) ) )
% 0.19/0.46 => ( ( P
% 0.19/0.46 @ ^ [A6: A] : C2 )
% 0.19/0.46 => ( ! [A2: A,B2: B,F2: A > B] :
% 0.19/0.46 ( ( finite_finite2 @ A
% 0.19/0.46 @ ( collect @ A
% 0.19/0.46 @ ^ [C3: A] :
% 0.19/0.46 ( ( F2 @ C3 )
% 0.19/0.46 != C2 ) ) )
% 0.19/0.46 => ( ( ( F2 @ A2 )
% 0.19/0.46 = C2 )
% 0.19/0.46 => ( ( B2 != C2 )
% 0.19/0.46 => ( ( P @ F2 )
% 0.19/0.46 => ( P @ ( fun_upd @ A @ B @ F2 @ A2 @ B2 ) ) ) ) ) )
% 0.19/0.46 => ( P @ F ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_update_induct
% 0.19/0.46 thf(fact_142_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.19/0.46 => ( ( finite_finite2 @ 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 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( finite_finite2 @ B @ ( rID_L @ A @ B @ C @ Ls ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.local_state_of_finite_restricted_global_state_is_finite(1)
% 0.19/0.46 thf(fact_143_SLC__ifTrue,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: 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 ) ) ) ),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 ) ) ) )] :
% 0.19/0.46 ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E1 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_ifTrue
% 0.19/0.46 thf(fact_144_SLC__ifFalse,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: 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 ) ) ) ),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 ) ) ) )] :
% 0.19/0.46 ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_ifFalse
% 0.19/0.46 thf(fact_145_expr_Oinject_I7_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X7: expr @ R @ L @ V,Y7: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ( rfork @ R @ L @ V @ X7 )
% 0.19/0.46 = ( rfork @ R @ L @ V @ Y7 ) )
% 0.19/0.46 = ( X7 = Y7 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.inject(7)
% 0.19/0.46 thf(fact_146_val_Oinject_I4_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X42: R,Y4: R] :
% 0.19/0.46 ( ( ( rid @ R @ L @ V @ X42 )
% 0.19/0.46 = ( rid @ R @ L @ V @ Y4 ) )
% 0.19/0.46 = ( X42 = Y4 ) ) ).
% 0.19/0.46
% 0.19/0.46 % val.inject(4)
% 0.19/0.46 thf(fact_147_expr_Oinject_I1_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,Y1: val @ R @ L @ V] :
% 0.19/0.46 ( ( ( ve @ R @ L @ V @ X1 )
% 0.19/0.46 = ( ve @ R @ L @ V @ Y1 ) )
% 0.19/0.46 = ( X1 = Y1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.inject(1)
% 0.19/0.46 thf(fact_148_injective__cntxt,axiom,
% 0.19/0.46 ! [C: $tType,B: $tType,A: $tType,E3: cntxt @ A @ B @ C,E1: expr @ A @ B @ C,E22: expr @ A @ B @ C] :
% 0.19/0.46 ( ( ( plug @ A @ B @ C @ E3 @ E1 )
% 0.19/0.46 = ( plug @ A @ B @ C @ E3 @ E22 ) )
% 0.19/0.46 = ( E1 = E22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % injective_cntxt
% 0.19/0.46 thf(fact_149_val_Oinject_I1_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X1: const,Y1: const] :
% 0.19/0.46 ( ( ( cv @ R @ L @ V @ X1 )
% 0.19/0.46 = ( cv @ R @ L @ V @ Y1 ) )
% 0.19/0.46 = ( X1 = Y1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % val.inject(1)
% 0.19/0.46 thf(fact_150_expr_Oinject_I8_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X8: expr @ R @ L @ V,Y8: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ( rjoin @ R @ L @ V @ X8 )
% 0.19/0.46 = ( rjoin @ R @ L @ V @ Y8 ) )
% 0.19/0.46 = ( X8 = Y8 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.inject(8)
% 0.19/0.46 thf(fact_151_revision__step_OifFalse,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E22 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step.ifFalse
% 0.19/0.46 thf(fact_152_revision__step_OifTrue,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E1 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step.ifTrue
% 0.19/0.46 thf(fact_153_revision__step__relaxed_OifFalse,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E22 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step_relaxed.ifFalse
% 0.19/0.46 thf(fact_154_revision__step__relaxed_OifTrue,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E1 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step_relaxed.ifTrue
% 0.19/0.46 thf(fact_155_ifFalse__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ifFalse_deterministic
% 0.19/0.46 thf(fact_156_ifTrue__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ifTrue_deterministic
% 0.19/0.46 thf(fact_157_expr_Odistinct_I35_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 0.19/0.46 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(35)
% 0.19/0.46 thf(fact_158_expr_Odistinct_I33_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 0.19/0.46 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(33)
% 0.19/0.46 thf(fact_159_expr_Odistinct_I3_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( ve @ R @ L @ V @ X1 )
% 0.19/0.46 != ( ite @ R @ L @ V @ X31 @ X32 @ X33 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(3)
% 0.19/0.46 thf(fact_160_const_Oexhaust,axiom,
% 0.19/0.46 ! [Y: const] :
% 0.19/0.46 ( ( Y != unit )
% 0.19/0.46 => ( ( Y != f )
% 0.19/0.46 => ( Y = t ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % const.exhaust
% 0.19/0.46 thf(fact_161_const_Oinduct,axiom,
% 0.19/0.46 ! [P: const > $o,Const: const] :
% 0.19/0.46 ( ( P @ unit )
% 0.19/0.46 => ( ( P @ f )
% 0.19/0.46 => ( ( P @ t )
% 0.19/0.46 => ( P @ Const ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % const.induct
% 0.19/0.46 thf(fact_162_const_Odistinct_I1_J,axiom,
% 0.19/0.46 unit != f ).
% 0.19/0.46
% 0.19/0.46 % const.distinct(1)
% 0.19/0.46 thf(fact_163_const_Odistinct_I3_J,axiom,
% 0.19/0.46 unit != t ).
% 0.19/0.46
% 0.19/0.46 % const.distinct(3)
% 0.19/0.46 thf(fact_164_substitution_Orevision__step_OifTrue,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step.ifTrue
% 0.19/0.46 thf(fact_165_substitution_Orevision__step_OifFalse,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step.ifFalse
% 0.19/0.46 thf(fact_166_substitution_OifTrue__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E1 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.ifTrue_deterministic
% 0.19/0.46 thf(fact_167_substitution_OifFalse__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E22 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.ifFalse_deterministic
% 0.19/0.46 thf(fact_168_substitution_Orevision__step__relaxed_OifTrue,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step_relaxed.ifTrue
% 0.19/0.46 thf(fact_169_substitution_Orevision__step__relaxed_OifFalse,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step_relaxed.ifFalse
% 0.19/0.46 thf(fact_170_substitution_OSLC__ifTrue,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: 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 ) ) ) ),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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E1 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.SLC_ifTrue
% 0.19/0.46 thf(fact_171_substitution_OSLC__ifFalse,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: 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 ) ) ) ),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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E22 ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.SLC_ifFalse
% 0.19/0.46 thf(fact_172_combine_Ocases,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,X2: product_prod @ ( A > ( option @ B ) ) @ ( product_prod @ ( A > ( option @ B ) ) @ A )] :
% 0.19/0.46 ~ ! [F2: A > ( option @ B ),G3: A > ( option @ B ),X4: A] :
% 0.19/0.46 ( X2
% 0.19/0.46 != ( product_Pair @ ( A > ( option @ B ) ) @ ( product_prod @ ( A > ( option @ B ) ) @ A ) @ F2 @ ( product_Pair @ ( A > ( option @ B ) ) @ A @ G3 @ X4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % combine.cases
% 0.19/0.46 thf(fact_173_LID__local__store_Ocases,axiom,
% 0.19/0.46 ! [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 ) )] :
% 0.19/0.46 ~ ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E2: expr @ R @ L @ V] :
% 0.19/0.46 ( X2
% 0.19/0.46 != ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ E2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % LID_local_store.cases
% 0.19/0.46 thf(fact_174_LID__local__store_Oinduct,axiom,
% 0.19/0.46 ! [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 ) )] :
% 0.19/0.46 ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E2: 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 ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ E2 ) ) )
% 0.19/0.46 => ( P @ A0 ) ) ).
% 0.19/0.46
% 0.19/0.46 % LID_local_store.induct
% 0.19/0.46 thf(fact_175_expr_Odistinct_I13_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ve @ R @ L @ V @ X1 )
% 0.19/0.46 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(13)
% 0.19/0.46 thf(fact_176_expr_Odistinct_I11_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X7: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ve @ R @ L @ V @ X1 )
% 0.19/0.46 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(11)
% 0.19/0.46 thf(fact_177_combine_Oelims,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,X2: A > ( option @ B ),Xa2: A > ( option @ B ),Xb: A,Y: option @ B] :
% 0.19/0.46 ( ( ( combine @ A @ B @ X2 @ Xa2 @ Xb )
% 0.19/0.46 = Y )
% 0.19/0.46 => ( ( ( ( Xa2 @ Xb )
% 0.19/0.46 = ( none @ B ) )
% 0.19/0.46 => ( Y
% 0.19/0.46 = ( X2 @ Xb ) ) )
% 0.19/0.46 & ( ( ( Xa2 @ Xb )
% 0.19/0.46 != ( none @ B ) )
% 0.19/0.46 => ( Y
% 0.19/0.46 = ( Xa2 @ Xb ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % combine.elims
% 0.19/0.46 thf(fact_178_combine_Osimps,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( combine @ A @ B )
% 0.19/0.46 = ( ^ [F3: A > ( option @ B ),G4: A > ( option @ B ),X: A] :
% 0.19/0.46 ( if @ ( option @ B )
% 0.19/0.46 @ ( ( G4 @ X )
% 0.19/0.46 = ( none @ B ) )
% 0.19/0.46 @ ( F3 @ X )
% 0.19/0.46 @ ( G4 @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % combine.simps
% 0.19/0.46 thf(fact_179_val_Odistinct_I5_J,axiom,
% 0.19/0.46 ! [L: $tType,V: $tType,R: $tType,X1: const,X42: R] :
% 0.19/0.46 ( ( cv @ R @ L @ V @ X1 )
% 0.19/0.46 != ( rid @ R @ L @ V @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % val.distinct(5)
% 0.19/0.46 thf(fact_180_expr_Odistinct_I55_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X7: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.19/0.46 ( ( rfork @ R @ L @ V @ X7 )
% 0.19/0.46 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(55)
% 0.19/0.46 thf(fact_181_empty__map__finite_I4_J,axiom,
% 0.19/0.46 ! [J: $tType,M2: $tType,K2: $tType] :
% 0.19/0.46 ( finite_finite2 @ J
% 0.19/0.46 @ ( lID_G @ K2 @ J @ M2
% 0.19/0.46 @ ^ [X: K2] : ( none @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( expr @ K2 @ J @ M2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % empty_map_finite(4)
% 0.19/0.46 thf(fact_182_fun__upd__upd,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B,Z: B] :
% 0.19/0.46 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X2 @ Y ) @ X2 @ Z )
% 0.19/0.46 = ( fun_upd @ A @ B @ F @ X2 @ Z ) ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_upd
% 0.19/0.46 thf(fact_183_fun__upd__triv,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,X2: A] :
% 0.19/0.46 ( ( fun_upd @ A @ B @ F @ X2 @ ( F @ X2 ) )
% 0.19/0.46 = F ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_triv
% 0.19/0.46 thf(fact_184_RID_092_060_094sub_062L__finite__invariant,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ( finite_finite2 @ l @ ( lID_G @ r @ l @ v @ S ) )
% 0.19/0.46 => ( finite_finite2 @ l @ ( lID_G @ r @ l @ v @ S2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % RID\<^sub>L_finite_invariant
% 0.19/0.46 thf(fact_185_reachable__imp__identifiers__finite_I2_J,axiom,
% 0.19/0.46 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( finite_finite2 @ l @ ( lID_G @ r @ l @ v @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % reachable_imp_identifiers_finite(2)
% 0.19/0.46 thf(fact_186_reachable__imp__identifiers__available_I2_J,axiom,
% 0.19/0.46 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( ~ ( finite_finite2 @ l @ ( top_top @ ( set @ l ) ) )
% 0.19/0.46 => ? [L2: l] :
% 0.19/0.46 ~ ( member @ l @ L2 @ ( lID_G @ r @ l @ v @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % reachable_imp_identifiers_available(2)
% 0.19/0.46 thf(fact_187_fun__upd__apply,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType] :
% 0.19/0.46 ( ( fun_upd @ B @ A )
% 0.19/0.46 = ( ^ [F3: B > A,X: B,Y2: A,Z2: B] : ( if @ A @ ( Z2 = X ) @ Y2 @ ( F3 @ Z2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_apply
% 0.19/0.46 thf(fact_188_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 0.19/0.46 ! [C: $tType,B: $tType,A: $tType,L3: 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] :
% 0.19/0.46 ( ( member @ B @ L3 @ ( 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 ) ) ) ) ) ) )
% 0.19/0.46 => ( member @ B @ L3 @ ( lID_G @ A @ B @ C @ S ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_restricted_global_in_unrestricted_global(2)
% 0.19/0.46 thf(fact_189_finite__state__imp__restriction__finite_I2_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( finite_finite2 @ B @ ( lID_G @ A @ B @ C @ S ) )
% 0.19/0.46 => ( finite_finite2 @ 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 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_state_imp_restriction_finite(2)
% 0.19/0.46 thf(fact_190_in__restricted__global__in__updated__global_I2_J,axiom,
% 0.19/0.46 ! [C: $tType,A: $tType,B: $tType,L3: 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 ) )] :
% 0.19/0.46 ( ( member @ B @ L3 @ ( 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 ) ) ) ) ) ) )
% 0.19/0.46 => ( member @ B @ L3 @ ( 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 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_restricted_global_in_updated_global(2)
% 0.19/0.46 thf(fact_191_fun__upd__idem__iff,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B] :
% 0.19/0.46 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y )
% 0.19/0.46 = F )
% 0.19/0.46 = ( ( F @ X2 )
% 0.19/0.46 = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_idem_iff
% 0.19/0.46 thf(fact_192_fun__upd__twist,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,A3: A,C2: A,M: A > B,B3: B,D: B] :
% 0.19/0.46 ( ( A3 != C2 )
% 0.19/0.46 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ A3 @ B3 ) @ C2 @ D )
% 0.19/0.46 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ C2 @ D ) @ A3 @ B3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_twist
% 0.19/0.46 thf(fact_193_fun__upd__other,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Z: A,X2: A,F: A > B,Y: B] :
% 0.19/0.46 ( ( Z != X2 )
% 0.19/0.46 => ( ( fun_upd @ A @ B @ F @ X2 @ Y @ Z )
% 0.19/0.46 = ( F @ Z ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_other
% 0.19/0.46 thf(fact_194_fun__upd__same,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: B > A,X2: B,Y: A] :
% 0.19/0.46 ( ( fun_upd @ B @ A @ F @ X2 @ Y @ X2 )
% 0.19/0.46 = Y ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_same
% 0.19/0.46 thf(fact_195_fun__upd__idem,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,F: B > A,X2: B,Y: A] :
% 0.19/0.46 ( ( ( F @ X2 )
% 0.19/0.46 = Y )
% 0.19/0.46 => ( ( fun_upd @ B @ A @ F @ X2 @ Y )
% 0.19/0.46 = F ) ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_idem
% 0.19/0.46 thf(fact_196_fun__upd__eqD,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B,G: A > B,Z: B] :
% 0.19/0.46 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y )
% 0.19/0.46 = ( fun_upd @ A @ B @ G @ X2 @ Z ) )
% 0.19/0.46 => ( Y = Z ) ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_eqD
% 0.19/0.46 thf(fact_197_fun__upd__def,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( fun_upd @ A @ B )
% 0.19/0.46 = ( ^ [F3: A > B,A6: A,B6: B,X: A] : ( if @ B @ ( X = A6 ) @ B6 @ ( F3 @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fun_upd_def
% 0.19/0.46 thf(fact_198_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ( finite_finite2 @ L @ ( lID_G @ R @ L @ V @ S ) )
% 0.19/0.46 => ( finite_finite2 @ L @ ( lID_G @ R @ L @ V @ S2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.RID\<^sub>L_finite_invariant
% 0.19/0.46 thf(fact_199_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 0.19/0.46 ! [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 ) ) ).
% 0.19/0.46
% 0.19/0.46 % ID_restricted_global_subset_unrestricted(1)
% 0.19/0.46 thf(fact_200_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 => ( finite_finite2 @ L @ ( lID_G @ R @ L @ V @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.reachable_imp_identifiers_finite(2)
% 0.19/0.46 thf(fact_201_substitution_Oempty__map__finite_I4_J,axiom,
% 0.19/0.46 ! [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 )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( finite_finite2 @ J
% 0.19/0.46 @ ( lID_G @ K2 @ J @ M2
% 0.19/0.46 @ ^ [X: K2] : ( none @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( expr @ K2 @ J @ M2 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.empty_map_finite(4)
% 0.19/0.46 thf(fact_202_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( finite_finite2 @ B @ ( lID_G @ A @ B @ C @ S ) )
% 0.19/0.46 => ( finite_finite2 @ 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 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.finite_state_imp_restriction_finite(2)
% 0.19/0.46 thf(fact_203_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 0.19/0.46 => ( ~ ( finite_finite2 @ L @ ( top_top @ ( set @ L ) ) )
% 0.19/0.46 => ? [L2: L] :
% 0.19/0.46 ~ ( member @ L @ L2 @ ( lID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.reachable_imp_identifiers_available(2)
% 0.19/0.46 thf(fact_204_only__new__introduces__lids_H,axiom,
% 0.19/0.46 ! [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 ) ) ) ),L3: l] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ! [Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,V3: val @ r @ l @ v] :
% 0.19/0.46 ( ( S @ R2 )
% 0.19/0.46 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 @ V3 ) ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S ) )
% 0.19/0.46 => ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % only_new_introduces_lids'
% 0.19/0.46 thf(fact_205_valid__stepE,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 => ? [R7: r] : ( revision_step @ r @ l @ v @ subst @ R7 @ S @ S2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % valid_stepE
% 0.19/0.46 thf(fact_206_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.19/0.46 => ( ( finite_finite2 @ 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 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( finite_finite2 @ A @ ( lID_L @ A @ B @ C @ Ls ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local_state_of_finite_restricted_global_state_is_finite(2)
% 0.19/0.46 thf(fact_207_LID_092_060_094sub_062GI,axiom,
% 0.19/0.46 ! [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 ) ),L3: A] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.19/0.46 => ( ( member @ A @ L3 @ ( lID_L @ A @ B @ C @ Ls ) )
% 0.19/0.46 => ( member @ A @ L3 @ ( lID_G @ B @ A @ C @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % LID\<^sub>GI
% 0.19/0.46 thf(fact_208_valid__stepI,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( 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 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % valid_stepI
% 0.19/0.46 thf(fact_209_maximal__execution__def,axiom,
% 0.19/0.46 ! [E4: 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 ) ) ) )] :
% 0.19/0.46 ( ( maximal_execution @ r @ l @ v @ subst @ E4 @ S @ S2 )
% 0.19/0.46 = ( ( execution @ r @ l @ v @ subst @ E4 @ S @ S2 )
% 0.19/0.46 & ~ ? [S6: 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 @ S6 ) @ ( steps @ r @ l @ v @ subst ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % maximal_execution_def
% 0.19/0.46 thf(fact_210_only__new__introduces__lids,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ! [Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,V3: val @ r @ l @ v] :
% 0.19/0.46 ( ( S @ R2 )
% 0.19/0.46 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 @ V3 ) ) ) ) ) ) )
% 0.19/0.46 => ( ord_less_eq @ ( set @ l ) @ ( lID_G @ r @ l @ v @ S2 ) @ ( lID_G @ r @ l @ v @ S ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % only_new_introduces_lids
% 0.19/0.46 thf(fact_211_substitution_Osteps_Ocong,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType] :
% 0.19/0.46 ( ( steps @ R @ L @ V )
% 0.19/0.46 = ( steps @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.steps.cong
% 0.19/0.46 thf(fact_212_expr_Odistinct_I5_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X42: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ve @ R @ L @ V @ X1 )
% 0.19/0.46 != ( ref @ R @ L @ V @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(5)
% 0.19/0.46 thf(fact_213_expr_Odistinct_I41_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X42: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ref @ R @ L @ V @ X42 )
% 0.19/0.46 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(41)
% 0.19/0.46 thf(fact_214_expr_Odistinct_I43_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X42: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ref @ R @ L @ V @ X42 )
% 0.19/0.46 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(43)
% 0.19/0.46 thf(fact_215_LID_092_060_094sub_062GE,axiom,
% 0.19/0.46 ! [C: $tType,B: $tType,A: $tType,L3: A,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) )] :
% 0.19/0.46 ( ( member @ A @ L3 @ ( lID_G @ B @ A @ C @ S ) )
% 0.19/0.46 => ~ ! [R7: B,Ls3: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) )] :
% 0.19/0.46 ( ( ( S @ R7 )
% 0.19/0.46 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls3 ) )
% 0.19/0.46 => ~ ( member @ A @ L3 @ ( lID_L @ A @ B @ C @ Ls3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % LID\<^sub>GE
% 0.19/0.46 thf(fact_216_substitution_Ovalid__stepE,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( 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 ) )
% 0.19/0.46 => ? [R7: R] : ( revision_step @ R @ L @ V @ Subst @ R7 @ S @ S2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.valid_stepE
% 0.19/0.46 thf(fact_217_substitution_Ovalid__stepI,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( 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 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.valid_stepI
% 0.19/0.46 thf(fact_218_substitution_Oonly__new__introduces__lids_H,axiom,
% 0.19/0.46 ! [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 ) ) ) ),L3: L] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,V3: val @ R @ L @ V] :
% 0.19/0.46 ( ( S @ R2 )
% 0.19/0.46 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ 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 @ V3 ) ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S ) )
% 0.19/0.46 => ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.only_new_introduces_lids'
% 0.19/0.46 thf(fact_219_substitution_Oonly__new__introduces__lids,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 => ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,V3: val @ R @ L @ V] :
% 0.19/0.46 ( ( S @ R2 )
% 0.19/0.46 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ 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 @ V3 ) ) ) ) ) ) )
% 0.19/0.46 => ( ord_less_eq @ ( set @ L ) @ ( lID_G @ R @ L @ V @ S2 ) @ ( lID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.only_new_introduces_lids
% 0.19/0.46 thf(fact_220_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.19/0.46 ! [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] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R3 )
% 0.19/0.46 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 0.19/0.46 => ( ( finite_finite2 @ 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 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( finite_finite2 @ A @ ( lID_L @ A @ B @ C @ Ls ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.local_state_of_finite_restricted_global_state_is_finite(2)
% 0.19/0.46 thf(fact_221_domains__subsume__def,axiom,
% 0.19/0.46 ( ( domains_subsume @ l @ r @ v )
% 0.19/0.46 = ( ^ [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 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % domains_subsume_def
% 0.19/0.46 thf(fact_222_SLC__new,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,V2: val @ 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 ) ) ) ),L3: l,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 ) ) ) )] :
% 0.19/0.46 ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S_1 ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( ( reachable @ r @ l @ v @ subst @ S_1 )
% 0.19/0.46 => ( ~ ( finite_finite2 @ l @ ( top_top @ ( set @ l ) ) )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_new
% 0.19/0.46 thf(fact_223_terminates__in__def,axiom,
% 0.19/0.46 ! [E4: 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 ) ) ) )] :
% 0.19/0.46 ( ( terminates_in @ r @ l @ v @ subst @ E4 @ S2 )
% 0.19/0.46 = ( ? [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 @ E4 @ S4 @ S2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % terminates_in_def
% 0.19/0.46 thf(fact_224_revision__step_Onew,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,V2: val @ r @ l @ v,L3: l] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step.new
% 0.19/0.46 thf(fact_225_new__pseudodeterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( ? [L4: l] :
% 0.19/0.46 ( ~ ( member @ l @ L4 @ ( lID_G @ r @ l @ v @ S ) )
% 0.19/0.46 & ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L4 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % new_pseudodeterministic
% 0.19/0.46 thf(fact_226_val_Odistinct_I3_J,axiom,
% 0.19/0.46 ! [R: $tType,V: $tType,L: $tType,X1: const,X34: L] :
% 0.19/0.46 ( ( cv @ R @ L @ V @ X1 )
% 0.19/0.46 != ( loc @ L @ R @ V @ X34 ) ) ).
% 0.19/0.46
% 0.19/0.46 % val.distinct(3)
% 0.19/0.46 thf(fact_227_val_Odistinct_I15_J,axiom,
% 0.19/0.46 ! [L: $tType,V: $tType,R: $tType,X34: L,X42: R] :
% 0.19/0.46 ( ( loc @ L @ R @ V @ X34 )
% 0.19/0.46 != ( rid @ R @ L @ V @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % val.distinct(15)
% 0.19/0.46 thf(fact_228_substitution_Omaximal__execution_Ocong,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType] :
% 0.19/0.46 ( ( maximal_execution @ R @ L @ V )
% 0.19/0.46 = ( maximal_execution @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.maximal_execution.cong
% 0.19/0.46 thf(fact_229_substitution_Odomains__subsume__def,axiom,
% 0.19/0.46 ! [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 ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( domains_subsume @ L @ R @ V @ Ls )
% 0.19/0.46 = ( ord_less_eq @ ( set @ L ) @ ( lID_L @ L @ R @ V @ Ls ) @ ( doms @ L @ R @ V @ Ls ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.domains_subsume_def
% 0.19/0.46 thf(fact_230_substitution_Onew__pseudodeterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( ? [L4: L] :
% 0.19/0.46 ( ~ ( member @ L @ L4 @ ( lID_G @ R @ L @ V @ S ) )
% 0.19/0.46 & ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L4 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L4 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.new_pseudodeterministic
% 0.19/0.46 thf(fact_231_substitution_Orevision__step_Onew,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,V2: val @ R @ L @ V,L3: L] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step.new
% 0.19/0.46 thf(fact_232_substitution_Omaximal__execution__def,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),E4: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( maximal_execution @ R @ L @ V @ Subst @ E4 @ S @ S2 )
% 0.19/0.46 = ( ( execution @ R @ L @ V @ Subst @ E4 @ S @ S2 )
% 0.19/0.46 & ~ ? [S6: 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 @ S6 ) @ ( steps @ R @ L @ V @ Subst ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.maximal_execution_def
% 0.19/0.46 thf(fact_233_substitution_OSLC__new,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,V2: val @ 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 ) ) ) ),L3: L,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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S_1 ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ( ( reachable @ R @ L @ V @ Subst @ S_1 )
% 0.19/0.46 => ( ~ ( finite_finite2 @ L @ ( top_top @ ( set @ L ) ) )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.SLC_new
% 0.19/0.46 thf(fact_234_revision__step__relaxed_Oset,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: l,V2: val @ r @ l @ v] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step_relaxed.set
% 0.19/0.46 thf(fact_235_substitution_Orevision__step__relaxed_Oset,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,L3: L,V2: val @ R @ L @ V] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step_relaxed.set
% 0.19/0.46 thf(fact_236_substitution_Oterminates__in_Ocong,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType] :
% 0.19/0.46 ( ( terminates_in @ R @ L @ V )
% 0.19/0.46 = ( terminates_in @ R @ L @ V ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.terminates_in.cong
% 0.19/0.46 thf(fact_237_expr_Odistinct_I9_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 0.19/0.46 ( ( ve @ R @ L @ V @ X1 )
% 0.19/0.46 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(9)
% 0.19/0.46 thf(fact_238_expr_Odistinct_I51_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 0.19/0.46 ( ( assign @ R @ L @ V @ X61 @ X62 )
% 0.19/0.46 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(51)
% 0.19/0.46 thf(fact_239_expr_Odistinct_I53_J,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 0.19/0.46 ( ( assign @ R @ L @ V @ X61 @ X62 )
% 0.19/0.46 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 0.19/0.46
% 0.19/0.46 % expr.distinct(53)
% 0.19/0.46 thf(fact_240_substitution_Oterminates__in__def,axiom,
% 0.19/0.46 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),E4: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( terminates_in @ R @ L @ V @ Subst @ E4 @ S2 )
% 0.19/0.46 = ( ? [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 @ E4 @ S4 @ S2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.terminates_in_def
% 0.19/0.46 thf(fact_241_SLC__set,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: l,V2: val @ 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 ) ) ) ),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 ) ) ) )] :
% 0.19/0.46 ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( member @ l @ L3 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_set
% 0.19/0.46 thf(fact_242_revision__step_Oset,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: l,V2: val @ r @ l @ v] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( member @ l @ L3 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % revision_step.set
% 0.19/0.46 thf(fact_243_dom__const,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B] :
% 0.19/0.46 ( ( dom @ A @ B
% 0.19/0.46 @ ^ [X: A] : ( some @ B @ ( F @ X ) ) )
% 0.19/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % dom_const
% 0.19/0.46 thf(fact_244_set__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: 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 ) ) ) )] :
% 0.19/0.46 ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( ( member @ l @ L3 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 ) ) )
% 0.19/0.46 & ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % set_deterministic
% 0.19/0.46 thf(fact_245_domD,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,A3: A,M: A > ( option @ B )] :
% 0.19/0.46 ( ( member @ A @ A3 @ ( dom @ A @ B @ M ) )
% 0.19/0.46 => ? [B2: B] :
% 0.19/0.46 ( ( M @ A3 )
% 0.19/0.46 = ( some @ B @ B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % domD
% 0.19/0.46 thf(fact_246_domI,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,M: B > ( option @ A ),A3: B,B3: A] :
% 0.19/0.46 ( ( ( M @ A3 )
% 0.19/0.46 = ( some @ A @ B3 ) )
% 0.19/0.46 => ( member @ B @ A3 @ ( dom @ B @ A @ M ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % domI
% 0.19/0.46 thf(fact_247_finite__map__freshness,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,F: A > ( option @ B )] :
% 0.19/0.46 ( ( finite_finite2 @ A @ ( dom @ A @ B @ F ) )
% 0.19/0.46 => ( ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.19/0.46 => ? [X4: A] :
% 0.19/0.46 ( ( F @ X4 )
% 0.19/0.46 = ( none @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % finite_map_freshness
% 0.19/0.46 thf(fact_248_dom__def,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( dom @ A @ B )
% 0.19/0.46 = ( ^ [M3: A > ( option @ B )] :
% 0.19/0.46 ( collect @ A
% 0.19/0.46 @ ^ [A6: A] :
% 0.19/0.46 ( ( M3 @ A6 )
% 0.19/0.46 != ( none @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % dom_def
% 0.19/0.46 thf(fact_249_domIff,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,A3: A,M: A > ( option @ B )] :
% 0.19/0.46 ( ( member @ A @ A3 @ ( dom @ A @ B @ M ) )
% 0.19/0.46 = ( ( M @ A3 )
% 0.19/0.46 != ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % domIff
% 0.19/0.46 thf(fact_250_substitution_Oset__deterministic,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,L3: 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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 0.19/0.46 = ( ( member @ L @ L3 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma2 @ Tau2 ) ) )
% 0.19/0.46 & ( S2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.set_deterministic
% 0.19/0.46 thf(fact_251_substitution_Orevision__step_Oset,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,L3: L,V2: val @ R @ L @ V] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( member @ L @ L3 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma2 @ Tau2 ) ) )
% 0.19/0.46 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.revision_step.set
% 0.19/0.46 thf(fact_252_substitution_OSLC__set,axiom,
% 0.19/0.46 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,L3: L,V2: val @ 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 ) ) ) ),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 ) ) ) )] :
% 0.19/0.46 ( ( substitution @ R @ L @ V @ Subst )
% 0.19/0.46 => ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( member @ L @ L3 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma2 @ Tau2 ) ) )
% 0.19/0.46 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substitution.SLC_set
% 0.19/0.46 thf(fact_253_reachability__closed__under__execution,axiom,
% 0.19/0.46 ! [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 ) ) ) )] :
% 0.19/0.46 ( ( reachable @ r @ l @ v @ subst @ S )
% 0.19/0.46 => ( ( 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 ) ) )
% 0.19/0.46 => ( reachable @ r @ l @ v @ subst @ S2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % reachability_closed_under_execution
% 0.19/0.46 thf(fact_254_SLC__get,axiom,
% 0.19/0.46 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: l,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 ) ) ) )] :
% 0.19/0.46 ( ( ( S_1 @ R2 )
% 0.19/0.46 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( read @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( S_2
% 0.19/0.46 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( the @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 @ L3 ) ) ) ) ) ) ) ) )
% 0.19/0.46 => ( ( member @ l @ L3 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 ) ) )
% 0.19/0.46 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 0.19/0.46 => ( ( R2 != R3 )
% 0.19/0.46 => ? [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 ) ) ) )] :
% 0.19/0.46 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 0.19/0.46 | ( S_2 = S_3 ) )
% 0.19/0.46 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 0.19/0.46 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SLC_get
% 0.19/0.46
% 0.19/0.46 % Type constructors (9)
% 0.19/0.46 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.19/0.46 ! [A7: $tType,A8: $tType] :
% 0.19/0.46 ( ( ( finite_finite @ A7 )
% 0.19/0.46 & ( finite_finite @ A8 ) )
% 0.19/0.46 => ( finite_finite @ ( A7 > A8 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.19/0.46 ! [A7: $tType,A8: $tType] :
% 0.19/0.46 ( ( order @ A8 )
% 0.19/0.46 => ( order @ ( A7 > A8 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Set_Oset___Finite__Set_Ofinite_1,axiom,
% 0.19/0.46 ! [A7: $tType] :
% 0.19/0.46 ( ( finite_finite @ A7 )
% 0.19/0.46 => ( finite_finite @ ( set @ A7 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.19/0.46 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_HOL_Obool___Finite__Set_Ofinite_3,axiom,
% 0.19/0.46 finite_finite @ $o ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_4,axiom,
% 0.19/0.46 order @ $o ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_5,axiom,
% 0.19/0.46 ! [A7: $tType,A8: $tType] :
% 0.19/0.46 ( ( ( finite_finite @ A7 )
% 0.19/0.46 & ( finite_finite @ A8 ) )
% 0.19/0.46 => ( finite_finite @ ( sum_sum @ A7 @ A8 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Option_Ooption___Finite__Set_Ofinite_6,axiom,
% 0.19/0.46 ! [A7: $tType] :
% 0.19/0.46 ( ( finite_finite @ A7 )
% 0.19/0.46 => ( finite_finite @ ( option @ A7 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_7,axiom,
% 0.19/0.46 ! [A7: $tType,A8: $tType] :
% 0.19/0.46 ( ( ( finite_finite @ A7 )
% 0.19/0.46 & ( finite_finite @ A8 ) )
% 0.19/0.46 => ( finite_finite @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Helper facts (3)
% 0.19/0.46 thf(help_If_3_1_T,axiom,
% 0.19/0.46 ! [P: $o] :
% 0.19/0.46 ( ( P = $true )
% 0.19/0.46 | ( P = $false ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_2_1_T,axiom,
% 0.19/0.46 ! [A: $tType,X2: A,Y: A] :
% 0.19/0.46 ( ( if @ A @ $false @ X2 @ Y )
% 0.19/0.46 = Y ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_1_1_T,axiom,
% 0.19/0.46 ! [A: $tType,X2: A,Y: A] :
% 0.19/0.46 ( ( if @ A @ $true @ X2 @ Y )
% 0.19/0.46 = X2 ) ).
% 0.19/0.46
% 0.19/0.46 % Conjectures (1)
% 0.19/0.46 thf(conj_0,conjecture,
% 0.19/0.46 r3 != right_forkee ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 3.20/1.69 ---- Embedded in THF ---
% 3.20/1.69 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.20/1.69 %%% Generated on Tue Feb 24 08:24:53 EST 2026
% 3.20/1.69 %%% using '$$dhol' embedding, version 1.3.0.
% 3.20/1.69 %%% Logic specification used:
% 3.20/1.69 %%% thf(spec, logic, $$dhol).
% 3.20/1.69
% 3.20/1.69 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZhcMuhrmrf/DTF2DTF12937.p
% 3.20/1.69 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.20/1.69 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 3.20/1.69 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 3.20/1.69 thf(ty_t_Data_Oconst, type, const: $tType).
% 3.20/1.69 thf(ty_t_Data_Ocntxt, type, cntxt: ($tType > ($tType > ($tType > $tType)))).
% 3.20/1.69 thf(ty_t_Data_Oexpr, type, expr: ($tType > ($tType > ($tType > $tType)))).
% 3.20/1.69 thf(ty_t_Data_Oval, type, val: ($tType > ($tType > ($tType > $tType)))).
% 3.20/1.69 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.20/1.69 thf(ty_tf_v, type, v: $tType).
% 3.20/1.69 thf(ty_tf_r, type, r: $tType).
% 3.20/1.69 thf(ty_tf_l, type, l: $tType).
% 3.20/1.69 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.20/1.69 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.20/1.69 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 3.20/1.69 thf(sy_cl_Nat_Osemiring__char__0, type, semiring_char_0: (!> [A:$tType]: ($o))).
% 3.20/1.69 thf(sy_c_Data_Ocombine, type, combine: (!> [A:$tType,B:$tType]: (((A > (option @ B)) > ((A > (option @ B)) > (A > (option @ B))))))).
% 3.20/1.69 thf(sy_c_Data_Oconst_OF, type, f: const).
% 3.20/1.69 thf(sy_c_Data_Oconst_OT, type, t: const).
% 3.20/1.69 thf(sy_c_Data_Oconst_OUnit, type, unit: const).
% 3.20/1.69 thf(sy_c_Data_Odoms, type, doms: (!> [L:$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))))).
% 3.20/1.69 thf(sy_c_Data_Oexpr_OAssign, type, assign: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))))).
% 3.20/1.69 thf(sy_c_Data_Oexpr_OIte, type, ite: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > ((((expr @ R) @ L) @ V) > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))))).
% 3.20/1.69 thf(sy_c_Data_Oexpr_ORead, type, read: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.20/1.69 thf(sy_c_Data_Oexpr_ORef, type, ref: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.20/1.69 thf(sy_c_Data_Oexpr_ORfork, type, rfork: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.20/1.69 thf(sy_c_Data_Oexpr_ORjoin, type, rjoin: (!> [R:$tType,L:$tType,V:$tType]: (((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.20/1.69 thf(sy_c_Data_Oexpr_OVE, type, ve: (!> [R:$tType,L:$tType,V:$tType]: (((((val @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))).
% 3.20/1.69 thf(sy_c_Data_Oplug, type, plug: (!> [R:$tType,L:$tType,V:$tType]: (((((cntxt @ R) @ L) @ V) > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))))).
% 3.20/1.69 thf(sy_c_Data_Oval_OCV, type, cv: (!> [R:$tType,L:$tType,V:$tType]: ((const > (((val @ R) @ L) @ V))))).
% 3.20/1.69 thf(sy_c_Data_Oval_OLoc, type, loc: (!> [L:$tType,R:$tType,V:$tType]: ((L > (((val @ R) @ L) @ V))))).
% 3.20/1.69 thf(sy_c_Data_Oval_ORid, type, rid: (!> [R:$tType,L:$tType,V:$tType]: ((R > (((val @ R) @ L) @ V))))).
% 3.20/1.69 thf(sy_c_Executions_Osubstitution_Oexecution, type, execution: (!> [R:$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))))) > $o))))))).
% 3.20/1.69 thf(sy_c_Executions_Osubstitution_Oinductive__invariant, type, inductive_invariant: (!> [R:$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) > $o))))).
% 3.20/1.69 thf(sy_c_Executions_Osubstitution_Omaximal__execution, type, maximal_execution: (!> [R:$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))))) > $o))))))).
% 3.20/1.70 thf(sy_c_Executions_Osubstitution_Oreachable, type, reachable: (!> [R:$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))))) > $o))))).
% 3.20/1.70 thf(sy_c_Executions_Osubstitution_Osteps, type, steps: (!> [R:$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))))))))))).
% 3.20/1.70 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))))) > $o)))))).
% 3.20/1.70 thf(sy_c_Finite__Set_Ofinite, type, finite_finite2: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.20/1.70 thf(sy_c_Fun_Ofun__upd, type, fun_upd: (!> [A:$tType,B:$tType]: (((A > B) > (A > (B > (A > B))))))).
% 3.20/1.70 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.20/1.70 thf(sy_c_Map_Odom, type, dom: (!> [A:$tType,B:$tType]: (((A > (option @ B)) > (set @ A))))).
% 3.20/1.70 thf(sy_c_Occurrences_OLID_092_060_094sub_062G, type, lID_G: (!> [R:$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))))).
% 3.20/1.70 thf(sy_c_Occurrences_OLID_092_060_094sub_062L, type, lID_L: (!> [L:$tType,R:$tType,V:$tType]: ((((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) > (set @ L))))).
% 3.20/1.70 thf(sy_c_Occurrences_ORID_092_060_094sub_062G, type, rID_G: (!> [R:$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))))).
% 3.20/1.70 thf(sy_c_Occurrences_ORID_092_060_094sub_062L, type, rID_L: (!> [L:$tType,R:$tType,V:$tType]: ((((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) > (set @ R))))).
% 3.20/1.70 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume, type, domains_subsume: (!> [L:$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))) > $o)))).
% 3.20/1.70 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally, type, domain398919503obally: (!> [R:$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))))) > $o)))).
% 3.20/1.70 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step, type, revision_step: (!> [R:$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))))) > $o))))))).
% 3.20/1.70 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed, type, revisi1433015572elaxed: (!> [R:$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))))) > $o))))))).
% 3.20/1.70 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible, type, subsumes_accessible: (!> [R:$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))))) > $o)))))).
% 3.20/1.70 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally, type, subsum380726323obally: (!> [R:$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))))) > $o)))).
% 3.20/1.70 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 3.20/1.70 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 3.20/1.70 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 3.20/1.70 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.20/1.70 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 3.20/1.70 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.20/1.70 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))))) > $o))))).
% 3.20/1.70 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.20/1.70 thf(sy_c_Substitution_Osubstitution, type, substitution: (!> [R:$tType,L:$tType,V:$tType]: ((((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))) > $o)))).
% 3.20/1.70 thf(sy_c_Transitive__Closure_Ortrancl, type, transitive_rtrancl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ A) @ A)))))).
% 3.20/1.70 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.20/1.70 thf(sy_v__092_060E_062, type, e: (((cntxt @ r) @ l) @ v)).
% 3.20/1.70 thf(sy_v__092_060E_062_H____, type, e2: (((cntxt @ r) @ l) @ v)).
% 3.20/1.70 thf(sy_v__092_060sigma_062, type, sigma: (l > (option @ (((val @ r) @ l) @ v)))).
% 3.20/1.70 thf(sy_v__092_060sigma_062_H____, type, sigma2: (l > (option @ (((val @ r) @ l) @ v)))).
% 3.20/1.70 thf(sy_v__092_060tau_062, type, tau: (l > (option @ (((val @ r) @ l) @ v)))).
% 3.20/1.70 thf(sy_v__092_060tau_062_H____, type, tau2: (l > (option @ (((val @ r) @ l) @ v)))).
% 3.20/1.70 thf(sy_v_e, type, e3: (((expr @ r) @ l) @ v)).
% 3.20/1.70 thf(sy_v_e_H____, type, e4: (((expr @ r) @ l) @ v)).
% 3.20/1.70 thf(sy_v_left__forkee, type, left_forkee: r).
% 3.20/1.70 thf(sy_v_r, type, r2: r).
% 3.20/1.70 thf(sy_v_r_H, type, r3: r).
% 3.20/1.70 thf(sy_v_right__forkee____, type, right_forkee: r).
% 3.20/1.70 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)))))).
% 3.20/1.70 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)))))).
% 3.20/1.70 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)))))).
% 3.20/1.70 thf(sy_v_subst, type, subst: ((((expr @ r) @ l) @ v) > (v > ((((expr @ r) @ l) @ v) > (((expr @ r) @ l) @ v))))).
% 3.20/1.70 thf(fact_0_local_Ofork_I3_J, axiom, (~ ((((member @ r) @ right_forkee) @ ((((rID_G @ r) @ l) @ v) @ s_1))))).
% 3.20/1.70 thf(fact_1_side, axiom, (~ ((((member @ r) @ left_forkee) @ ((((rID_G @ r) @ l) @ v) @ s_1))))).
% 3.20/1.70 thf(fact_2_neq, axiom, (r2 != r3)).
% 3.20/1.70 thf(fact_3__092_060open_062r_H_A_092_060noteq_062_Aleft__forkee_092_060close_062, axiom, (r3 != left_forkee)).
% 3.20/1.70 thf(fact_4_r_H__unchanged__left, axiom, ((s_2 @ r3) = (s_1 @ r3))).
% 3.20/1.70 thf(fact_5__092_060open_062r_A_092_060noteq_062_Aright__forkee_092_060close_062, axiom, (r2 != right_forkee)).
% 3.20/1.70 thf(fact_6_local_Ofork_I2_J, axiom, ((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))) @ sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ tau2) @ (((((plug @ r) @ l) @ v) @ e2) @ ((((rfork @ r) @ l) @ v) @ e4))))))).
% 3.20/1.70 thf(fact_7_right, axiom, (((((((revision_step @ r) @ l) @ v) @ subst) @ r3) @ s_1) @ s_22)).
% 3.20/1.70 thf(fact_8_local_Ofork_I1_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))) @ sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ tau2) @ (((((plug @ r) @ l) @ v) @ e2) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ right_forkee)))))))) @ right_forkee) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((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)) @ sigma2) @ tau2)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ e4)))))).
% 3.20/1.70 thf(fact_9__092_060open_062r_A_092_060noteq_062_Aleft__forkee_092_060close_062, axiom, (r2 != left_forkee)).
% 3.20/1.70 thf(fact_10_r__unchanged__right, axiom, ((s_22 @ r2) = (s_1 @ r2))).
% 3.20/1.70 thf(fact_11_reach, axiom, (((((reachable @ r) @ l) @ v) @ subst) @ s_1)).
% 3.20/1.70 thf(fact_12_left__step, axiom, (((((((revision_step @ r) @ l) @ v) @ subst) @ r2) @ s_1) @ s_2)).
% 3.20/1.70 thf(fact_13_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) => ((! [Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E2:(((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)))))))) => ((~ ((((member @ r) @ R3) @ ((((rID_G @ r) @ l) @ v) @ S)))) => (~ ((((member @ r) @ R3) @ ((((rID_G @ r) @ l) @ v) @ S2)))))))))).
% 3.20/1.70 thf(fact_14_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),E4:(((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))) @ 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)))) => (((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ E4)))))))))).
% 3.20/1.70 thf(fact_15_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),E4:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((rfork @ r) @ l) @ v) @ E4)))))) => ((((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((rfork @ r) @ l) @ v) @ E4)))))))))) & (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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ E4))))))))))))).
% 3.20/1.70 thf(fact_16_substitution__axioms, axiom, ((((substitution @ r) @ l) @ v) @ subst)).
% 3.20/1.70 thf(fact_17_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),E4:(((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))) @ 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)))) => (((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ E4)))))))))).
% 3.20/1.70 thf(fact_18_local__and__fork__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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),R5:r,E4:(((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))))) @ (((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R5)))))))) @ 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))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ E4))))) => (((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))) @ 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) @ R5) @ ((((rID_G @ r) @ l) @ v) @ S_2)))) => ((((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ R5)))))))) @ 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))) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (^ [X:l]: ((none @ (((val @ r) @ l) @ v))))) @ E4))))) @ R2) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ X2))) => ((R2 != R3) => ((R2 != R5) => (? [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)))))))))))))))).
% 3.20/1.70 thf(fact_19_s_092_060_094sub_0622, 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))))) @ (((((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)) @ tau) @ (((((plug @ r) @ l) @ v) @ e) @ ((((ve @ r) @ l) @ v) @ ((((rid @ r) @ l) @ v) @ left_forkee)))))))) @ left_forkee) @ ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((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))))) @ e3)))))).
% 3.20/1.70 thf(fact_20_restrictions__inwards, axiom, (! [A:$tType,B:$tType,X2:A,X3:A,F:(A > (option @ B)),Y:B]: (((X2 != X3) => ((((((fun_upd @ A) @ (option @ B)) @ (((((fun_upd @ A) @ (option @ B)) @ F) @ X2) @ ((some @ B) @ Y))) @ X3) @ (none @ B)) = (((((fun_upd @ A) @ (option @ B)) @ (((((fun_upd @ A) @ (option @ B)) @ F) @ X3) @ (none @ B))) @ X2) @ ((some @ B) @ Y))))))).
% 3.20/1.70 thf(fact_21_empty__upd__none, axiom, (! [B:$tType,A:$tType,X2:A]: (((((((fun_upd @ A) @ (option @ B)) @ (^ [X:A]: ((none @ B)))) @ X2) @ (none @ B)) = (^ [X:A]: ((none @ B))))))).
% 3.20/1.70 thf(fact_22_RID_092_060_094sub_062GI_I1_J, axiom, (! [C:$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)))))).
% 3.20/1.70 thf(fact_23_not__None__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((X2 != (none @ A)) = (? [Y2:A]: ((X2 = ((some @ A) @ Y2)))))))).
% 3.20/1.70 thf(fact_24_not__Some__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((! [Y2:A]: ((X2 != ((some @ A) @ Y2)))) = (X2 = (none @ A)))))).
% 3.20/1.70 thf(fact_25_s_092_060_094sub_0621__r, axiom, ((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) @ ((((rfork @ r) @ l) @ v) @ e3))))))).
% 3.20/1.70 thf(fact_26_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))))))))))))).
% 3.20/1.70 thf(fact_27_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) => ((! [Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((cntxt @ r) @ l) @ v),E2:(((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)))))))) => (((ord_less_eq @ (set @ r)) @ ((((rID_G @ r) @ l) @ v) @ S2)) @ ((((rID_G @ r) @ l) @ v) @ S))))))).
% 3.20/1.70 thf(fact_28_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)))))).
% 3.20/1.70 thf(fact_29_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_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)))))]: (((((((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)))))) => (? [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)))))))))).
% 3.20/1.70 thf(fact_30_SLC__commute, axiom, (! [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))))),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 = S_36) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_2) @ S_35) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S_22) @ S_36) => ((((((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)))))))))).
% 3.20/1.70 thf(fact_31_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)))))).
% 3.20/1.70 thf(fact_32_option_Oinject, axiom, (! [A:$tType,X22:A,Y22:A]: (((((some @ A) @ X22) = ((some @ A) @ Y22)) = (X22 = Y22))))).
% 3.20/1.70 thf(fact_33_transition__relations__equivalent, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),R2:r,S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = (((((((revisi1433015572elaxed @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2)))))).
% 3.20/1.70 thf(fact_34_in__restricted__global__in__unrestricted__global_I1_J, axiom, (! [C:$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)))))).
% 3.20/1.70 thf(fact_35_in__restricted__global__in__updated__global_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,R3:A,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A,Ls:((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))]: (((((member @ A) @ R3) @ ((((rID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))) => (((member @ A) @ R3) @ ((((rID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ ((some @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))) @ Ls)))))))).
% 3.20/1.70 thf(fact_36_reachable__def, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) = (? [E5:(((expr @ r) @ l) @ v),S3:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: ((((((((execution @ r) @ l) @ v) @ subst) @ E5) @ S3) @ S))))))).
% 3.20/1.70 thf(fact_37_substitution_Olocal__determinism, axiom, (! [V:$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))))))).
% 3.20/1.70 thf(fact_38_substitution_OSLC__commute, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S_35:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S_36:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R3:R,S_2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,S_22:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((S_35 = S_36) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_35) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_36) => ((((((eq_states @ R) @ L) @ V) @ S_35) @ S_36) & (((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_2) @ S_35) | (S_2 = S_35)) & ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S_22) @ S_36) | (S_22 = S_36))))))))))).
% 3.20/1.70 thf(fact_39_substitution_OSLC__sym, axiom, (! [V:$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_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)))))]: (((((((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)))))) => (? [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))))))))))).
% 3.20/1.70 thf(fact_40_ID__restricted__global__subset__unrestricted_I2_J, axiom, (! [C:$tType,A:$tType,B:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R2:B]: ((((ord_less_eq @ (set @ B)) @ ((((rID_G @ B) @ A) @ C) @ (((((fun_upd @ B) @ (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))))) @ ((((rID_G @ B) @ A) @ C) @ S))))).
% 3.20/1.70 thf(fact_41_substitution_Olocal__steps__commute, axiom, (! [V:$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)))))))))))))).
% 3.20/1.70 thf(fact_42_substitution_Olocal__and__fork__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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),R5:R,E4:(((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))))) @ (((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R5)))))))) @ 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))) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (^ [X:L]: ((none @ (((val @ R) @ L) @ V))))) @ E4))))) => (((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))) @ 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) @ R5) @ ((((rID_G @ R) @ L) @ V) @ S_2)))) => ((((((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R5)))))))) @ 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))) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (^ [X:L]: ((none @ (((val @ R) @ L) @ V))))) @ E4))))) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ X2))) => ((R2 != R3) => ((R2 != R5) => (? [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))))))))))))))))).
% 3.20/1.70 thf(fact_43_combine__options__cases, axiom, (! [A:$tType,B:$tType,X2:(option @ A),P:((option @ A) > ((option @ B) > $o)),Y:(option @ B)]: ((((X2 = (none @ A)) => ((P @ X2) @ Y)) => (((Y = (none @ B)) => ((P @ X2) @ Y)) => ((! [A2:A,B2:B]: (((X2 = ((some @ A) @ A2)) => ((Y = ((some @ B) @ B2)) => ((P @ X2) @ Y))))) => ((P @ X2) @ Y))))))).
% 3.20/1.70 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 3.20/1.70 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 3.20/1.70 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.20/1.70 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 3.20/1.70 thf(fact_48_split__option__all, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((! [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) & (! [X:A]: ((P3 @ ((some @ A) @ X))))))))))).
% 3.20/1.70 thf(fact_49_split__option__ex, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((? [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) | (? [X:A]: ((P3 @ ((some @ A) @ X))))))))))).
% 3.20/1.70 thf(fact_50_option_Oinducts, axiom, (! [A:$tType,P:((option @ A) > $o),Option:(option @ A)]: (((P @ (none @ A)) => ((! [X4:A]: ((P @ ((some @ A) @ X4)))) => (P @ Option)))))).
% 3.20/1.70 thf(fact_51_option_Oexhaust, axiom, (! [A:$tType,Y:(option @ A)]: (((Y != (none @ A)) => (~ ((! [X23:A]: ((Y != ((some @ A) @ X23)))))))))).
% 3.20/1.70 thf(fact_52_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X22:A]: (((Option = ((some @ A) @ X22)) => (Option != (none @ A)))))).
% 3.20/1.70 thf(fact_53_option_Odistinct_I1_J, axiom, (! [A:$tType,X22:A]: (((none @ A) != ((some @ A) @ X22))))).
% 3.20/1.70 thf(fact_54_map__upd__Some__unfold, axiom, (! [B:$tType,A:$tType,M:(B > (option @ A)),A3:B,B3:A,X2:B,Y:A]: (((((((((fun_upd @ B) @ (option @ A)) @ M) @ A3) @ ((some @ A) @ B3)) @ X2) = ((some @ A) @ Y)) = (((X2 = A3) & (B3 = Y)) | ((X2 != A3) & ((M @ X2) = ((some @ A) @ Y)))))))).
% 3.20/1.70 thf(fact_55_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))))).
% 3.20/1.70 thf(fact_56_map__upd__eqD1, axiom, (! [A:$tType,B:$tType,M:(A > (option @ B)),A3:A,X2:B,N:(A > (option @ B)),Y:B]: ((((((((fun_upd @ A) @ (option @ B)) @ M) @ A3) @ ((some @ B) @ X2)) = (((((fun_upd @ A) @ (option @ B)) @ N) @ A3) @ ((some @ B) @ Y))) => (X2 = Y))))).
% 3.20/1.70 thf(fact_57_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))))))).
% 3.20/1.70 thf(fact_58_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E4:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((rfork @ R) @ L) @ V) @ E4)))))) => ((((((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((rfork @ R) @ L) @ V) @ E4)))))))))) & (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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (^ [X:L]: ((none @ (((val @ R) @ L) @ V))))) @ E4)))))))))))))).
% 3.20/1.70 thf(fact_59_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))))) > $o)]: (((((((reachable @ r) @ l) @ v) @ subst) @ S) => ((((((inductive_invariant @ r) @ l) @ v) @ subst) @ P) => (P @ S)))))).
% 3.20/1.70 thf(fact_60_substitution_Orevision__step__relaxed_Ofork, axiom, (! [V:$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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E4:(((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))) @ 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)))) => (((((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (^ [X:L]: ((none @ (((val @ R) @ L) @ V))))) @ E4))))))))))).
% 3.20/1.70 thf(fact_61_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E4:(((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))) @ 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)))) => (((((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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)) @ Sigma2) @ Tau2)) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (^ [X:L]: ((none @ (((val @ R) @ L) @ V))))) @ E4))))))))))).
% 3.20/1.70 thf(fact_62_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) => ((! [Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E2:(((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)))))))) => (((ord_less_eq @ (set @ R)) @ ((((rID_G @ R) @ L) @ V) @ S2)) @ ((((rID_G @ R) @ L) @ V) @ S)))))))).
% 3.20/1.70 thf(fact_63_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))))).
% 3.20/1.70 thf(fact_64_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) => ((! [Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),E2:(((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)))))))) => ((~ ((((member @ R) @ R3) @ ((((rID_G @ R) @ L) @ V) @ S)))) => (~ ((((member @ R) @ R3) @ ((((rID_G @ R) @ L) @ V) @ S2))))))))))).
% 3.20/1.70 thf(fact_65_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)))))))))))))).
% 3.20/1.70 thf(fact_66_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)))))))))))).
% 3.20/1.70 thf(fact_67_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)))))))))))).
% 3.20/1.70 thf(fact_68_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)))))))).
% 3.20/1.70 thf(fact_69_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))))))))))))).
% 3.20/1.70 thf(fact_70_substitution_Orevision__step_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((revision_step @ R) @ L) @ V) = (((revision_step @ R) @ L) @ V))))).
% 3.20/1.70 thf(fact_71_substitution_Orevision__step__relaxed_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((revisi1433015572elaxed @ R) @ L) @ V) = (((revisi1433015572elaxed @ R) @ L) @ V))))).
% 3.20/1.70 thf(fact_72_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062, axiom, (! [L:$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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))))))))))))).
% 3.20/1.70 thf(fact_73_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062, axiom, (! [L:$tType,V:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),R3:R]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((rjoin @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((rid @ R) @ L) @ V) @ R3)))))))) => (((S @ R3) = (none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (^ [X:R]: ((none @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))))))))).
% 3.20/1.70 thf(fact_74_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic, axiom, (! [L:$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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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)))))))))))))).
% 3.20/1.70 thf(fact_75_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))))))))))))))).
% 3.20/1.70 thf(fact_76_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)))))).
% 3.20/1.70 thf(fact_77_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))))))).
% 3.20/1.70 thf(fact_78_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))))))).
% 3.20/1.70 thf(fact_79_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,Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E2:(((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))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ E2)))) => ((((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))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ E2)))))) => ((((domain398919503obally @ R) @ L) @ V) @ S)))))).
% 3.20/1.70 thf(fact_80_substitution_Otransition__relations__equivalent, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2))))))).
% 3.20/1.70 thf(fact_81_domains__subsume__globallyI, axiom, (! [S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((! [R7:r,Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E2:(((expr @ r) @ l) @ v)]: ((((S @ R7) = ((some @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ E2)))) => ((((domains_subsume @ l) @ r) @ v) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))) @ Sigma) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau) @ E2)))))) => ((((domain398919503obally @ r) @ l) @ v) @ S))))).
% 3.47/1.70 thf(fact_82_substitution_Oreachable__def, axiom, (! [V:$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)))))))).
% 3.47/1.70 thf(fact_83_substitution_Oreachable_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((reachable @ R) @ L) @ V) = (((reachable @ R) @ L) @ V))))).
% 3.47/1.70 thf(fact_84_substitution_Oinductive__invariant_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((inductive_invariant @ R) @ L) @ V) = (((inductive_invariant @ R) @ L) @ V))))).
% 3.47/1.70 thf(fact_85_substitution_Oexecution_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((execution @ R) @ L) @ V) = (((execution @ R) @ L) @ V))))).
% 3.47/1.70 thf(fact_86_substitution_Onice__ind__inv__is__inductive__invariant, axiom, (! [V:$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))))))))).
% 3.47/1.70 thf(fact_87_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:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => (((((domain398919503obally @ R) @ L) @ V) @ S) => (((((subsum380726323obally @ R) @ L) @ V) @ S) => ((((subsum380726323obally @ R) @ L) @ V) @ S2)))))))).
% 3.47/1.70 thf(fact_88_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J, axiom, (! [V:$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)))))))).
% 3.47/1.70 thf(fact_89_substitution_Odomains__subsume__globally__def, axiom, (! [L:$tType,V:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((((domain398919503obally @ R) @ L) @ V) @ S) = (! [R6:R,Ls2:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))]: ((((S @ R6) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ Ls2)) => ((((domains_subsume @ L) @ R) @ V) @ Ls2))))))))).
% 3.47/1.70 thf(fact_90_substitution_Oreachability__closed__under__execution__step, axiom, (! [V:$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))))))).
% 3.47/1.70 thf(fact_91_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((((domain398919503obally @ R) @ L) @ V) @ S)))))).
% 3.47/1.70 thf(fact_92_substitution_Oinductive__invariant__is__execution__invariant, axiom, (! [V:$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))))) > $o)]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S) => ((((((inductive_invariant @ R) @ L) @ V) @ Subst) @ P) => (P @ S))))))).
% 3.47/1.70 thf(fact_93_substitution_Osubsumes__accessible__globallyI, axiom, (! [V:$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)))))).
% 3.47/1.70 thf(fact_94_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),Tau3:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau2) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau2) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)))))))))))))))).
% 3.47/1.70 thf(fact_95_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau2) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)))))))))))))).
% 3.47/1.70 thf(fact_96_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau2) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))))))))))).
% 3.47/1.70 thf(fact_97_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_finite2 @ r) @ ((((rID_G @ r) @ l) @ v) @ S)))))).
% 3.47/1.70 thf(fact_98_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau2) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))))))))))).
% 3.47/1.70 thf(fact_99_empty__map__finite_I3_J, axiom, (! [H:$tType,I:$tType,G2:$tType]: (((finite_finite2 @ G2) @ ((((rID_G @ G2) @ H) @ I) @ (^ [X:G2]: ((none @ ((product_prod @ (H > (option @ (((val @ G2) @ H) @ I)))) @ ((product_prod @ (H > (option @ (((val @ G2) @ H) @ I)))) @ (((expr @ G2) @ H) @ I))))))))))).
% 3.47/1.70 thf(fact_100_rid__inf, axiom, (~ (((finite_finite2 @ r) @ (top_top @ (set @ r)))))).
% 3.47/1.70 thf(fact_101_RID_092_060_094sub_062G__finite__invariant, axiom, (! [R2:r,S:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v))))),S2:(r > (option @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ ((product_prod @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)))))]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => (((finite_finite2 @ r) @ ((((rID_G @ r) @ l) @ v) @ S)) => ((finite_finite2 @ r) @ ((((rID_G @ r) @ l) @ v) @ S2))))))).
% 3.47/1.70 thf(fact_102_finite__state__imp__restriction__finite_I1_J, axiom, (! [C:$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_finite2 @ A) @ ((((rID_G @ A) @ B) @ C) @ S)) => ((finite_finite2 @ 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))))))))))).
% 3.47/1.70 thf(fact_103_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))))).
% 3.47/1.70 thf(fact_104_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Tau2) @ Tau3)) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((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)))))))))))).
% 3.47/1.70 thf(fact_105_substitution_ORID_092_060_094sub_062G__finite__invariant, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => (((finite_finite2 @ R) @ ((((rID_G @ R) @ L) @ V) @ S)) => ((finite_finite2 @ R) @ ((((rID_G @ R) @ L) @ V) @ S2)))))))).
% 3.47/1.70 thf(fact_106_substitution_Oreachable__imp__identifiers__finite_I1_J, axiom, (! [V:$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_finite2 @ R) @ ((((rID_G @ R) @ L) @ V) @ S))))))).
% 3.47/1.70 thf(fact_107_substitution_Oempty__map__finite_I3_J, axiom, (! [R:$tType,L:$tType,V:$tType,H:$tType,I:$tType,G2:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((finite_finite2 @ G2) @ ((((rID_G @ G2) @ H) @ I) @ (^ [X:G2]: ((none @ ((product_prod @ (H > (option @ (((val @ G2) @ H) @ I)))) @ ((product_prod @ (H > (option @ (((val @ G2) @ H) @ I)))) @ (((expr @ G2) @ H) @ I)))))))))))).
% 3.47/1.70 thf(fact_108_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_finite2 @ A) @ ((((rID_G @ A) @ B) @ C) @ S)) => ((finite_finite2 @ 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)))))))))))).
% 3.47/1.70 thf(fact_109_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau2) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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)))))))))))).
% 3.47/1.70 thf(fact_110_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau2) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))))))))))))).
% 3.47/1.70 thf(fact_111_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau2) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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)))))))))))).
% 3.47/1.70 thf(fact_112_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau2) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))))))))))))))).
% 3.47/1.70 thf(fact_113_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),Tau3:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau2) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Tau2) @ Tau3)) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((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))))))))))))))))).
% 3.47/1.70 thf(fact_114_finite__Collect__subsets, axiom, (! [A:$tType,A4:(set @ A)]: ((((finite_finite2 @ A) @ A4) => ((finite_finite2 @ (set @ A)) @ ((collect @ (set @ A)) @ (^ [B4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B4) @ A4))))))))).
% 3.47/1.70 thf(fact_115_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_finite2 @ r) @ (top_top @ (set @ r))))) => (? [R7:r]: ((~ ((((member @ r) @ R7) @ ((((rID_G @ r) @ l) @ v) @ S))))))))))).
% 3.47/1.70 thf(fact_116_finite__Collect__conjI, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((finite_finite2 @ A) @ ((collect @ A) @ P)) | ((finite_finite2 @ A) @ ((collect @ A) @ Q))) => ((finite_finite2 @ A) @ ((collect @ A) @ (^ [X:A]: (((P @ X) & (Q @ X)))))))))).
% 3.47/1.70 thf(fact_117_finite__Collect__disjI, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((finite_finite2 @ A) @ ((collect @ A) @ (^ [X:A]: (((P @ X) | (Q @ X)))))) = (((finite_finite2 @ A) @ ((collect @ A) @ P)) & ((finite_finite2 @ A) @ ((collect @ A) @ Q))))))).
% 3.47/1.70 thf(fact_118_local__state__of__finite__restricted__global__state__is__finite_I1_J, axiom, (! [C:$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_finite2 @ 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_finite2 @ B) @ ((((rID_L @ A) @ B) @ C) @ Ls)))))))).
% 3.47/1.70 thf(fact_119_finite__code, axiom, (! [A:$tType]: (((finite_finite @ A) => ((finite_finite2 @ A) = (^ [A5:(set @ A)]: ($true))))))).
% 3.47/1.70 thf(fact_120_finite__option__UNIV, axiom, (! [A:$tType]: ((((finite_finite2 @ (option @ A)) @ (top_top @ (set @ (option @ A)))) = ((finite_finite2 @ A) @ (top_top @ (set @ A))))))).
% 3.47/1.70 thf(fact_121_finite__Plus__UNIV__iff, axiom, (! [A:$tType,B:$tType]: ((((finite_finite2 @ ((sum_sum @ A) @ B)) @ (top_top @ (set @ ((sum_sum @ A) @ B)))) = (((finite_finite2 @ A) @ (top_top @ (set @ A))) & ((finite_finite2 @ B) @ (top_top @ (set @ B)))))))).
% 3.47/1.70 thf(fact_122_finite__Collect__not, axiom, (! [A:$tType,P:(A > $o)]: ((((finite_finite2 @ A) @ ((collect @ A) @ P)) => (((finite_finite2 @ A) @ ((collect @ A) @ (^ [X:A]: ((~ ((P @ X))))))) = ((finite_finite2 @ A) @ (top_top @ (set @ A)))))))).
% 3.47/1.70 thf(fact_123_RID_092_060_094sub_062GI_I2_J, axiom, (! [C:$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))))))).
% 3.47/1.70 thf(fact_124_Finite__Set_Ofinite__set, axiom, (! [A:$tType]: ((((finite_finite2 @ (set @ A)) @ (top_top @ (set @ (set @ A)))) = ((finite_finite2 @ A) @ (top_top @ (set @ A))))))).
% 3.47/1.70 thf(fact_125_finite__prod, axiom, (! [A:$tType,B:$tType]: ((((finite_finite2 @ ((product_prod @ A) @ B)) @ (top_top @ (set @ ((product_prod @ A) @ B)))) = (((finite_finite2 @ A) @ (top_top @ (set @ A))) & ((finite_finite2 @ B) @ (top_top @ (set @ B)))))))).
% 3.47/1.70 thf(fact_126_ex__new__if__finite, axiom, (! [A:$tType,A4:(set @ A)]: (((~ (((finite_finite2 @ A) @ (top_top @ (set @ A))))) => (((finite_finite2 @ A) @ A4) => (? [A2:A]: ((~ ((((member @ A) @ A2) @ A4)))))))))).
% 3.47/1.70 thf(fact_127_finite__Prod__UNIV, axiom, (! [B:$tType,A:$tType]: ((((finite_finite2 @ A) @ (top_top @ (set @ A))) => (((finite_finite2 @ B) @ (top_top @ (set @ B))) => ((finite_finite2 @ ((product_prod @ A) @ B)) @ (top_top @ (set @ ((product_prod @ A) @ B))))))))).
% 3.47/1.70 thf(fact_128_finite__fun__UNIVD2, axiom, (! [A:$tType,B:$tType]: ((((finite_finite2 @ (A > B)) @ (top_top @ (set @ (A > B)))) => ((finite_finite2 @ B) @ (top_top @ (set @ B))))))).
% 3.47/1.70 thf(fact_129_infinite__UNIV__char__0, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (~ (((finite_finite2 @ A) @ (top_top @ (set @ A))))))))).
% 3.47/1.70 thf(fact_130_finite__UNIV, axiom, (! [A:$tType]: (((finite_finite @ A) => ((finite_finite2 @ A) @ (top_top @ (set @ A))))))).
% 3.47/1.70 thf(fact_131_finite, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A4:(set @ A)]: (((finite_finite2 @ A) @ A4))))))).
% 3.47/1.70 thf(fact_132_finite__set__choice, axiom, (! [B:$tType,A:$tType,A4:(set @ A),P:(A > (B > $o))]: ((((finite_finite2 @ A) @ A4) => ((! [X4:A]: (((((member @ A) @ X4) @ A4) => (? [X_1:B]: (((P @ X4) @ X_1)))))) => (? [F2:(A > B)]: ((! [X6:A]: (((((member @ A) @ X6) @ A4) => ((P @ X6) @ (F2 @ X6)))))))))))).
% 3.47/1.70 thf(fact_133_pigeonhole__infinite__rel, axiom, (! [B:$tType,A:$tType,A4:(set @ A),B5:(set @ B),R8:(A > (B > $o))]: (((~ (((finite_finite2 @ A) @ A4))) => (((finite_finite2 @ B) @ B5) => ((! [X4:A]: (((((member @ A) @ X4) @ A4) => (? [Xa:B]: (((((member @ B) @ Xa) @ B5) & ((R8 @ X4) @ Xa))))))) => (? [X4:B]: (((((member @ B) @ X4) @ B5) & (~ (((finite_finite2 @ A) @ ((collect @ A) @ (^ [A6:A]: (((((member @ A) @ A6) @ A4) & ((R8 @ A6) @ X4))))))))))))))))).
% 3.47/1.70 thf(fact_134_not__finite__existsD, axiom, (! [A:$tType,P:(A > $o)]: (((~ (((finite_finite2 @ A) @ ((collect @ A) @ P)))) => (? [X_12:A]: ((P @ X_12))))))).
% 3.47/1.70 thf(fact_135_substitution_Oreachable__imp__identifiers__available_I1_J, axiom, (! [V:$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_finite2 @ R) @ (top_top @ (set @ R))))) => (? [R7:R]: ((~ ((((member @ R) @ R7) @ ((((rID_G @ R) @ L) @ V) @ S)))))))))))).
% 3.47/1.70 thf(fact_136_finite__has__minimal2, axiom, (! [A:$tType]: (((order @ A) => (! [A4:(set @ A),A3:A]: ((((finite_finite2 @ A) @ A4) => ((((member @ A) @ A3) @ A4) => (? [X4:A]: (((((member @ A) @ X4) @ A4) & ((((ord_less_eq @ A) @ X4) @ A3) & (! [Xa:A]: (((((member @ A) @ Xa) @ A4) => ((((ord_less_eq @ A) @ Xa) @ X4) => (X4 = Xa))))))))))))))))).
% 3.47/1.70 thf(fact_137_finite__has__maximal2, axiom, (! [A:$tType]: (((order @ A) => (! [A4:(set @ A),A3:A]: ((((finite_finite2 @ A) @ A4) => ((((member @ A) @ A3) @ A4) => (? [X4:A]: (((((member @ A) @ X4) @ A4) & ((((ord_less_eq @ A) @ A3) @ X4) & (! [Xa:A]: (((((member @ A) @ Xa) @ A4) => ((((ord_less_eq @ A) @ X4) @ Xa) => (X4 = Xa))))))))))))))))).
% 3.47/1.70 thf(fact_138_finite__subset, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (((finite_finite2 @ A) @ B5) => ((finite_finite2 @ A) @ A4)))))).
% 3.47/1.70 thf(fact_139_infinite__super, axiom, (! [A:$tType,S5:(set @ A),T2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ S5) @ T2) => ((~ (((finite_finite2 @ A) @ S5))) => (~ (((finite_finite2 @ A) @ T2)))))))).
% 3.47/1.70 thf(fact_140_rev__finite__subset, axiom, (! [A:$tType,B5:(set @ A),A4:(set @ A)]: ((((finite_finite2 @ A) @ B5) => ((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((finite_finite2 @ A) @ A4)))))).
% 3.47/1.70 thf(fact_141_finite__update__induct, axiom, (! [B:$tType,A:$tType,F:(A > B),C2:B,P:((A > B) > $o)]: ((((finite_finite2 @ A) @ ((collect @ A) @ (^ [A6:A]: (((F @ A6) != C2))))) => ((P @ (^ [A6:A]: (C2))) => ((! [A2:A,B2:B,F2:(A > B)]: ((((finite_finite2 @ A) @ ((collect @ A) @ (^ [C3:A]: (((F2 @ C3) != C2))))) => (((F2 @ A2) = C2) => ((B2 != C2) => ((P @ F2) => (P @ (((((fun_upd @ A) @ B) @ F2) @ A2) @ B2)))))))) => (P @ F))))))).
% 3.47/1.70 thf(fact_142_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J, axiom, (! [V:$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_finite2 @ 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_finite2 @ B) @ ((((rID_L @ A) @ B) @ C) @ Ls))))))))).
% 3.47/1.70 thf(fact_143_SLC__ifTrue, 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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),E1:(((expr @ r) @ l) @ v),E22:(((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))))),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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((((ite @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ t))) @ E1) @ E22)))))) => ((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)))) @ ((((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) @ E1)))))) => ((((((((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))))))))))))).
% 3.47/1.70 thf(fact_144_SLC__ifFalse, 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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),E1:(((expr @ r) @ l) @ v),E22:(((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))))),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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((((ite @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ f))) @ E1) @ E22)))))) => ((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)))) @ ((((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) @ E22)))))) => ((((((((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))))))))))))).
% 3.47/1.70 thf(fact_145_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))))).
% 3.47/1.70 thf(fact_146_val_Oinject_I4_J, axiom, (! [V:$tType,L:$tType,R:$tType,X42:R,Y4:R]: (((((((rid @ R) @ L) @ V) @ X42) = ((((rid @ R) @ L) @ V) @ Y4)) = (X42 = Y4))))).
% 3.47/1.70 thf(fact_147_expr_Oinject_I1_J, axiom, (! [V:$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))))).
% 3.47/1.70 thf(fact_148_injective__cntxt, axiom, (! [C:$tType,B:$tType,A:$tType,E3:(((cntxt @ A) @ B) @ C),E1:(((expr @ A) @ B) @ C),E22:(((expr @ A) @ B) @ C)]: ((((((((plug @ A) @ B) @ C) @ E3) @ E1) = (((((plug @ A) @ B) @ C) @ E3) @ E22)) = (E1 = E22))))).
% 3.47/1.70 thf(fact_149_val_Oinject_I1_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:const,Y1:const]: (((((((cv @ R) @ L) @ V) @ X1) = ((((cv @ R) @ L) @ V) @ Y1)) = (X1 = Y1))))).
% 3.47/1.70 thf(fact_150_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))))).
% 3.47/1.70 thf(fact_151_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ E22)))))))))).
% 3.47/1.70 thf(fact_152_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ E1)))))))))).
% 3.47/1.70 thf(fact_153_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ E22)))))))))).
% 3.47/1.70 thf(fact_154_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ E1)))))))))).
% 3.47/1.70 thf(fact_155_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ E22))))))))))).
% 3.47/1.70 thf(fact_156_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ E1))))))))))).
% 3.47/1.70 thf(fact_157_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))))).
% 3.47/1.70 thf(fact_158_expr_Odistinct_I33_J, axiom, (! [V:$tType,L:$tType,R:$tType,X31:(((expr @ R) @ L) @ V),X32:(((expr @ R) @ L) @ V),X33:(((expr @ R) @ L) @ V),X7:(((expr @ R) @ L) @ V)]: ((((((((ite @ R) @ L) @ V) @ X31) @ X32) @ X33) != ((((rfork @ R) @ L) @ V) @ X7))))).
% 3.47/1.70 thf(fact_159_expr_Odistinct_I3_J, axiom, (! [V:$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))))).
% 3.47/1.70 thf(fact_160_const_Oexhaust, axiom, (! [Y:const]: (((Y != unit) => ((Y != f) => (Y = t)))))).
% 3.47/1.70 thf(fact_161_const_Oinduct, axiom, (! [P:(const > $o),Const:const]: (((P @ unit) => ((P @ f) => ((P @ t) => (P @ Const))))))).
% 3.47/1.70 thf(fact_162_const_Odistinct_I1_J, axiom, (unit != f)).
% 3.47/1.70 thf(fact_163_const_Odistinct_I3_J, axiom, (unit != t)).
% 3.47/1.70 thf(fact_164_substitution_Orevision__step_OifTrue, axiom, (! [V:$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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ E1))))))))))).
% 3.47/1.70 thf(fact_165_substitution_Orevision__step_OifFalse, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ f))) @ E1) @ E22)))))) => (((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ E22))))))))))).
% 3.47/1.70 thf(fact_166_substitution_OifTrue__deterministic, axiom, (! [V:$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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ E1)))))))))))).
% 3.47/1.70 thf(fact_167_substitution_OifFalse__deterministic, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ f))) @ E1) @ E22)))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = (S2 = (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ E22)))))))))))).
% 3.47/1.70 thf(fact_168_substitution_Orevision__step__relaxed_OifTrue, axiom, (! [V:$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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ E1))))))))))).
% 3.47/1.70 thf(fact_169_substitution_Orevision__step__relaxed_OifFalse, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((expr @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ f))) @ E1) @ E22)))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ E22))))))))))).
% 3.47/1.70 thf(fact_170_substitution_OSLC__ifTrue, axiom, (! [V:$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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((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))))),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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ t))) @ E1) @ E22)))))) => ((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)))) @ ((((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) @ E1)))))) => ((((((((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)))))))))))))).
% 3.47/1.70 thf(fact_171_substitution_OSLC__ifFalse, 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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),E1:(((expr @ R) @ L) @ V),E22:(((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))))),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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((((ite @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ f))) @ E1) @ E22)))))) => ((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)))) @ ((((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) @ E22)))))) => ((((((((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)))))))))))))).
% 3.47/1.70 thf(fact_172_combine_Ocases, axiom, (! [B:$tType,A:$tType,X2:((product_prod @ (A > (option @ B))) @ ((product_prod @ (A > (option @ B))) @ A))]: ((~ ((! [F2:(A > (option @ B)),G3:(A > (option @ B)),X4:A]: ((X2 != ((((product_Pair @ (A > (option @ B))) @ ((product_prod @ (A > (option @ B))) @ A)) @ F2) @ ((((product_Pair @ (A > (option @ B))) @ A) @ G3) @ X4)))))))))).
% 3.47/1.70 thf(fact_173_LID__local__store_Ocases, axiom, (! [V:$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)))]: ((~ ((! [Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E2:(((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))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ E2)))))))))).
% 3.47/1.70 thf(fact_174_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))) > $o),A0:((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))]: (((! [Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E2:(((expr @ R) @ L) @ V)]: ((P @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ E2))))) => (P @ A0))))).
% 3.47/1.70 thf(fact_175_expr_Odistinct_I13_J, axiom, (! [V:$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))))).
% 3.47/1.70 thf(fact_176_expr_Odistinct_I11_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X7:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != ((((rfork @ R) @ L) @ V) @ X7))))).
% 3.47/1.70 thf(fact_177_combine_Oelims, axiom, (! [B:$tType,A:$tType,X2:(A > (option @ B)),Xa2:(A > (option @ B)),Xb:A,Y:(option @ B)]: ((((((((combine @ A) @ B) @ X2) @ Xa2) @ Xb) = Y) => ((((Xa2 @ Xb) = (none @ B)) => (Y = (X2 @ Xb))) & (((Xa2 @ Xb) != (none @ B)) => (Y = (Xa2 @ Xb)))))))).
% 3.47/1.70 thf(fact_178_combine_Osimps, axiom, (! [B:$tType,A:$tType]: ((((combine @ A) @ B) = (^ [F3:(A > (option @ B)),G4:(A > (option @ B)),X:A]: (((((if @ (option @ B)) @ ((G4 @ X) = (none @ B))) @ (F3 @ X)) @ (G4 @ X)))))))).
% 3.47/1.70 thf(fact_179_val_Odistinct_I5_J, axiom, (! [L:$tType,V:$tType,R:$tType,X1:const,X42:R]: ((((((cv @ R) @ L) @ V) @ X1) != ((((rid @ R) @ L) @ V) @ X42))))).
% 3.47/1.70 thf(fact_180_expr_Odistinct_I55_J, axiom, (! [V:$tType,L:$tType,R:$tType,X7:(((expr @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: ((((((rfork @ R) @ L) @ V) @ X7) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.47/1.70 thf(fact_181_empty__map__finite_I4_J, axiom, (! [J:$tType,M2:$tType,K2:$tType]: (((finite_finite2 @ 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))))))))))).
% 3.47/1.70 thf(fact_182_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))))).
% 3.47/1.70 thf(fact_183_fun__upd__triv, axiom, (! [B:$tType,A:$tType,F:(A > B),X2:A]: (((((((fun_upd @ A) @ B) @ F) @ X2) @ (F @ X2)) = F)))).
% 3.47/1.70 thf(fact_184_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_finite2 @ l) @ ((((lID_G @ r) @ l) @ v) @ S)) => ((finite_finite2 @ l) @ ((((lID_G @ r) @ l) @ v) @ S2))))))).
% 3.47/1.70 thf(fact_185_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_finite2 @ l) @ ((((lID_G @ r) @ l) @ v) @ S)))))).
% 3.47/1.70 thf(fact_186_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_finite2 @ l) @ (top_top @ (set @ l))))) => (? [L2:l]: ((~ ((((member @ l) @ L2) @ ((((lID_G @ r) @ l) @ v) @ S))))))))))).
% 3.47/1.70 thf(fact_187_fun__upd__apply, axiom, (! [A:$tType,B:$tType]: ((((fun_upd @ B) @ A) = (^ [F3:(B > A),X:B,Y2:A,Z2:B]: (((((if @ A) @ (Z2 = X)) @ Y2) @ (F3 @ Z2)))))))).
% 3.47/1.70 thf(fact_188_in__restricted__global__in__unrestricted__global_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,L3:B,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A]: (((((member @ B) @ L3) @ ((((lID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))) => (((member @ B) @ L3) @ ((((lID_G @ A) @ B) @ C) @ S)))))).
% 3.47/1.70 thf(fact_189_finite__state__imp__restriction__finite_I2_J, axiom, (! [C:$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_finite2 @ B) @ ((((lID_G @ A) @ B) @ C) @ S)) => ((finite_finite2 @ 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))))))))))).
% 3.47/1.70 thf(fact_190_in__restricted__global__in__updated__global_I2_J, axiom, (! [C:$tType,A:$tType,B:$tType,L3:B,S:(A > (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))),R2:A,Ls:((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))]: (((((member @ B) @ L3) @ ((((lID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))))) => (((member @ B) @ L3) @ ((((lID_G @ A) @ B) @ C) @ (((((fun_upd @ A) @ (option @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C))))) @ S) @ R2) @ ((some @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ ((product_prod @ (B > (option @ (((val @ A) @ B) @ C)))) @ (((expr @ A) @ B) @ C)))) @ Ls)))))))).
% 3.47/1.70 thf(fact_191_fun__upd__idem__iff, axiom, (! [A:$tType,B:$tType,F:(A > B),X2:A,Y:B]: ((((((((fun_upd @ A) @ B) @ F) @ X2) @ Y) = F) = ((F @ X2) = Y))))).
% 3.47/1.70 thf(fact_192_fun__upd__twist, axiom, (! [A:$tType,B:$tType,A3:A,C2:A,M:(A > B),B3:B,D:B]: (((A3 != C2) => ((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M) @ A3) @ B3)) @ C2) @ D) = (((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M) @ C2) @ D)) @ A3) @ B3)))))).
% 3.47/1.70 thf(fact_193_fun__upd__other, axiom, (! [B:$tType,A:$tType,Z:A,X2:A,F:(A > B),Y:B]: (((Z != X2) => (((((((fun_upd @ A) @ B) @ F) @ X2) @ Y) @ Z) = (F @ Z)))))).
% 3.47/1.70 thf(fact_194_fun__upd__same, axiom, (! [B:$tType,A:$tType,F:(B > A),X2:B,Y:A]: ((((((((fun_upd @ B) @ A) @ F) @ X2) @ Y) @ X2) = Y)))).
% 3.47/1.70 thf(fact_195_fun__upd__idem, axiom, (! [A:$tType,B:$tType,F:(B > A),X2:B,Y:A]: ((((F @ X2) = Y) => ((((((fun_upd @ B) @ A) @ F) @ X2) @ Y) = F))))).
% 3.47/1.70 thf(fact_196_fun__upd__eqD, axiom, (! [A:$tType,B:$tType,F:(A > B),X2:A,Y:B,G:(A > B),Z:B]: ((((((((fun_upd @ A) @ B) @ F) @ X2) @ Y) = (((((fun_upd @ A) @ B) @ G) @ X2) @ Z)) => (Y = Z))))).
% 3.47/1.70 thf(fact_197_fun__upd__def, axiom, (! [B:$tType,A:$tType]: ((((fun_upd @ A) @ B) = (^ [F3:(A > B),A6:A,B6:B,X:A]: (((((if @ B) @ (X = A6)) @ B6) @ (F3 @ X)))))))).
% 3.47/1.70 thf(fact_198_substitution_ORID_092_060_094sub_062L__finite__invariant, axiom, (! [V:$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_finite2 @ L) @ ((((lID_G @ R) @ L) @ V) @ S)) => ((finite_finite2 @ L) @ ((((lID_G @ R) @ L) @ V) @ S2)))))))).
% 3.47/1.70 thf(fact_199_ID__restricted__global__subset__unrestricted_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,S:(B > (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))),R2:B]: ((((ord_less_eq @ (set @ A)) @ ((((lID_G @ B) @ A) @ C) @ (((((fun_upd @ B) @ (option @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))) @ S) @ R2) @ (none @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ ((product_prod @ (A > (option @ (((val @ B) @ A) @ C)))) @ (((expr @ B) @ A) @ C))))))) @ ((((lID_G @ B) @ A) @ C) @ S))))).
% 3.47/1.70 thf(fact_200_substitution_Oreachable__imp__identifiers__finite_I2_J, axiom, (! [V:$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_finite2 @ L) @ ((((lID_G @ R) @ L) @ V) @ S))))))).
% 3.47/1.70 thf(fact_201_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_finite2 @ 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)))))))))))).
% 3.47/1.70 thf(fact_202_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_finite2 @ B) @ ((((lID_G @ A) @ B) @ C) @ S)) => ((finite_finite2 @ 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)))))))))))).
% 3.47/1.70 thf(fact_203_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_finite2 @ L) @ (top_top @ (set @ L))))) => (? [L2:L]: ((~ ((((member @ L) @ L2) @ ((((lID_G @ R) @ L) @ V) @ S)))))))))))).
% 3.47/1.70 thf(fact_204_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))))),L3:l]: (((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) => ((! [Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((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))) @ 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) @ V3))))))))) => ((~ ((((member @ l) @ L3) @ ((((lID_G @ r) @ l) @ v) @ S)))) => (~ ((((member @ l) @ L3) @ ((((lID_G @ r) @ l) @ v) @ S2)))))))))).
% 3.47/1.70 thf(fact_205_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))))))).
% 3.47/1.70 thf(fact_206_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_finite2 @ 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_finite2 @ A) @ ((((lID_L @ A) @ B) @ C) @ Ls)))))))).
% 3.47/1.70 thf(fact_207_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))),L3: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) @ L3) @ ((((lID_L @ A) @ B) @ C) @ Ls)) => (((member @ A) @ L3) @ ((((lID_G @ B) @ A) @ C) @ S))))))).
% 3.47/1.70 thf(fact_208_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)))))).
% 3.47/1.70 thf(fact_209_maximal__execution__def, axiom, (! [E4:(((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) @ E4) @ S) @ S2) = ((((((((execution @ r) @ l) @ v) @ subst) @ E4) @ S) @ S2) & (~ ((? [S6:(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) @ S6)) @ ((((steps @ r) @ l) @ v) @ subst))))))))))).
% 3.47/1.70 thf(fact_210_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) => ((! [Sigma:(l > (option @ (((val @ r) @ l) @ v))),Tau:(l > (option @ (((val @ r) @ l) @ v))),E:(((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))) @ 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) @ V3))))))))) => (((ord_less_eq @ (set @ l)) @ ((((lID_G @ r) @ l) @ v) @ S2)) @ ((((lID_G @ r) @ l) @ v) @ S))))))).
% 3.47/1.70 thf(fact_211_substitution_Osteps_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((steps @ R) @ L) @ V) = (((steps @ R) @ L) @ V))))).
% 3.47/1.70 thf(fact_212_expr_Odistinct_I5_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X42:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != ((((ref @ R) @ L) @ V) @ X42))))).
% 3.47/1.70 thf(fact_213_expr_Odistinct_I41_J, axiom, (! [V:$tType,L:$tType,R:$tType,X42:(((expr @ R) @ L) @ V),X7:(((expr @ R) @ L) @ V)]: ((((((ref @ R) @ L) @ V) @ X42) != ((((rfork @ R) @ L) @ V) @ X7))))).
% 3.47/1.70 thf(fact_214_expr_Odistinct_I43_J, axiom, (! [V:$tType,L:$tType,R:$tType,X42:(((expr @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: ((((((ref @ R) @ L) @ V) @ X42) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.47/1.70 thf(fact_215_LID_092_060_094sub_062GE, axiom, (! [C:$tType,B:$tType,A:$tType,L3: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) @ L3) @ ((((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) @ L3) @ ((((lID_L @ A) @ B) @ C) @ Ls3))))))))))))).
% 3.47/1.70 thf(fact_216_substitution_Ovalid__stepE, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((member @ ((product_prod @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))) @ ((((product_Pair @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ S) @ S2)) @ ((((steps @ R) @ L) @ V) @ Subst)) => (? [R7:R]: ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R7) @ S) @ S2)))))))).
% 3.47/1.70 thf(fact_217_substitution_Ovalid__stepI, axiom, (! [V:$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))))))).
% 3.47/1.70 thf(fact_218_substitution_Oonly__new__introduces__lids_H, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),R2:R,S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),L3:L]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) => ((! [Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((cntxt @ R) @ L) @ V),V3:(((val @ R) @ L) @ V)]: (((S @ R2) != ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau) @ (((((plug @ R) @ L) @ V) @ E) @ ((((ref @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ V3))))))))) => ((~ ((((member @ L) @ L3) @ ((((lID_G @ R) @ L) @ V) @ S)))) => (~ ((((member @ L) @ L3) @ ((((lID_G @ R) @ L) @ V) @ S2))))))))))).
% 3.47/1.70 thf(fact_219_substitution_Oonly__new__introduces__lids, axiom, (! [V:$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) => ((! [Sigma:(L > (option @ (((val @ R) @ L) @ V))),Tau:(L > (option @ (((val @ R) @ L) @ V))),E:(((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))) @ 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) @ V3))))))))) => (((ord_less_eq @ (set @ L)) @ ((((lID_G @ R) @ L) @ V) @ S2)) @ ((((lID_G @ R) @ L) @ V) @ S)))))))).
% 3.47/1.70 thf(fact_220_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_finite2 @ 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_finite2 @ A) @ ((((lID_L @ A) @ B) @ C) @ Ls))))))))).
% 3.47/1.70 thf(fact_221_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)))))).
% 3.47/1.70 thf(fact_222_SLC__new, 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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),V2:(((val @ 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))))),L3:l,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))) @ 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) @ V2))))))) => ((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)))) @ ((((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)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau2) @ L3) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L3)))))))) => ((~ ((((member @ l) @ L3) @ ((((lID_G @ r) @ l) @ v) @ S_1)))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R3) @ S_1) @ S_22) => ((R2 != R3) => ((((((reachable @ r) @ l) @ v) @ subst) @ S_1) => ((~ (((finite_finite2 @ l) @ (top_top @ (set @ l))))) => (? [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)))))))))))))))).
% 3.47/1.70 thf(fact_223_terminates__in__def, axiom, (! [E4:(((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) @ E4) @ 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) @ E4) @ S4) @ S2))))))).
% 3.47/1.70 thf(fact_224_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),V2:(((val @ r) @ l) @ v),L3: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))) @ 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) @ V2))))))) => ((~ ((((member @ l) @ L3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau2) @ L3) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L3))))))))))))).
% 3.47/1.70 thf(fact_225_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((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))) @ 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) @ 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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau2) @ L4) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L4)))))))))))))))).
% 3.47/1.70 thf(fact_226_val_Odistinct_I3_J, axiom, (! [R:$tType,V:$tType,L:$tType,X1:const,X34:L]: ((((((cv @ R) @ L) @ V) @ X1) != ((((loc @ L) @ R) @ V) @ X34))))).
% 3.47/1.70 thf(fact_227_val_Odistinct_I15_J, axiom, (! [L:$tType,V:$tType,R:$tType,X34:L,X42:R]: ((((((loc @ L) @ R) @ V) @ X34) != ((((rid @ R) @ L) @ V) @ X42))))).
% 3.47/1.70 thf(fact_228_substitution_Omaximal__execution_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((maximal_execution @ R) @ L) @ V) = (((maximal_execution @ R) @ L) @ V))))).
% 3.47/1.70 thf(fact_229_substitution_Odomains__subsume__def, axiom, (! [V:$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))))))).
% 3.47/1.70 thf(fact_230_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((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))) @ 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) @ 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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau2) @ L4) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L4))))))))))))))))).
% 3.47/1.70 thf(fact_231_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),V2:(((val @ R) @ L) @ V),L3: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))) @ 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) @ V2))))))) => ((~ ((((member @ L) @ L3) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau2) @ L3) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L3)))))))))))))).
% 3.47/1.70 thf(fact_232_substitution_Omaximal__execution__def, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),E4:(((expr @ R) @ L) @ V),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),S2:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((((substitution @ R) @ L) @ V) @ Subst) => ((((((((maximal_execution @ R) @ L) @ V) @ Subst) @ E4) @ S) @ S2) = ((((((((execution @ R) @ L) @ V) @ Subst) @ E4) @ S) @ S2) & (~ ((? [S6:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))]: ((((member @ ((product_prod @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))))) @ ((((product_Pair @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ (R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))))) @ S2) @ S6)) @ ((((steps @ R) @ L) @ V) @ Subst)))))))))))).
% 3.47/1.70 thf(fact_233_substitution_OSLC__new, axiom, (! [V:$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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),V2:(((val @ 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))))),L3:L,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))) @ 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) @ V2))))))) => ((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)))) @ ((((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)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau2) @ L3) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L3)))))))) => ((~ ((((member @ L) @ L3) @ ((((lID_G @ R) @ L) @ V) @ S_1)))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R3) @ S_1) @ S_22) => ((R2 != R3) => ((((((reachable @ R) @ L) @ V) @ Subst) @ S_1) => ((~ (((finite_finite2 @ L) @ (top_top @ (set @ L))))) => (? [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))))))))))))))))).
% 3.47/1.70 thf(fact_234_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),L3: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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ (((((assign @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L3))) @ ((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau2) @ L3) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))))))).
% 3.47/1.70 thf(fact_235_substitution_Orevision__step__relaxed_Oset, axiom, (! [R:$tType,L:$tType,V:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),S:(R > (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))),R2:R,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),L3:L,V2:(((val @ R) @ L) @ V)]: ((((((substitution @ R) @ L) @ V) @ Subst) => (((S @ R2) = ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ (((((assign @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L3))) @ ((((ve @ R) @ L) @ V) @ V2))))))) => (((((((revisi1433015572elaxed @ R) @ L) @ V) @ Subst) @ R2) @ S) @ (((((fun_upd @ R) @ (option @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))))) @ S) @ R2) @ ((some @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)))) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ ((product_prod @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau2) @ L3) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit))))))))))))).
% 3.47/1.70 thf(fact_236_substitution_Oterminates__in_Ocong, axiom, (! [V:$tType,L:$tType,R:$tType]: (((((terminates_in @ R) @ L) @ V) = (((terminates_in @ R) @ L) @ V))))).
% 3.47/1.70 thf(fact_237_expr_Odistinct_I9_J, axiom, (! [V:$tType,L:$tType,R:$tType,X1:(((val @ R) @ L) @ V),X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V)]: ((((((ve @ R) @ L) @ V) @ X1) != (((((assign @ R) @ L) @ V) @ X61) @ X62))))).
% 3.47/1.70 thf(fact_238_expr_Odistinct_I51_J, axiom, (! [V:$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))))).
% 3.47/1.70 thf(fact_239_expr_Odistinct_I53_J, axiom, (! [V:$tType,L:$tType,R:$tType,X61:(((expr @ R) @ L) @ V),X62:(((expr @ R) @ L) @ V),X8:(((expr @ R) @ L) @ V)]: (((((((assign @ R) @ L) @ V) @ X61) @ X62) != ((((rjoin @ R) @ L) @ V) @ X8))))).
% 3.47/1.70 thf(fact_240_substitution_Oterminates__in__def, axiom, (! [V:$tType,L:$tType,R:$tType,Subst:((((expr @ R) @ L) @ V) > (V > ((((expr @ R) @ L) @ V) > (((expr @ R) @ L) @ V)))),E4:(((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) @ E4) @ 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) @ E4) @ S4) @ S2)))))))).
% 3.47/1.70 thf(fact_241_SLC__set, 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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),L3:l,V2:(((val @ 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))))),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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ (((((assign @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L3))) @ ((((ve @ r) @ l) @ v) @ V2))))))) => ((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)))) @ ((((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)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau2) @ L3) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))) => ((((member @ l) @ L3) @ (((dom @ l) @ (((val @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma2) @ Tau2))) => ((((((((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)))))))))))))).
% 3.47/1.70 thf(fact_242_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),L3: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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ (((((assign @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L3))) @ ((((ve @ r) @ l) @ v) @ V2))))))) => ((((member @ l) @ L3) @ (((dom @ l) @ (((val @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma2) @ Tau2))) => (((((((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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau2) @ L3) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit))))))))))))).
% 3.47/1.70 thf(fact_243_dom__const, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((dom @ A) @ B) @ (^ [X:A]: (((some @ B) @ (F @ X))))) = (top_top @ (set @ A)))))).
% 3.47/1.70 thf(fact_244_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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),L3: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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ (((((assign @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L3))) @ ((((ve @ r) @ l) @ v) @ V2))))))) => ((((((((revision_step @ r) @ l) @ v) @ subst) @ R2) @ S) @ S2) = ((((member @ l) @ L3) @ (((dom @ l) @ (((val @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma2) @ Tau2))) & (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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ (((((fun_upd @ l) @ (option @ (((val @ r) @ l) @ v))) @ Tau2) @ L3) @ ((some @ (((val @ r) @ l) @ v)) @ V2))) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((ve @ r) @ l) @ v) @ ((((cv @ r) @ l) @ v) @ unit)))))))))))))).
% 3.47/1.70 thf(fact_245_domD, axiom, (! [A:$tType,B:$tType,A3:A,M:(A > (option @ B))]: (((((member @ A) @ A3) @ (((dom @ A) @ B) @ M)) => (? [B2:B]: (((M @ A3) = ((some @ B) @ B2)))))))).
% 3.47/1.70 thf(fact_246_domI, axiom, (! [A:$tType,B:$tType,M:(B > (option @ A)),A3:B,B3:A]: ((((M @ A3) = ((some @ A) @ B3)) => (((member @ B) @ A3) @ (((dom @ B) @ A) @ M)))))).
% 3.47/1.70 thf(fact_247_finite__map__freshness, axiom, (! [A:$tType,B:$tType,F:(A > (option @ B))]: ((((finite_finite2 @ A) @ (((dom @ A) @ B) @ F)) => ((~ (((finite_finite2 @ A) @ (top_top @ (set @ A))))) => (? [X4:A]: (((F @ X4) = (none @ B))))))))).
% 3.47/1.70 thf(fact_248_dom__def, axiom, (! [B:$tType,A:$tType]: ((((dom @ A) @ B) = (^ [M3:(A > (option @ B))]: (((collect @ A) @ (^ [A6:A]: (((M3 @ A6) != (none @ B))))))))))).
% 3.47/1.70 thf(fact_249_domIff, axiom, (! [A:$tType,B:$tType,A3:A,M:(A > (option @ B))]: (((((member @ A) @ A3) @ (((dom @ A) @ B) @ M)) = ((M @ A3) != (none @ B)))))).
% 3.47/1.70 thf(fact_250_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),L3: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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ (((((assign @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L3))) @ ((((ve @ R) @ L) @ V) @ V2))))))) => ((((((((revision_step @ R) @ L) @ V) @ Subst) @ R2) @ S) @ S2) = ((((member @ L) @ L3) @ (((dom @ L) @ (((val @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma2) @ Tau2))) & (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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau2) @ L3) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit))))))))))))))).
% 3.47/1.70 thf(fact_251_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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),L3: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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ (((((assign @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L3))) @ ((((ve @ R) @ L) @ V) @ V2))))))) => ((((member @ L) @ L3) @ (((dom @ L) @ (((val @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma2) @ Tau2))) => (((((((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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau2) @ L3) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))))))))).
% 3.47/1.70 thf(fact_252_substitution_OSLC__set, 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,Sigma2:(L > (option @ (((val @ R) @ L) @ V))),Tau2:(L > (option @ (((val @ R) @ L) @ V))),E3:(((cntxt @ R) @ L) @ V),L3:L,V2:(((val @ 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))))),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))) @ Sigma2) @ ((((product_Pair @ (L > (option @ (((val @ R) @ L) @ V)))) @ (((expr @ R) @ L) @ V)) @ Tau2) @ (((((plug @ R) @ L) @ V) @ E3) @ (((((assign @ R) @ L) @ V) @ ((((ve @ R) @ L) @ V) @ ((((loc @ L) @ R) @ V) @ L3))) @ ((((ve @ R) @ L) @ V) @ V2))))))) => ((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)))) @ ((((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)) @ (((((fun_upd @ L) @ (option @ (((val @ R) @ L) @ V))) @ Tau2) @ L3) @ ((some @ (((val @ R) @ L) @ V)) @ V2))) @ (((((plug @ R) @ L) @ V) @ E3) @ ((((ve @ R) @ L) @ V) @ ((((cv @ R) @ L) @ V) @ unit)))))))) => ((((member @ L) @ L3) @ (((dom @ L) @ (((val @ R) @ L) @ V)) @ ((((combine @ L) @ (((val @ R) @ L) @ V)) @ Sigma2) @ Tau2))) => ((((((((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))))))))))))))).
% 3.47/1.70 thf(fact_253_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)))))).
% 3.47/1.70 thf(fact_254_SLC__get, 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,Sigma2:(l > (option @ (((val @ r) @ l) @ v))),Tau2:(l > (option @ (((val @ r) @ l) @ v))),E3:(((cntxt @ r) @ l) @ v),L3:l,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))) @ Sigma2) @ ((((product_Pair @ (l > (option @ (((val @ r) @ l) @ v)))) @ (((expr @ r) @ l) @ v)) @ Tau2) @ (((((plug @ r) @ l) @ v) @ E3) @ ((((read @ r) @ l) @ v) @ ((((ve @ r) @ l) @ v) @ ((((loc @ l) @ r) @ v) @ L3)))))))) => ((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)))) @ ((((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) @ ((((ve @ r) @ l) @ v) @ ((the @ (((val @ r) @ l) @ v)) @ (((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma2) @ Tau2) @ L3))))))))) => ((((member @ l) @ L3) @ (((dom @ l) @ (((val @ r) @ l) @ v)) @ ((((combine @ l) @ (((val @ r) @ l) @ v)) @ Sigma2) @ Tau2))) => ((((((((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)))))))))))))).
% 3.47/1.70 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A7:$tType,A8:$tType]: ((((finite_finite @ A7) & (finite_finite @ A8)) => (finite_finite @ (A7 > A8)))))).
% 3.47/1.70 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 3.47/1.70 thf(tcon_Set_Oset___Finite__Set_Ofinite_1, axiom, (! [A7:$tType]: (((finite_finite @ A7) => (finite_finite @ (set @ A7)))))).
% 3.47/1.70 thf(tcon_Set_Oset___Orderings_Oorder_2, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 3.47/1.70 thf(tcon_HOL_Obool___Finite__Set_Ofinite_3, axiom, (finite_finite @ $o)).
% 3.47/1.70 thf(tcon_HOL_Obool___Orderings_Oorder_4, axiom, (order @ $o)).
% 3.47/1.70 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_5, axiom, (! [A7:$tType,A8:$tType]: ((((finite_finite @ A7) & (finite_finite @ A8)) => (finite_finite @ ((sum_sum @ A7) @ A8)))))).
% 3.47/1.70 thf(tcon_Option_Ooption___Finite__Set_Ofinite_6, axiom, (! [A7:$tType]: (((finite_finite @ A7) => (finite_finite @ (option @ A7)))))).
% 3.47/1.70 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_7, axiom, (! [A7:$tType,A8:$tType]: ((((finite_finite @ A7) & (finite_finite @ A8)) => (finite_finite @ ((product_prod @ A7) @ A8)))))).
% 3.47/1.70 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.47/1.70 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 3.47/1.70 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 3.47/1.70 thf(conj_0, conjecture, (r3 != right_forkee)).
% 3.47/1.70 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZhcMuhrmrf/DTF2DTF12937.p
% 3.47/1.70 ------------------------
% 3.49/1.83 ---- Cleaned THF ---
% 3.49/1.83 thf(ty_t_Product__Type_Oprod,type,
% 3.49/1.83 product_prod: $tType > $tType > $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_t_Sum__Type_Osum,type,
% 3.49/1.83 sum_sum: $tType > $tType > $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_t_Option_Ooption,type,
% 3.49/1.83 option: $tType > $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_t_Data_Oconst,type,
% 3.49/1.83 const: $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_t_Data_Ocntxt,type,
% 3.49/1.83 cntxt: $tType > $tType > $tType > $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_t_Data_Oexpr,type,
% 3.49/1.83 expr: $tType > $tType > $tType > $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_t_Data_Oval,type,
% 3.49/1.83 val: $tType > $tType > $tType > $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_t_Set_Oset,type,
% 3.49/1.83 set: $tType > $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_tf_v,type,
% 3.49/1.83 v: $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_tf_r,type,
% 3.49/1.83 r: $tType ).
% 3.49/1.83
% 3.49/1.83 thf(ty_tf_l,type,
% 3.49/1.83 l: $tType ).
% 3.49/1.83
% 3.49/1.83 thf(sy_cl_HOL_Otype,type,
% 3.49/1.83 type:
% 3.49/1.83 !>[A: $tType] : $o ).
% 3.49/1.83
% 3.49/1.83 thf(sy_cl_Orderings_Oorder,type,
% 3.49/1.83 order:
% 3.49/1.83 !>[A: $tType] : $o ).
% 3.49/1.83
% 3.49/1.83 thf(sy_cl_Finite__Set_Ofinite,type,
% 3.49/1.83 finite_finite:
% 3.49/1.83 !>[A: $tType] : $o ).
% 3.49/1.83
% 3.49/1.83 thf(sy_cl_Nat_Osemiring__char__0,type,
% 3.49/1.83 semiring_char_0:
% 3.49/1.83 !>[A: $tType] : $o ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Ocombine,type,
% 3.49/1.83 combine:
% 3.49/1.83 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( A > ( option @ B ) ) > A > ( option @ B ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oconst_OF,type,
% 3.49/1.83 f: const ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oconst_OT,type,
% 3.49/1.83 t: const ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oconst_OUnit,type,
% 3.49/1.83 unit: const ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Odoms,type,
% 3.49/1.83 doms:
% 3.49/1.83 !>[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 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oexpr_OAssign,type,
% 3.49/1.83 assign:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oexpr_OIte,type,
% 3.49/1.83 ite:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oexpr_ORead,type,
% 3.49/1.83 read:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oexpr_ORef,type,
% 3.49/1.83 ref:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oexpr_ORfork,type,
% 3.49/1.83 rfork:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oexpr_ORjoin,type,
% 3.49/1.83 rjoin:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oexpr_OVE,type,
% 3.49/1.83 ve:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( val @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oplug,type,
% 3.49/1.83 plug:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( cntxt @ R @ L @ V ) > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oval_OCV,type,
% 3.49/1.83 cv:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( const > ( val @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oval_OLoc,type,
% 3.49/1.83 loc:
% 3.49/1.83 !>[L: $tType,R: $tType,V: $tType] : ( L > ( val @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Data_Oval_ORid,type,
% 3.49/1.83 rid:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( R > ( val @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Executions_Osubstitution_Oexecution,type,
% 3.49/1.83 execution:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Executions_Osubstitution_Oinductive__invariant,type,
% 3.49/1.83 inductive_invariant:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Executions_Osubstitution_Omaximal__execution,type,
% 3.49/1.83 maximal_execution:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Executions_Osubstitution_Oreachable,type,
% 3.49/1.83 reachable:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Executions_Osubstitution_Osteps,type,
% 3.49/1.83 steps:
% 3.49/1.83 !>[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 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Executions_Osubstitution_Oterminates__in,type,
% 3.49/1.83 terminates_in:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Finite__Set_Ofinite,type,
% 3.49/1.83 finite_finite2:
% 3.49/1.83 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Fun_Ofun__upd,type,
% 3.49/1.83 fun_upd:
% 3.49/1.83 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_If,type,
% 3.49/1.83 if:
% 3.49/1.83 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Map_Odom,type,
% 3.49/1.83 dom:
% 3.49/1.83 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Occurrences_OLID_092_060_094sub_062G,type,
% 3.49/1.83 lID_G:
% 3.49/1.83 !>[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 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Occurrences_OLID_092_060_094sub_062L,type,
% 3.49/1.83 lID_L:
% 3.49/1.83 !>[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 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Occurrences_ORID_092_060_094sub_062G,type,
% 3.49/1.83 rID_G:
% 3.49/1.83 !>[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 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Occurrences_ORID_092_060_094sub_062L,type,
% 3.49/1.83 rID_L:
% 3.49/1.83 !>[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 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume,type,
% 3.49/1.83 domains_subsume:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally,type,
% 3.49/1.83 domain398919503obally:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step,type,
% 3.49/1.83 revision_step:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed,type,
% 3.49/1.83 revisi1433015572elaxed:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible,type,
% 3.49/1.83 subsumes_accessible:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally,type,
% 3.49/1.83 subsum380726323obally:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Option_Ooption_ONone,type,
% 3.49/1.83 none:
% 3.49/1.83 !>[A: $tType] : ( option @ A ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Option_Ooption_OSome,type,
% 3.49/1.83 some:
% 3.49/1.83 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Option_Ooption_Othe,type,
% 3.49/1.83 the:
% 3.49/1.83 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.49/1.83 ord_less_eq:
% 3.49/1.83 !>[A: $tType] : ( A > A > $o ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Orderings_Otop__class_Otop,type,
% 3.49/1.83 top_top:
% 3.49/1.83 !>[A: $tType] : A ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Product__Type_OPair,type,
% 3.49/1.83 product_Pair:
% 3.49/1.83 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Renaming_Oeq__states,type,
% 3.49/1.83 eq_states:
% 3.49/1.83 !>[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 ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Set_OCollect,type,
% 3.49/1.83 collect:
% 3.49/1.83 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Substitution_Osubstitution,type,
% 3.49/1.83 substitution:
% 3.49/1.83 !>[R: $tType,L: $tType,V: $tType] : ( ( ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ) ) > $o ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_Transitive__Closure_Ortrancl,type,
% 3.49/1.83 transitive_rtrancl:
% 3.49/1.83 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_c_member,type,
% 3.49/1.83 member:
% 3.49/1.83 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v__092_060E_062,type,
% 3.49/1.83 e: cntxt @ r @ l @ v ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v__092_060E_062_H____,type,
% 3.49/1.83 e2: cntxt @ r @ l @ v ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v__092_060sigma_062,type,
% 3.49/1.83 sigma: l > ( option @ ( val @ r @ l @ v ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v__092_060sigma_062_H____,type,
% 3.49/1.83 sigma2: l > ( option @ ( val @ r @ l @ v ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v__092_060tau_062,type,
% 3.49/1.83 tau: l > ( option @ ( val @ r @ l @ v ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v__092_060tau_062_H____,type,
% 3.49/1.83 tau2: l > ( option @ ( val @ r @ l @ v ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_e,type,
% 3.49/1.83 e3: expr @ r @ l @ v ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_e_H____,type,
% 3.49/1.83 e4: expr @ r @ l @ v ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_left__forkee,type,
% 3.49/1.83 left_forkee: r ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_r,type,
% 3.49/1.83 r2: r ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_r_H,type,
% 3.49/1.83 r3: r ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_right__forkee____,type,
% 3.49/1.83 right_forkee: r ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_s_092_060_094sub_0621,type,
% 3.49/1.83 s_1: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_s_092_060_094sub_0622,type,
% 3.49/1.83 s_2: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_s_092_060_094sub_0622_H,type,
% 3.49/1.83 s_22: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(sy_v_subst,type,
% 3.49/1.83 subst: ( expr @ r @ l @ v ) > v > ( expr @ r @ l @ v ) > ( expr @ r @ l @ v ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_0_local_Ofork_I3_J,axiom,
% 3.49/1.83 ~ ( member @ r @ right_forkee @ ( rID_G @ r @ l @ v @ s_1 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_1_side,axiom,
% 3.49/1.83 ~ ( member @ r @ left_forkee @ ( rID_G @ r @ l @ v @ s_1 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_2_neq,axiom,
% 3.49/1.83 r2 != r3 ).
% 3.49/1.83
% 3.49/1.83 thf(fact_3__092_060open_062r_H_A_092_060noteq_062_Aleft__forkee_092_060close_062,axiom,
% 3.49/1.83 r3 != left_forkee ).
% 3.49/1.83
% 3.49/1.83 thf(fact_4_r_H__unchanged__left,axiom,
% 3.49/1.83 ( ( s_2 @ r3 )
% 3.49/1.83 = ( s_1 @ r3 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_5__092_060open_062r_A_092_060noteq_062_Aright__forkee_092_060close_062,axiom,
% 3.49/1.83 r2 != right_forkee ).
% 3.49/1.83
% 3.49/1.83 thf(fact_6_local_Ofork_I2_J,axiom,
% 3.49/1.83 ( ( s_1 @ r3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ e2 @ ( rfork @ r @ l @ v @ e4 ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_7_right,axiom,
% 3.49/1.83 revision_step @ r @ l @ v @ subst @ r3 @ s_1 @ s_22 ).
% 3.49/1.83
% 3.49/1.83 thf(fact_8_local_Ofork_I1_J,axiom,
% 3.49/1.83 ( s_22
% 3.49/1.83 = ( 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 ) ) @ sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ tau2 @ ( plug @ r @ l @ v @ e2 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ right_forkee ) ) ) ) ) ) ) @ right_forkee
% 3.49/1.83 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.49/1.83 @ ( 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 ) @ sigma2 @ tau2 )
% 3.49/1.83 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.49/1.83 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.49/1.83 @ e4 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_9__092_060open_062r_A_092_060noteq_062_Aleft__forkee_092_060close_062,axiom,
% 3.49/1.83 r2 != left_forkee ).
% 3.49/1.83
% 3.49/1.83 thf(fact_10_r__unchanged__right,axiom,
% 3.49/1.83 ( ( s_22 @ r2 )
% 3.49/1.83 = ( s_1 @ r2 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_11_reach,axiom,
% 3.49/1.83 reachable @ r @ l @ v @ subst @ s_1 ).
% 3.49/1.83
% 3.49/1.83 thf(fact_12_left__step,axiom,
% 3.49/1.83 revision_step @ r @ l @ v @ subst @ r2 @ s_1 @ s_2 ).
% 3.49/1.83
% 3.49/1.83 thf(fact_13_only__fork__introduces__rids_H,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ! [Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v] :
% 3.49/1.83 ( ( S @ R2 )
% 3.49/1.83 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 3.49/1.83 => ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S2 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_14_revision__step_Ofork,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: expr @ r @ l @ v,R3: r] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 3.49/1.83 => ( revision_step @ r @ l @ v @ subst @ R2 @ S
% 3.49/1.83 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) @ R3
% 3.49/1.83 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.49/1.83 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.49/1.83 @ E4 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_15_fork__pseudodeterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( ? [R4: r] :
% 3.49/1.83 ( ~ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( rfork @ r @ l @ v @ E4 ) ) ) ) ) ) ) )
% 3.49/1.83 & ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R4 ) ) ) ) ) ) ) @ R4
% 3.49/1.83 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.49/1.83 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.49/1.83 @ E4 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_16_substitution__axioms,axiom,
% 3.49/1.83 substitution @ r @ l @ v @ subst ).
% 3.49/1.83
% 3.49/1.83 thf(fact_17_revision__step__relaxed_Ofork,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E4: expr @ r @ l @ v,R3: r] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ r @ R3 @ ( rID_G @ r @ l @ v @ S ) )
% 3.49/1.83 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S
% 3.49/1.83 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) @ R3
% 3.49/1.83 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.49/1.83 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.49/1.83 @ E4 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_18_local__and__fork__commute,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,R5: r,E4: expr @ r @ l @ v] :
% 3.49/1.83 ( ( S_2
% 3.49/1.83 = ( 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 ) ) )
% 3.49/1.83 => ( ( S_22
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) @ R5
% 3.49/1.83 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.49/1.83 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.49/1.83 @ E4 ) ) ) ) )
% 3.49/1.83 => ( ( ( S_2 @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ r @ R5 @ ( rID_G @ r @ l @ v @ S_2 ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22
% 3.49/1.83 @ ( fun_upd @ r @ ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )
% 3.49/1.83 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) @ R5
% 3.49/1.83 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.49/1.83 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.49/1.83 @ E4 ) ) ) )
% 3.49/1.83 @ R2
% 3.49/1.83 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ X2 ) ) )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( ( R2 != R5 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_19_s_092_060_094sub_0622,axiom,
% 3.49/1.83 ( s_2
% 3.49/1.83 = ( 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 ) @ tau @ ( plug @ r @ l @ v @ e @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ left_forkee ) ) ) ) ) ) ) @ left_forkee
% 3.49/1.83 @ ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) )
% 3.49/1.83 @ ( 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 )
% 3.49/1.83 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v )
% 3.49/1.83 @ ^ [X: l] : ( none @ ( val @ r @ l @ v ) )
% 3.49/1.83 @ e3 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_20_restrictions__inwards,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,X2: A,X3: A,F: A > ( option @ B ),Y: B] :
% 3.49/1.83 ( ( X2 != X3 )
% 3.49/1.83 => ( ( fun_upd @ A @ ( option @ B ) @ ( fun_upd @ A @ ( option @ B ) @ F @ X2 @ ( some @ B @ Y ) ) @ X3 @ ( none @ B ) )
% 3.49/1.83 = ( fun_upd @ A @ ( option @ B ) @ ( fun_upd @ A @ ( option @ B ) @ F @ X3 @ ( none @ B ) ) @ X2 @ ( some @ B @ Y ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_21_empty__upd__none,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,X2: A] :
% 3.49/1.83 ( ( fun_upd @ A @ ( option @ B )
% 3.49/1.83 @ ^ [X: A] : ( none @ B )
% 3.49/1.83 @ X2
% 3.49/1.83 @ ( none @ B ) )
% 3.49/1.83 = ( ^ [X: A] : ( none @ B ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_22_RID_092_060_094sub_062GI_I1_J,axiom,
% 3.49/1.83 ! [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 ) )] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ V2 ) )
% 3.49/1.83 => ( member @ B @ R2 @ ( rID_G @ B @ A @ C @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_23_not__None__eq,axiom,
% 3.49/1.83 ! [A: $tType,X2: option @ A] :
% 3.49/1.83 ( ( X2
% 3.49/1.83 != ( none @ A ) )
% 3.49/1.83 = ( ? [Y2: A] :
% 3.49/1.83 ( X2
% 3.49/1.83 = ( some @ A @ Y2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_24_not__Some__eq,axiom,
% 3.49/1.83 ! [A: $tType,X2: option @ A] :
% 3.49/1.83 ( ( ! [Y2: A] :
% 3.49/1.83 ( X2
% 3.49/1.83 != ( some @ A @ Y2 ) ) )
% 3.49/1.83 = ( X2
% 3.49/1.83 = ( none @ A ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_25_s_092_060_094sub_0621__r,axiom,
% 3.49/1.83 ( ( s_1 @ r2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 @ e3 ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_26_local__steps__commute,axiom,
% 3.49/1.83 ! [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 ) )] :
% 3.49/1.83 ( ( S_2
% 3.49/1.83 = ( 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 ) ) )
% 3.49/1.83 => ( ( S_22
% 3.49/1.83 = ( 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 ) ) )
% 3.49/1.83 => ( ( 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 ) ) )
% 3.49/1.83 => ( ( 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 ) ) )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_27_only__fork__introduces__rids,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ! [Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,E2: expr @ r @ l @ v] :
% 3.49/1.83 ( ( S @ R2 )
% 3.49/1.83 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 ) ) ) ) ) )
% 3.49/1.83 => ( ord_less_eq @ ( set @ r ) @ ( rID_G @ r @ l @ v @ S2 ) @ ( rID_G @ r @ l @ v @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_28_local__determinism,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_1 @ S_2 )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_1 @ S_22 )
% 3.49/1.83 => ( eq_states @ r @ l @ v @ S_2 @ S_22 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_29_SLC__sym,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_33 @ S_34 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_33 )
% 3.49/1.83 | ( S_2 = S_33 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_34 )
% 3.49/1.83 | ( S_22 = S_34 ) ) )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_3 )
% 3.49/1.83 | ( S_22 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_32 )
% 3.49/1.83 | ( S_2 = S_32 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_30_SLC__commute,axiom,
% 3.49/1.83 ! [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 ) ) ) ),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 ) ) ) )] :
% 3.49/1.83 ( ( S_35 = S_36 )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_35 )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_36 )
% 3.49/1.83 => ( ( eq_states @ r @ l @ v @ S_35 @ S_36 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_35 )
% 3.49/1.83 | ( S_2 = S_35 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_36 )
% 3.49/1.83 | ( S_22 = S_36 ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_31_reachability__closed__under__execution__step,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( reachable @ r @ l @ v @ subst @ S2 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_32_option_Oinject,axiom,
% 3.49/1.83 ! [A: $tType,X22: A,Y22: A] :
% 3.49/1.83 ( ( ( some @ A @ X22 )
% 3.49/1.83 = ( some @ A @ Y22 ) )
% 3.49/1.83 = ( X22 = Y22 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_33_transition__relations__equivalent,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S @ S2 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_34_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( 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 ) ) ) ) ) ) )
% 3.49/1.83 => ( member @ A @ R3 @ ( rID_G @ A @ B @ C @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_35_in__restricted__global__in__updated__global_I1_J,axiom,
% 3.49/1.83 ! [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 ) )] :
% 3.49/1.83 ( ( 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 ) ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_36_reachable__def,axiom,
% 3.49/1.83 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 = ( ? [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 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_37_substitution_Olocal__determinism,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_1 @ S_2 )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_1 @ S_22 )
% 3.49/1.83 => ( eq_states @ R @ L @ V @ S_2 @ S_22 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_38_substitution_OSLC__commute,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ 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 ) ) ) ),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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( S_35 = S_36 )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_35 )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_36 )
% 3.49/1.83 => ( ( eq_states @ R @ L @ V @ S_35 @ S_36 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_35 )
% 3.49/1.83 | ( S_2 = S_35 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_36 )
% 3.49/1.83 | ( S_22 = S_36 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_39_substitution_OSLC__sym,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_33 @ S_34 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_33 )
% 3.49/1.83 | ( S_2 = S_33 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_34 )
% 3.49/1.83 | ( S_22 = S_34 ) ) )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_3 )
% 3.49/1.83 | ( S_22 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_32 )
% 3.49/1.83 | ( S_2 = S_32 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_40_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 3.49/1.83 ! [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 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_41_substitution_Olocal__steps__commute,axiom,
% 3.49/1.83 ! [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 ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) )
% 3.49/1.83 => ( ( S_22
% 3.49/1.83 = ( 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 ) ) )
% 3.49/1.83 => ( ( 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 ) ) )
% 3.49/1.83 => ( ( 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 ) ) )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_42_substitution_Olocal__and__fork__commute,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,R5: R,E4: expr @ R @ L @ V] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) )
% 3.49/1.83 => ( ( S_22
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) @ R5
% 3.49/1.83 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 3.49/1.83 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 3.49/1.83 @ E4 ) ) ) ) )
% 3.49/1.83 => ( ( ( S_2 @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ R @ R5 @ ( rID_G @ R @ L @ V @ S_2 ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22
% 3.49/1.83 @ ( fun_upd @ R @ ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )
% 3.49/1.83 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) @ R5
% 3.49/1.83 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 3.49/1.83 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 3.49/1.83 @ E4 ) ) ) )
% 3.49/1.83 @ R2
% 3.49/1.83 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ X2 ) ) )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( ( R2 != R5 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_43_combine__options__cases,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,X2: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 3.49/1.83 ( ( ( X2
% 3.49/1.83 = ( none @ A ) )
% 3.49/1.83 => ( P @ X2 @ Y ) )
% 3.49/1.83 => ( ( ( Y
% 3.49/1.83 = ( none @ B ) )
% 3.49/1.83 => ( P @ X2 @ Y ) )
% 3.49/1.83 => ( ! [A2: A,B2: B] :
% 3.49/1.83 ( ( X2
% 3.49/1.83 = ( some @ A @ A2 ) )
% 3.49/1.83 => ( ( Y
% 3.49/1.83 = ( some @ B @ B2 ) )
% 3.49/1.83 => ( P @ X2 @ Y ) ) )
% 3.49/1.83 => ( P @ X2 @ Y ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_44_mem__Collect__eq,axiom,
% 3.49/1.83 ! [A: $tType,A3: A,P: A > $o] :
% 3.49/1.83 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 3.49/1.83 = ( P @ A3 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_45_Collect__mem__eq,axiom,
% 3.49/1.83 ! [A: $tType,A4: set @ A] :
% 3.49/1.83 ( ( collect @ A
% 3.49/1.83 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 3.49/1.83 = A4 ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_46_Collect__cong,axiom,
% 3.49/1.83 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.49/1.83 ( ! [X4: A] :
% 3.49/1.83 ( ( P @ X4 )
% 3.49/1.83 = ( Q @ X4 ) )
% 3.49/1.83 => ( ( collect @ A @ P )
% 3.49/1.83 = ( collect @ A @ Q ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_47_ext,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.49/1.83 ( ! [X4: A] :
% 3.49/1.83 ( ( F @ X4 )
% 3.49/1.83 = ( G @ X4 ) )
% 3.49/1.83 => ( F = G ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_48_split__option__all,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( ^ [P2: ( option @ A ) > $o] :
% 3.49/1.83 ! [X5: option @ A] : ( P2 @ X5 ) )
% 3.49/1.83 = ( ^ [P3: ( option @ A ) > $o] :
% 3.49/1.83 ( ( P3 @ ( none @ A ) )
% 3.49/1.83 & ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_49_split__option__ex,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( ^ [P2: ( option @ A ) > $o] :
% 3.49/1.83 ? [X5: option @ A] : ( P2 @ X5 ) )
% 3.49/1.83 = ( ^ [P3: ( option @ A ) > $o] :
% 3.49/1.83 ( ( P3 @ ( none @ A ) )
% 3.49/1.83 | ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_50_option_Oinducts,axiom,
% 3.49/1.83 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 3.49/1.83 ( ( P @ ( none @ A ) )
% 3.49/1.83 => ( ! [X4: A] : ( P @ ( some @ A @ X4 ) )
% 3.49/1.83 => ( P @ Option ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_51_option_Oexhaust,axiom,
% 3.49/1.83 ! [A: $tType,Y: option @ A] :
% 3.49/1.83 ( ( Y
% 3.49/1.83 != ( none @ A ) )
% 3.49/1.83 => ~ ! [X23: A] :
% 3.49/1.83 ( Y
% 3.49/1.83 != ( some @ A @ X23 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_52_option_OdiscI,axiom,
% 3.49/1.83 ! [A: $tType,Option: option @ A,X22: A] :
% 3.49/1.83 ( ( Option
% 3.49/1.83 = ( some @ A @ X22 ) )
% 3.49/1.83 => ( Option
% 3.49/1.83 != ( none @ A ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_53_option_Odistinct_I1_J,axiom,
% 3.49/1.83 ! [A: $tType,X22: A] :
% 3.49/1.83 ( ( none @ A )
% 3.49/1.83 != ( some @ A @ X22 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_54_map__upd__Some__unfold,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,M: B > ( option @ A ),A3: B,B3: A,X2: B,Y: A] :
% 3.49/1.83 ( ( ( fun_upd @ B @ ( option @ A ) @ M @ A3 @ ( some @ A @ B3 ) @ X2 )
% 3.49/1.83 = ( some @ A @ Y ) )
% 3.49/1.83 = ( ( ( X2 = A3 )
% 3.49/1.83 & ( B3 = Y ) )
% 3.49/1.83 | ( ( X2 != A3 )
% 3.49/1.83 & ( ( M @ X2 )
% 3.49/1.83 = ( some @ A @ Y ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_55_map__upd__triv,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,T: B > ( option @ A ),K: B,X2: A] :
% 3.49/1.83 ( ( ( T @ K )
% 3.49/1.83 = ( some @ A @ X2 ) )
% 3.49/1.83 => ( ( fun_upd @ B @ ( option @ A ) @ T @ K @ ( some @ A @ X2 ) )
% 3.49/1.83 = T ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_56_map__upd__eqD1,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,M: A > ( option @ B ),A3: A,X2: B,N: A > ( option @ B ),Y: B] :
% 3.49/1.83 ( ( ( fun_upd @ A @ ( option @ B ) @ M @ A3 @ ( some @ B @ X2 ) )
% 3.49/1.83 = ( fun_upd @ A @ ( option @ B ) @ N @ A3 @ ( some @ B @ Y ) ) )
% 3.49/1.83 => ( X2 = Y ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_57_map__upd__nonempty,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,T: A > ( option @ B ),K: A,X2: B] :
% 3.49/1.83 ( ( fun_upd @ A @ ( option @ B ) @ T @ K @ ( some @ B @ X2 ) )
% 3.49/1.83 != ( ^ [X: A] : ( none @ B ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_58_substitution_Ofork__pseudodeterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( ? [R4: R] :
% 3.49/1.83 ( ~ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( rfork @ R @ L @ V @ E4 ) ) ) ) ) ) ) )
% 3.49/1.83 & ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R4 ) ) ) ) ) ) ) @ R4
% 3.49/1.83 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 3.49/1.83 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 3.49/1.83 @ E4 ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_59_inductive__invariant__is__execution__invariant,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 => ( ( inductive_invariant @ r @ l @ v @ subst @ P )
% 3.49/1.83 => ( P @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_60_substitution_Orevision__step__relaxed_Ofork,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: expr @ R @ L @ V,R3: R] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 3.49/1.83 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S
% 3.49/1.83 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) @ R3
% 3.49/1.83 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 3.49/1.83 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 3.49/1.83 @ E4 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_61_substitution_Orevision__step_Ofork,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E4: expr @ R @ L @ V,R3: R] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 3.49/1.83 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S
% 3.49/1.83 @ ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) @ R3
% 3.49/1.83 @ ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) )
% 3.49/1.83 @ ( 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 ) @ Sigma2 @ Tau2 )
% 3.49/1.83 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V )
% 3.49/1.83 @ ^ [X: L] : ( none @ ( val @ R @ L @ V ) )
% 3.49/1.83 @ E4 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_62_substitution_Oonly__fork__introduces__rids,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V] :
% 3.49/1.83 ( ( S @ R2 )
% 3.49/1.83 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ 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 ) ) ) ) ) )
% 3.49/1.83 => ( ord_less_eq @ ( set @ R ) @ ( rID_G @ R @ L @ V @ S2 ) @ ( rID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_63_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 3.49/1.83 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 => ( domain398919503obally @ r @ l @ v @ S ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_64_substitution_Oonly__fork__introduces__rids_H,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,E2: expr @ R @ L @ V] :
% 3.49/1.83 ( ( S @ R2 )
% 3.49/1.83 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ 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 ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S ) )
% 3.49/1.83 => ~ ( member @ R @ R3 @ ( rID_G @ R @ L @ V @ S2 ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_65_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S_1 @ R5 )
% 3.49/1.83 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_66_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,R3: r] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 3.49/1.83 => ( revisi1433015572elaxed @ r @ l @ v @ subst @ R2 @ S
% 3.49/1.83 @ ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_67_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,R3: r] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 3.49/1.83 => ( revision_step @ r @ l @ v @ subst @ R2 @ S
% 3.49/1.83 @ ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_68_domains__subsume__globally__def,axiom,
% 3.49/1.83 ( ( domain398919503obally @ r @ l @ v )
% 3.49/1.83 = ( ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ! [R6: r,Ls2: product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) )] :
% 3.49/1.83 ( ( ( S4 @ R6 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ Ls2 ) )
% 3.49/1.83 => ( domains_subsume @ l @ r @ v @ Ls2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_69_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( S2
% 3.49/1.83 = ( ^ [X: r] : ( none @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_70_substitution_Orevision__step_Ocong,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType] :
% 3.49/1.83 ( ( revision_step @ R @ L @ V )
% 3.49/1.83 = ( revision_step @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_71_substitution_Orevision__step__relaxed_Ocong,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType] :
% 3.49/1.83 ( ( revisi1433015572elaxed @ R @ L @ V )
% 3.49/1.83 = ( revisi1433015572elaxed @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_72_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,R3: R] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 3.49/1.83 => ( revision_step @ R @ L @ V @ Subst @ R2 @ S
% 3.49/1.83 @ ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_73_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,R3: R] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 3.49/1.83 => ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S
% 3.49/1.83 @ ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_74_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( S2
% 3.49/1.83 = ( ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_75_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( ^ [X: R] : ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S_1 @ R5 )
% 3.49/1.83 = ( none @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_76_nice__ind__inv__is__inductive__invariant,axiom,
% 3.49/1.83 ( inductive_invariant @ r @ l @ v @ subst
% 3.49/1.83 @ ^ [S4: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ( domain398919503obally @ r @ l @ v @ S4 )
% 3.49/1.83 & ( subsum380726323obally @ r @ l @ v @ S4 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_77_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ( domain398919503obally @ r @ l @ v @ S )
% 3.49/1.83 => ( ( subsum380726323obally @ r @ l @ v @ S )
% 3.49/1.83 => ( subsum380726323obally @ r @ l @ v @ S2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_78_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ( domain398919503obally @ r @ l @ v @ S )
% 3.49/1.83 => ( ( subsum380726323obally @ r @ l @ v @ S )
% 3.49/1.83 => ( domain398919503obally @ r @ l @ v @ S2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_79_substitution_Odomains__subsume__globallyI,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ! [R7: R,Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E2: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ( S @ R7 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ E2 ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ E2 ) ) ) )
% 3.49/1.83 => ( domain398919503obally @ R @ L @ V @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_80_substitution_Otransition__relations__equivalent,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( revisi1433015572elaxed @ R @ L @ V @ Subst @ R2 @ S @ S2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_81_domains__subsume__globallyI,axiom,
% 3.49/1.83 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ! [R7: r,Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E2: expr @ r @ l @ v] :
% 3.49/1.83 ( ( ( S @ R7 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ E2 ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau @ E2 ) ) ) )
% 3.49/1.83 => ( domain398919503obally @ r @ l @ v @ S ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_82_substitution_Oreachable__def,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 = ( ? [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 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_83_substitution_Oreachable_Ocong,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType] :
% 3.49/1.83 ( ( reachable @ R @ L @ V )
% 3.49/1.83 = ( reachable @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_84_substitution_Oinductive__invariant_Ocong,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType] :
% 3.49/1.83 ( ( inductive_invariant @ R @ L @ V )
% 3.49/1.83 = ( inductive_invariant @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_85_substitution_Oexecution_Ocong,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType] :
% 3.49/1.83 ( ( execution @ R @ L @ V )
% 3.49/1.83 = ( execution @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_86_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( inductive_invariant @ R @ L @ V @ Subst
% 3.49/1.83 @ ^ [S4: R > ( option @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) )] :
% 3.49/1.83 ( ( domain398919503obally @ R @ L @ V @ S4 )
% 3.49/1.83 & ( subsum380726323obally @ R @ L @ V @ S4 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_87_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ( domain398919503obally @ R @ L @ V @ S )
% 3.49/1.83 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 3.49/1.83 => ( subsum380726323obally @ R @ L @ V @ S2 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_88_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ( domain398919503obally @ R @ L @ V @ S )
% 3.49/1.83 => ( ( subsum380726323obally @ R @ L @ V @ S )
% 3.49/1.83 => ( domain398919503obally @ R @ L @ V @ S2 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_89_substitution_Odomains__subsume__globally__def,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( domain398919503obally @ R @ L @ V @ S )
% 3.49/1.83 = ( ! [R6: R,Ls2: product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) )] :
% 3.49/1.83 ( ( ( S @ R6 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ Ls2 ) )
% 3.49/1.83 => ( domains_subsume @ L @ R @ V @ Ls2 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_90_substitution_Oreachability__closed__under__execution__step,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( reachable @ R @ L @ V @ Subst @ S2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_91_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 => ( domain398919503obally @ R @ L @ V @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_92_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 => ( ( inductive_invariant @ R @ L @ V @ Subst @ P )
% 3.49/1.83 => ( P @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_93_substitution_Osubsumes__accessible__globallyI,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ! [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] :
% 3.49/1.83 ( ( ( S @ R_1 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ 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 ) ) ) )
% 3.49/1.83 => ( ( ( S @ R_2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ 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 ) ) ) )
% 3.49/1.83 => ( subsumes_accessible @ R @ L @ V @ R_1 @ R_2 @ S ) ) )
% 3.49/1.83 => ( subsum380726323obally @ R @ L @ V @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_94_join__and__local__commute,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),Tau3: l > ( option @ ( val @ r @ l @ v ) ),E3: 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] :
% 3.49/1.83 ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ( S_22
% 3.49/1.83 = ( 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 ) ) )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( ( R3 != R5 )
% 3.49/1.83 => ( ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) )
% 3.49/1.83 => ( ( ( S_22 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S_22 @ R5 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_95_SLC__join,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R5 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S_1 @ R5 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_96_revision__step__relaxed_Ojoin,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_97_reachable__imp__identifiers__finite_I1_J,axiom,
% 3.49/1.83 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 => ( finite_finite2 @ r @ ( rID_G @ r @ l @ v @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_98_revision__step_Ojoin,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_99_empty__map__finite_I3_J,axiom,
% 3.49/1.83 ! [H: $tType,I: $tType,G2: $tType] :
% 3.49/1.83 ( finite_finite2 @ G2
% 3.49/1.83 @ ( rID_G @ G2 @ H @ I
% 3.49/1.83 @ ^ [X: G2] : ( none @ ( product_prod @ ( H > ( option @ ( val @ G2 @ H @ I ) ) ) @ ( product_prod @ ( H > ( option @ ( val @ G2 @ H @ I ) ) ) @ ( expr @ G2 @ H @ I ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_100_rid__inf,axiom,
% 3.49/1.83 ~ ( finite_finite2 @ r @ ( top_top @ ( set @ r ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_101_RID_092_060_094sub_062G__finite__invariant,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ( finite_finite2 @ r @ ( rID_G @ r @ l @ v @ S ) )
% 3.49/1.83 => ( finite_finite2 @ r @ ( rID_G @ r @ l @ v @ S2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_102_finite__state__imp__restriction__finite_I1_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( finite_finite2 @ A @ ( rID_G @ A @ B @ C @ S ) )
% 3.49/1.83 => ( finite_finite2 @ 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 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_103_subsumes__accessible__globallyI,axiom,
% 3.49/1.83 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ! [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] :
% 3.49/1.83 ( ( ( S @ R_1 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ 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 ) ) ) )
% 3.49/1.83 => ( ( ( S @ R_2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ 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 ) ) ) )
% 3.49/1.83 => ( subsumes_accessible @ r @ l @ v @ R_1 @ R_2 @ S ) ) )
% 3.49/1.83 => ( subsum380726323obally @ r @ l @ v @ S ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_104_rjoin__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( rjoin @ r @ l @ v @ ( ve @ r @ l @ v @ ( rid @ r @ l @ v @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Tau2 @ Tau3 ) @ ( plug @ r @ l @ v @ E3 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_105_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ( finite_finite2 @ R @ ( rID_G @ R @ L @ V @ S ) )
% 3.49/1.83 => ( finite_finite2 @ R @ ( rID_G @ R @ L @ V @ S2 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_106_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 => ( finite_finite2 @ R @ ( rID_G @ R @ L @ V @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_107_substitution_Oempty__map__finite_I3_J,axiom,
% 3.49/1.83 ! [R: $tType,L: $tType,V: $tType,H: $tType,I: $tType,G2: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( finite_finite2 @ G2
% 3.49/1.83 @ ( rID_G @ G2 @ H @ I
% 3.49/1.83 @ ^ [X: G2] : ( none @ ( product_prod @ ( H > ( option @ ( val @ G2 @ H @ I ) ) ) @ ( product_prod @ ( H > ( option @ ( val @ G2 @ H @ I ) ) ) @ ( expr @ G2 @ H @ I ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_108_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( finite_finite2 @ A @ ( rID_G @ A @ B @ C @ S ) )
% 3.49/1.83 => ( finite_finite2 @ 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 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_109_substitution_Orevision__step_Ojoin,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_110_substitution_Orjoin__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_111_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_112_substitution_OSLC__join,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S_1 @ R5 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_113_substitution_Ojoin__and__local__commute,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),Tau3: L > ( option @ ( val @ R @ L @ V ) ),E3: 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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) ) ) ) )
% 3.49/1.83 => ( ( S_22
% 3.49/1.83 = ( 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 ) ) )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( ( R3 != R5 )
% 3.49/1.83 => ( ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Tau2 @ Tau3 ) @ ( plug @ R @ L @ V @ E3 @ ( 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 ) ) )
% 3.49/1.83 => ( ( ( S_22 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( rjoin @ R @ L @ V @ ( ve @ R @ L @ V @ ( rid @ R @ L @ V @ R5 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( ( S_22 @ R5 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 ) ) ) ) )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_114_finite__Collect__subsets,axiom,
% 3.49/1.83 ! [A: $tType,A4: set @ A] :
% 3.49/1.83 ( ( finite_finite2 @ A @ A4 )
% 3.49/1.83 => ( finite_finite2 @ ( set @ A )
% 3.49/1.83 @ ( collect @ ( set @ A )
% 3.49/1.83 @ ^ [B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_115_reachable__imp__identifiers__available_I1_J,axiom,
% 3.49/1.83 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 => ( ~ ( finite_finite2 @ r @ ( top_top @ ( set @ r ) ) )
% 3.49/1.83 => ? [R7: r] :
% 3.49/1.83 ~ ( member @ r @ R7 @ ( rID_G @ r @ l @ v @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_116_finite__Collect__conjI,axiom,
% 3.49/1.83 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.49/1.83 ( ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 3.49/1.83 | ( finite_finite2 @ A @ ( collect @ A @ Q ) ) )
% 3.49/1.83 => ( finite_finite2 @ A
% 3.49/1.83 @ ( collect @ A
% 3.49/1.83 @ ^ [X: A] :
% 3.49/1.83 ( ( P @ X )
% 3.49/1.83 & ( Q @ X ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_117_finite__Collect__disjI,axiom,
% 3.49/1.83 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.49/1.83 ( ( finite_finite2 @ A
% 3.49/1.83 @ ( collect @ A
% 3.49/1.83 @ ^ [X: A] :
% 3.49/1.83 ( ( P @ X )
% 3.49/1.83 | ( Q @ X ) ) ) )
% 3.49/1.83 = ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 3.49/1.83 & ( finite_finite2 @ A @ ( collect @ A @ Q ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_118_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.49/1.83 => ( ( finite_finite2 @ 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 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( finite_finite2 @ B @ ( rID_L @ A @ B @ C @ Ls ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_119_finite__code,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( finite_finite @ A )
% 3.49/1.83 => ( ( finite_finite2 @ A )
% 3.49/1.83 = ( ^ [A5: set @ A] : $true ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_120_finite__option__UNIV,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( finite_finite2 @ ( option @ A ) @ ( top_top @ ( set @ ( option @ A ) ) ) )
% 3.49/1.83 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_121_finite__Plus__UNIV__iff,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType] :
% 3.49/1.83 ( ( finite_finite2 @ ( sum_sum @ A @ B ) @ ( top_top @ ( set @ ( sum_sum @ A @ B ) ) ) )
% 3.49/1.83 = ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 3.49/1.83 & ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_122_finite__Collect__not,axiom,
% 3.49/1.83 ! [A: $tType,P: A > $o] :
% 3.49/1.83 ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 3.49/1.83 => ( ( finite_finite2 @ A
% 3.49/1.83 @ ( collect @ A
% 3.49/1.83 @ ^ [X: A] :
% 3.49/1.83 ~ ( P @ X ) ) )
% 3.49/1.83 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_123_RID_092_060_094sub_062GI_I2_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.49/1.83 => ( ( member @ B @ R2 @ ( rID_L @ A @ B @ C @ Ls ) )
% 3.49/1.83 => ( member @ B @ R2 @ ( rID_G @ B @ A @ C @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_124_Finite__Set_Ofinite__set,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( finite_finite2 @ ( set @ A ) @ ( top_top @ ( set @ ( set @ A ) ) ) )
% 3.49/1.83 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_125_finite__prod,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType] :
% 3.49/1.83 ( ( finite_finite2 @ ( product_prod @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 3.49/1.83 = ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 3.49/1.83 & ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_126_ex__new__if__finite,axiom,
% 3.49/1.83 ! [A: $tType,A4: set @ A] :
% 3.49/1.83 ( ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 3.49/1.83 => ( ( finite_finite2 @ A @ A4 )
% 3.49/1.83 => ? [A2: A] :
% 3.49/1.83 ~ ( member @ A @ A2 @ A4 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_127_finite__Prod__UNIV,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType] :
% 3.49/1.83 ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 3.49/1.83 => ( ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) )
% 3.49/1.83 => ( finite_finite2 @ ( product_prod @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_128_finite__fun__UNIVD2,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType] :
% 3.49/1.83 ( ( finite_finite2 @ ( A > B ) @ ( top_top @ ( set @ ( A > B ) ) ) )
% 3.49/1.83 => ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_129_infinite__UNIV__char__0,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( semiring_char_0 @ A )
% 3.49/1.83 => ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_130_finite__UNIV,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( finite_finite @ A )
% 3.49/1.83 => ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_131_finite,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( finite_finite @ A )
% 3.49/1.83 => ! [A4: set @ A] : ( finite_finite2 @ A @ A4 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_132_finite__set__choice,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,A4: set @ A,P: A > B > $o] :
% 3.49/1.83 ( ( finite_finite2 @ A @ A4 )
% 3.49/1.83 => ( ! [X4: A] :
% 3.49/1.83 ( ( member @ A @ X4 @ A4 )
% 3.49/1.83 => ? [X_1: B] : ( P @ X4 @ X_1 ) )
% 3.49/1.83 => ? [F2: A > B] :
% 3.49/1.83 ! [X6: A] :
% 3.49/1.83 ( ( member @ A @ X6 @ A4 )
% 3.49/1.83 => ( P @ X6 @ ( F2 @ X6 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_133_pigeonhole__infinite__rel,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,A4: set @ A,B5: set @ B,R8: A > B > $o] :
% 3.49/1.83 ( ~ ( finite_finite2 @ A @ A4 )
% 3.49/1.83 => ( ( finite_finite2 @ B @ B5 )
% 3.49/1.83 => ( ! [X4: A] :
% 3.49/1.83 ( ( member @ A @ X4 @ A4 )
% 3.49/1.83 => ? [Xa: B] :
% 3.49/1.83 ( ( member @ B @ Xa @ B5 )
% 3.49/1.83 & ( R8 @ X4 @ Xa ) ) )
% 3.49/1.83 => ? [X4: B] :
% 3.49/1.83 ( ( member @ B @ X4 @ B5 )
% 3.49/1.83 & ~ ( finite_finite2 @ A
% 3.49/1.83 @ ( collect @ A
% 3.49/1.83 @ ^ [A6: A] :
% 3.49/1.83 ( ( member @ A @ A6 @ A4 )
% 3.49/1.83 & ( R8 @ A6 @ X4 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_134_not__finite__existsD,axiom,
% 3.49/1.83 ! [A: $tType,P: A > $o] :
% 3.49/1.83 ( ~ ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 3.49/1.83 => ? [X_12: A] : ( P @ X_12 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_135_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 => ( ~ ( finite_finite2 @ R @ ( top_top @ ( set @ R ) ) )
% 3.49/1.83 => ? [R7: R] :
% 3.49/1.83 ~ ( member @ R @ R7 @ ( rID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_136_finite__has__minimal2,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( order @ A )
% 3.49/1.83 => ! [A4: set @ A,A3: A] :
% 3.49/1.83 ( ( finite_finite2 @ A @ A4 )
% 3.49/1.83 => ( ( member @ A @ A3 @ A4 )
% 3.49/1.83 => ? [X4: A] :
% 3.49/1.83 ( ( member @ A @ X4 @ A4 )
% 3.49/1.83 & ( ord_less_eq @ A @ X4 @ A3 )
% 3.49/1.83 & ! [Xa: A] :
% 3.49/1.83 ( ( member @ A @ Xa @ A4 )
% 3.49/1.83 => ( ( ord_less_eq @ A @ Xa @ X4 )
% 3.49/1.83 => ( X4 = Xa ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_137_finite__has__maximal2,axiom,
% 3.49/1.83 ! [A: $tType] :
% 3.49/1.83 ( ( order @ A )
% 3.49/1.83 => ! [A4: set @ A,A3: A] :
% 3.49/1.83 ( ( finite_finite2 @ A @ A4 )
% 3.49/1.83 => ( ( member @ A @ A3 @ A4 )
% 3.49/1.83 => ? [X4: A] :
% 3.49/1.83 ( ( member @ A @ X4 @ A4 )
% 3.49/1.83 & ( ord_less_eq @ A @ A3 @ X4 )
% 3.49/1.83 & ! [Xa: A] :
% 3.49/1.83 ( ( member @ A @ Xa @ A4 )
% 3.49/1.83 => ( ( ord_less_eq @ A @ X4 @ Xa )
% 3.49/1.83 => ( X4 = Xa ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_138_finite__subset,axiom,
% 3.49/1.83 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 3.49/1.83 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 3.49/1.83 => ( ( finite_finite2 @ A @ B5 )
% 3.49/1.83 => ( finite_finite2 @ A @ A4 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_139_infinite__super,axiom,
% 3.49/1.83 ! [A: $tType,S5: set @ A,T2: set @ A] :
% 3.49/1.83 ( ( ord_less_eq @ ( set @ A ) @ S5 @ T2 )
% 3.49/1.83 => ( ~ ( finite_finite2 @ A @ S5 )
% 3.49/1.83 => ~ ( finite_finite2 @ A @ T2 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_140_rev__finite__subset,axiom,
% 3.49/1.83 ! [A: $tType,B5: set @ A,A4: set @ A] :
% 3.49/1.83 ( ( finite_finite2 @ A @ B5 )
% 3.49/1.83 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 3.49/1.83 => ( finite_finite2 @ A @ A4 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_141_finite__update__induct,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,F: A > B,C2: B,P: ( A > B ) > $o] :
% 3.49/1.83 ( ( finite_finite2 @ A
% 3.49/1.83 @ ( collect @ A
% 3.49/1.83 @ ^ [A6: A] :
% 3.49/1.83 ( ( F @ A6 )
% 3.49/1.83 != C2 ) ) )
% 3.49/1.83 => ( ( P
% 3.49/1.83 @ ^ [A6: A] : C2 )
% 3.49/1.83 => ( ! [A2: A,B2: B,F2: A > B] :
% 3.49/1.83 ( ( finite_finite2 @ A
% 3.49/1.83 @ ( collect @ A
% 3.49/1.83 @ ^ [C3: A] :
% 3.49/1.83 ( ( F2 @ C3 )
% 3.49/1.83 != C2 ) ) )
% 3.49/1.83 => ( ( ( F2 @ A2 )
% 3.49/1.83 = C2 )
% 3.49/1.83 => ( ( B2 != C2 )
% 3.49/1.83 => ( ( P @ F2 )
% 3.49/1.83 => ( P @ ( fun_upd @ A @ B @ F2 @ A2 @ B2 ) ) ) ) ) )
% 3.49/1.83 => ( P @ F ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_142_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.49/1.83 => ( ( finite_finite2 @ 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 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( finite_finite2 @ B @ ( rID_L @ A @ B @ C @ Ls ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_143_SLC__ifTrue,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: 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 ) ) ) ),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 ) ) ) )] :
% 3.49/1.83 ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E1 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_144_SLC__ifFalse,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: 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 ) ) ) ),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 ) ) ) )] :
% 3.49/1.83 ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_145_expr_Oinject_I7_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X7: expr @ R @ L @ V,Y7: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ( rfork @ R @ L @ V @ X7 )
% 3.49/1.83 = ( rfork @ R @ L @ V @ Y7 ) )
% 3.49/1.83 = ( X7 = Y7 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_146_val_Oinject_I4_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X42: R,Y4: R] :
% 3.49/1.83 ( ( ( rid @ R @ L @ V @ X42 )
% 3.49/1.83 = ( rid @ R @ L @ V @ Y4 ) )
% 3.49/1.83 = ( X42 = Y4 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_147_expr_Oinject_I1_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,Y1: val @ R @ L @ V] :
% 3.49/1.83 ( ( ( ve @ R @ L @ V @ X1 )
% 3.49/1.83 = ( ve @ R @ L @ V @ Y1 ) )
% 3.49/1.83 = ( X1 = Y1 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_148_injective__cntxt,axiom,
% 3.49/1.83 ! [C: $tType,B: $tType,A: $tType,E3: cntxt @ A @ B @ C,E1: expr @ A @ B @ C,E22: expr @ A @ B @ C] :
% 3.49/1.83 ( ( ( plug @ A @ B @ C @ E3 @ E1 )
% 3.49/1.83 = ( plug @ A @ B @ C @ E3 @ E22 ) )
% 3.49/1.83 = ( E1 = E22 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_149_val_Oinject_I1_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X1: const,Y1: const] :
% 3.49/1.83 ( ( ( cv @ R @ L @ V @ X1 )
% 3.49/1.83 = ( cv @ R @ L @ V @ Y1 ) )
% 3.49/1.83 = ( X1 = Y1 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_150_expr_Oinject_I8_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X8: expr @ R @ L @ V,Y8: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ( rjoin @ R @ L @ V @ X8 )
% 3.49/1.83 = ( rjoin @ R @ L @ V @ Y8 ) )
% 3.49/1.83 = ( X8 = Y8 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_151_revision__step_OifFalse,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E22 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_152_revision__step_OifTrue,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E1 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_153_revision__step__relaxed_OifFalse,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E22 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_154_revision__step__relaxed_OifTrue,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,E1: expr @ r @ l @ v,E22: expr @ r @ l @ v] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E1 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_155_ifFalse__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_156_ifTrue__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( ite @ r @ l @ v @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_157_expr_Odistinct_I35_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 3.49/1.83 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_158_expr_Odistinct_I33_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( ite @ R @ L @ V @ X31 @ X32 @ X33 )
% 3.49/1.83 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_159_expr_Odistinct_I3_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( ve @ R @ L @ V @ X1 )
% 3.49/1.83 != ( ite @ R @ L @ V @ X31 @ X32 @ X33 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_160_const_Oexhaust,axiom,
% 3.49/1.83 ! [Y: const] :
% 3.49/1.83 ( ( Y != unit )
% 3.49/1.83 => ( ( Y != f )
% 3.49/1.83 => ( Y = t ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_161_const_Oinduct,axiom,
% 3.49/1.83 ! [P: const > $o,Const: const] :
% 3.49/1.83 ( ( P @ unit )
% 3.49/1.83 => ( ( P @ f )
% 3.49/1.83 => ( ( P @ t )
% 3.49/1.83 => ( P @ Const ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_162_const_Odistinct_I1_J,axiom,
% 3.49/1.83 unit != f ).
% 3.49/1.83
% 3.49/1.83 thf(fact_163_const_Odistinct_I3_J,axiom,
% 3.49/1.83 unit != t ).
% 3.49/1.83
% 3.49/1.83 thf(fact_164_substitution_Orevision__step_OifTrue,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_165_substitution_Orevision__step_OifFalse,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_166_substitution_OifTrue__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E1 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_167_substitution_OifFalse__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E22 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_168_substitution_Orevision__step__relaxed_OifTrue,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_169_substitution_Orevision__step__relaxed_OifFalse,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: expr @ R @ L @ V] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_170_substitution_OSLC__ifTrue,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: 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 ) ) ) ),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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E1 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_171_substitution_OSLC__ifFalse,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,E1: expr @ R @ L @ V,E22: 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 ) ) ) ),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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( ite @ R @ L @ V @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau2 @ ( plug @ R @ L @ V @ E3 @ E22 ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_172_combine_Ocases,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,X2: product_prod @ ( A > ( option @ B ) ) @ ( product_prod @ ( A > ( option @ B ) ) @ A )] :
% 3.49/1.83 ~ ! [F2: A > ( option @ B ),G3: A > ( option @ B ),X4: A] :
% 3.49/1.83 ( X2
% 3.49/1.83 != ( product_Pair @ ( A > ( option @ B ) ) @ ( product_prod @ ( A > ( option @ B ) ) @ A ) @ F2 @ ( product_Pair @ ( A > ( option @ B ) ) @ A @ G3 @ X4 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_173_LID__local__store_Ocases,axiom,
% 3.49/1.83 ! [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 ) )] :
% 3.49/1.83 ~ ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E2: expr @ R @ L @ V] :
% 3.49/1.83 ( X2
% 3.49/1.83 != ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ E2 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_174_LID__local__store_Oinduct,axiom,
% 3.49/1.83 ! [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 ) )] :
% 3.49/1.83 ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E2: 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 ) ) @ Sigma @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ Tau @ E2 ) ) )
% 3.49/1.83 => ( P @ A0 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_175_expr_Odistinct_I13_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ve @ R @ L @ V @ X1 )
% 3.49/1.83 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_176_expr_Odistinct_I11_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X7: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ve @ R @ L @ V @ X1 )
% 3.49/1.83 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_177_combine_Oelims,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,X2: A > ( option @ B ),Xa2: A > ( option @ B ),Xb: A,Y: option @ B] :
% 3.49/1.83 ( ( ( combine @ A @ B @ X2 @ Xa2 @ Xb )
% 3.49/1.83 = Y )
% 3.49/1.83 => ( ( ( ( Xa2 @ Xb )
% 3.49/1.83 = ( none @ B ) )
% 3.49/1.83 => ( Y
% 3.49/1.83 = ( X2 @ Xb ) ) )
% 3.49/1.83 & ( ( ( Xa2 @ Xb )
% 3.49/1.83 != ( none @ B ) )
% 3.49/1.83 => ( Y
% 3.49/1.83 = ( Xa2 @ Xb ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_178_combine_Osimps,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType] :
% 3.49/1.83 ( ( combine @ A @ B )
% 3.49/1.83 = ( ^ [F3: A > ( option @ B ),G4: A > ( option @ B ),X: A] :
% 3.49/1.83 ( if @ ( option @ B )
% 3.49/1.83 @ ( ( G4 @ X )
% 3.49/1.83 = ( none @ B ) )
% 3.49/1.83 @ ( F3 @ X )
% 3.49/1.83 @ ( G4 @ X ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_179_val_Odistinct_I5_J,axiom,
% 3.49/1.83 ! [L: $tType,V: $tType,R: $tType,X1: const,X42: R] :
% 3.49/1.83 ( ( cv @ R @ L @ V @ X1 )
% 3.49/1.83 != ( rid @ R @ L @ V @ X42 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_180_expr_Odistinct_I55_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X7: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.49/1.83 ( ( rfork @ R @ L @ V @ X7 )
% 3.49/1.83 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_181_empty__map__finite_I4_J,axiom,
% 3.49/1.83 ! [J: $tType,M2: $tType,K2: $tType] :
% 3.49/1.83 ( finite_finite2 @ J
% 3.49/1.83 @ ( lID_G @ K2 @ J @ M2
% 3.49/1.83 @ ^ [X: K2] : ( none @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( expr @ K2 @ J @ M2 ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_182_fun__upd__upd,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B,Z: B] :
% 3.49/1.83 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X2 @ Y ) @ X2 @ Z )
% 3.49/1.83 = ( fun_upd @ A @ B @ F @ X2 @ Z ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_183_fun__upd__triv,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,F: A > B,X2: A] :
% 3.49/1.83 ( ( fun_upd @ A @ B @ F @ X2 @ ( F @ X2 ) )
% 3.49/1.83 = F ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_184_RID_092_060_094sub_062L__finite__invariant,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ( finite_finite2 @ l @ ( lID_G @ r @ l @ v @ S ) )
% 3.49/1.83 => ( finite_finite2 @ l @ ( lID_G @ r @ l @ v @ S2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_185_reachable__imp__identifiers__finite_I2_J,axiom,
% 3.49/1.83 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 => ( finite_finite2 @ l @ ( lID_G @ r @ l @ v @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_186_reachable__imp__identifiers__available_I2_J,axiom,
% 3.49/1.83 ! [S: r > ( option @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) )] :
% 3.49/1.83 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.83 => ( ~ ( finite_finite2 @ l @ ( top_top @ ( set @ l ) ) )
% 3.49/1.83 => ? [L2: l] :
% 3.49/1.83 ~ ( member @ l @ L2 @ ( lID_G @ r @ l @ v @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_187_fun__upd__apply,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType] :
% 3.49/1.83 ( ( fun_upd @ B @ A )
% 3.49/1.83 = ( ^ [F3: B > A,X: B,Y2: A,Z2: B] : ( if @ A @ ( Z2 = X ) @ Y2 @ ( F3 @ Z2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_188_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 3.49/1.83 ! [C: $tType,B: $tType,A: $tType,L3: 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] :
% 3.49/1.83 ( ( member @ B @ L3 @ ( 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 ) ) ) ) ) ) )
% 3.49/1.83 => ( member @ B @ L3 @ ( lID_G @ A @ B @ C @ S ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_189_finite__state__imp__restriction__finite_I2_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( finite_finite2 @ B @ ( lID_G @ A @ B @ C @ S ) )
% 3.49/1.83 => ( finite_finite2 @ 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 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_190_in__restricted__global__in__updated__global_I2_J,axiom,
% 3.49/1.83 ! [C: $tType,A: $tType,B: $tType,L3: 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 ) )] :
% 3.49/1.83 ( ( member @ B @ L3 @ ( 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 ) ) ) ) ) ) )
% 3.49/1.83 => ( member @ B @ L3 @ ( 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 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_191_fun__upd__idem__iff,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B] :
% 3.49/1.83 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y )
% 3.49/1.83 = F )
% 3.49/1.83 = ( ( F @ X2 )
% 3.49/1.83 = Y ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_192_fun__upd__twist,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,A3: A,C2: A,M: A > B,B3: B,D: B] :
% 3.49/1.83 ( ( A3 != C2 )
% 3.49/1.83 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ A3 @ B3 ) @ C2 @ D )
% 3.49/1.83 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ C2 @ D ) @ A3 @ B3 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_193_fun__upd__other,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,Z: A,X2: A,F: A > B,Y: B] :
% 3.49/1.83 ( ( Z != X2 )
% 3.49/1.83 => ( ( fun_upd @ A @ B @ F @ X2 @ Y @ Z )
% 3.49/1.83 = ( F @ Z ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_194_fun__upd__same,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,F: B > A,X2: B,Y: A] :
% 3.49/1.83 ( ( fun_upd @ B @ A @ F @ X2 @ Y @ X2 )
% 3.49/1.83 = Y ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_195_fun__upd__idem,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,F: B > A,X2: B,Y: A] :
% 3.49/1.83 ( ( ( F @ X2 )
% 3.49/1.83 = Y )
% 3.49/1.83 => ( ( fun_upd @ B @ A @ F @ X2 @ Y )
% 3.49/1.83 = F ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_196_fun__upd__eqD,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,F: A > B,X2: A,Y: B,G: A > B,Z: B] :
% 3.49/1.83 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y )
% 3.49/1.83 = ( fun_upd @ A @ B @ G @ X2 @ Z ) )
% 3.49/1.83 => ( Y = Z ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_197_fun__upd__def,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType] :
% 3.49/1.83 ( ( fun_upd @ A @ B )
% 3.49/1.83 = ( ^ [F3: A > B,A6: A,B6: B,X: A] : ( if @ B @ ( X = A6 ) @ B6 @ ( F3 @ X ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_198_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ( finite_finite2 @ L @ ( lID_G @ R @ L @ V @ S ) )
% 3.49/1.83 => ( finite_finite2 @ L @ ( lID_G @ R @ L @ V @ S2 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_199_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 3.49/1.83 ! [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 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_200_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 => ( finite_finite2 @ L @ ( lID_G @ R @ L @ V @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_201_substitution_Oempty__map__finite_I4_J,axiom,
% 3.49/1.83 ! [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 )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( finite_finite2 @ J
% 3.49/1.83 @ ( lID_G @ K2 @ J @ M2
% 3.49/1.83 @ ^ [X: K2] : ( none @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( product_prod @ ( J > ( option @ ( val @ K2 @ J @ M2 ) ) ) @ ( expr @ K2 @ J @ M2 ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_202_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( finite_finite2 @ B @ ( lID_G @ A @ B @ C @ S ) )
% 3.49/1.83 => ( finite_finite2 @ 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 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_203_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S )
% 3.49/1.83 => ( ~ ( finite_finite2 @ L @ ( top_top @ ( set @ L ) ) )
% 3.49/1.83 => ? [L2: L] :
% 3.49/1.83 ~ ( member @ L @ L2 @ ( lID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_204_only__new__introduces__lids_H,axiom,
% 3.49/1.83 ! [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 ) ) ) ),L3: l] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ! [Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,V3: val @ r @ l @ v] :
% 3.49/1.83 ( ( S @ R2 )
% 3.49/1.83 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 @ V3 ) ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S ) )
% 3.49/1.83 => ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S2 ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_205_valid__stepE,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( 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 ) )
% 3.49/1.83 => ? [R7: r] : ( revision_step @ r @ l @ v @ subst @ R7 @ S @ S2 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_206_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.49/1.83 => ( ( finite_finite2 @ 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 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( finite_finite2 @ A @ ( lID_L @ A @ B @ C @ Ls ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_207_LID_092_060_094sub_062GI,axiom,
% 3.49/1.83 ! [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 ) ),L3: A] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.49/1.83 => ( ( member @ A @ L3 @ ( lID_L @ A @ B @ C @ Ls ) )
% 3.49/1.83 => ( member @ A @ L3 @ ( lID_G @ B @ A @ C @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_208_valid__stepI,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( 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 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_209_maximal__execution__def,axiom,
% 3.49/1.83 ! [E4: 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 ) ) ) )] :
% 3.49/1.83 ( ( maximal_execution @ r @ l @ v @ subst @ E4 @ S @ S2 )
% 3.49/1.83 = ( ( execution @ r @ l @ v @ subst @ E4 @ S @ S2 )
% 3.49/1.83 & ~ ? [S6: 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 @ S6 ) @ ( steps @ r @ l @ v @ subst ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_210_only__new__introduces__lids,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ! [Sigma: l > ( option @ ( val @ r @ l @ v ) ),Tau: l > ( option @ ( val @ r @ l @ v ) ),E: cntxt @ r @ l @ v,V3: val @ r @ l @ v] :
% 3.49/1.83 ( ( S @ R2 )
% 3.49/1.83 != ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) ) ) @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ 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 @ V3 ) ) ) ) ) ) )
% 3.49/1.83 => ( ord_less_eq @ ( set @ l ) @ ( lID_G @ r @ l @ v @ S2 ) @ ( lID_G @ r @ l @ v @ S ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_211_substitution_Osteps_Ocong,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType] :
% 3.49/1.83 ( ( steps @ R @ L @ V )
% 3.49/1.83 = ( steps @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_212_expr_Odistinct_I5_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X42: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ve @ R @ L @ V @ X1 )
% 3.49/1.83 != ( ref @ R @ L @ V @ X42 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_213_expr_Odistinct_I41_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X42: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ref @ R @ L @ V @ X42 )
% 3.49/1.83 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_214_expr_Odistinct_I43_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X42: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ref @ R @ L @ V @ X42 )
% 3.49/1.83 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_215_LID_092_060_094sub_062GE,axiom,
% 3.49/1.83 ! [C: $tType,B: $tType,A: $tType,L3: A,S: B > ( option @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) )] :
% 3.49/1.83 ( ( member @ A @ L3 @ ( lID_G @ B @ A @ C @ S ) )
% 3.49/1.83 => ~ ! [R7: B,Ls3: product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) )] :
% 3.49/1.83 ( ( ( S @ R7 )
% 3.49/1.83 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls3 ) )
% 3.49/1.83 => ~ ( member @ A @ L3 @ ( lID_L @ A @ B @ C @ Ls3 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_216_substitution_Ovalid__stepE,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( 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 ) )
% 3.49/1.83 => ? [R7: R] : ( revision_step @ R @ L @ V @ Subst @ R7 @ S @ S2 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_217_substitution_Ovalid__stepI,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( 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 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_218_substitution_Oonly__new__introduces__lids_H,axiom,
% 3.49/1.83 ! [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 ) ) ) ),L3: L] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,V3: val @ R @ L @ V] :
% 3.49/1.83 ( ( S @ R2 )
% 3.49/1.83 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ 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 @ V3 ) ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S ) )
% 3.49/1.83 => ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S2 ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_219_substitution_Oonly__new__introduces__lids,axiom,
% 3.49/1.83 ! [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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 => ( ! [Sigma: L > ( option @ ( val @ R @ L @ V ) ),Tau: L > ( option @ ( val @ R @ L @ V ) ),E: cntxt @ R @ L @ V,V3: val @ R @ L @ V] :
% 3.49/1.83 ( ( S @ R2 )
% 3.49/1.83 != ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) ) ) @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ 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 @ V3 ) ) ) ) ) ) )
% 3.49/1.83 => ( ord_less_eq @ ( set @ L ) @ ( lID_G @ R @ L @ V @ S2 ) @ ( lID_G @ R @ L @ V @ S ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_220_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 3.49/1.83 ! [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] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R3 )
% 3.49/1.83 = ( some @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( product_prod @ ( A > ( option @ ( val @ B @ A @ C ) ) ) @ ( expr @ B @ A @ C ) ) ) @ Ls ) )
% 3.49/1.83 => ( ( finite_finite2 @ 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 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( finite_finite2 @ A @ ( lID_L @ A @ B @ C @ Ls ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_221_domains__subsume__def,axiom,
% 3.49/1.83 ( ( domains_subsume @ l @ r @ v )
% 3.49/1.83 = ( ^ [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 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_222_SLC__new,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,V2: val @ 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 ) ) ) ),L3: l,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 ) ) ) )] :
% 3.49/1.83 ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S_1 ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( ( reachable @ r @ l @ v @ subst @ S_1 )
% 3.49/1.83 => ( ~ ( finite_finite2 @ l @ ( top_top @ ( set @ l ) ) )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_223_terminates__in__def,axiom,
% 3.49/1.83 ! [E4: 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 ) ) ) )] :
% 3.49/1.83 ( ( terminates_in @ r @ l @ v @ subst @ E4 @ S2 )
% 3.49/1.83 = ( ? [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 @ E4 @ S4 @ S2 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_224_revision__step_Onew,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,V2: val @ r @ l @ v,L3: l] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ l @ L3 @ ( lID_G @ r @ l @ v @ S ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_225_new__pseudodeterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( ? [L4: l] :
% 3.49/1.83 ( ~ ( member @ l @ L4 @ ( lID_G @ r @ l @ v @ S ) )
% 3.49/1.83 & ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L4 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_226_val_Odistinct_I3_J,axiom,
% 3.49/1.83 ! [R: $tType,V: $tType,L: $tType,X1: const,X34: L] :
% 3.49/1.83 ( ( cv @ R @ L @ V @ X1 )
% 3.49/1.83 != ( loc @ L @ R @ V @ X34 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_227_val_Odistinct_I15_J,axiom,
% 3.49/1.83 ! [L: $tType,V: $tType,R: $tType,X34: L,X42: R] :
% 3.49/1.83 ( ( loc @ L @ R @ V @ X34 )
% 3.49/1.83 != ( rid @ R @ L @ V @ X42 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_228_substitution_Omaximal__execution_Ocong,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType] :
% 3.49/1.83 ( ( maximal_execution @ R @ L @ V )
% 3.49/1.83 = ( maximal_execution @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_229_substitution_Odomains__subsume__def,axiom,
% 3.49/1.83 ! [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 ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( domains_subsume @ L @ R @ V @ Ls )
% 3.49/1.83 = ( ord_less_eq @ ( set @ L ) @ ( lID_L @ L @ R @ V @ Ls ) @ ( doms @ L @ R @ V @ Ls ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_230_substitution_Onew__pseudodeterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( ? [L4: L] :
% 3.49/1.83 ( ~ ( member @ L @ L4 @ ( lID_G @ R @ L @ V @ S ) )
% 3.49/1.83 & ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L4 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L4 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_231_substitution_Orevision__step_Onew,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,V2: val @ R @ L @ V,L3: L] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_232_substitution_Omaximal__execution__def,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),E4: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( maximal_execution @ R @ L @ V @ Subst @ E4 @ S @ S2 )
% 3.49/1.83 = ( ( execution @ R @ L @ V @ Subst @ E4 @ S @ S2 )
% 3.49/1.83 & ~ ? [S6: 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 @ S6 ) @ ( steps @ R @ L @ V @ Subst ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_233_substitution_OSLC__new,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,V2: val @ 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 ) ) ) ),L3: L,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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ~ ( member @ L @ L3 @ ( lID_G @ R @ L @ V @ S_1 ) )
% 3.49/1.83 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ( ( reachable @ R @ L @ V @ Subst @ S_1 )
% 3.49/1.83 => ( ~ ( finite_finite2 @ L @ ( top_top @ ( set @ L ) ) )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_234_revision__step__relaxed_Oset,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: l,V2: val @ r @ l @ v] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_235_substitution_Orevision__step__relaxed_Oset,axiom,
% 3.49/1.83 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,L3: L,V2: val @ R @ L @ V] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_236_substitution_Oterminates__in_Ocong,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType] :
% 3.49/1.83 ( ( terminates_in @ R @ L @ V )
% 3.49/1.83 = ( terminates_in @ R @ L @ V ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_237_expr_Odistinct_I9_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X1: val @ R @ L @ V,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V] :
% 3.49/1.83 ( ( ve @ R @ L @ V @ X1 )
% 3.49/1.83 != ( assign @ R @ L @ V @ X61 @ X62 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_238_expr_Odistinct_I51_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,X7: expr @ R @ L @ V] :
% 3.49/1.83 ( ( assign @ R @ L @ V @ X61 @ X62 )
% 3.49/1.83 != ( rfork @ R @ L @ V @ X7 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_239_expr_Odistinct_I53_J,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,X61: expr @ R @ L @ V,X62: expr @ R @ L @ V,X8: expr @ R @ L @ V] :
% 3.49/1.83 ( ( assign @ R @ L @ V @ X61 @ X62 )
% 3.49/1.83 != ( rjoin @ R @ L @ V @ X8 ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_240_substitution_Oterminates__in__def,axiom,
% 3.49/1.83 ! [V: $tType,L: $tType,R: $tType,Subst: ( expr @ R @ L @ V ) > V > ( expr @ R @ L @ V ) > ( expr @ R @ L @ V ),E4: 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 ) ) ) )] :
% 3.49/1.83 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.83 => ( ( terminates_in @ R @ L @ V @ Subst @ E4 @ S2 )
% 3.49/1.83 = ( ? [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 @ E4 @ S4 @ S2 ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_241_SLC__set,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: l,V2: val @ 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 ) ) ) ),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 ) ) ) )] :
% 3.49/1.83 ( ( ( S_1 @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( S_2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) )
% 3.49/1.83 => ( ( member @ l @ L3 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.49/1.83 => ( ( R2 != R3 )
% 3.49/1.83 => ? [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 ) ) ) )] :
% 3.49/1.83 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.83 | ( S_2 = S_3 ) )
% 3.49/1.83 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.83 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_242_revision__step_Oset,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: l,V2: val @ r @ l @ v] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( member @ l @ L3 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 ) ) )
% 3.49/1.83 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_243_dom__const,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType,F: A > B] :
% 3.49/1.83 ( ( dom @ A @ B
% 3.49/1.83 @ ^ [X: A] : ( some @ B @ ( F @ X ) ) )
% 3.49/1.83 = ( top_top @ ( set @ A ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_244_set__deterministic,axiom,
% 3.49/1.83 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: 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 ) ) ) )] :
% 3.49/1.83 ( ( ( S @ R2 )
% 3.49/1.83 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( assign @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) @ ( ve @ r @ l @ v @ V2 ) ) ) ) ) ) )
% 3.49/1.83 => ( ( revision_step @ r @ l @ v @ subst @ R2 @ S @ S2 )
% 3.49/1.83 = ( ( member @ l @ L3 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 ) ) )
% 3.49/1.83 & ( S2
% 3.49/1.83 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ ( fun_upd @ l @ ( option @ ( val @ r @ l @ v ) ) @ Tau2 @ L3 @ ( some @ ( val @ r @ l @ v ) @ V2 ) ) @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( cv @ r @ l @ v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_245_domD,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,A3: A,M: A > ( option @ B )] :
% 3.49/1.83 ( ( member @ A @ A3 @ ( dom @ A @ B @ M ) )
% 3.49/1.83 => ? [B2: B] :
% 3.49/1.83 ( ( M @ A3 )
% 3.49/1.83 = ( some @ B @ B2 ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_246_domI,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,M: B > ( option @ A ),A3: B,B3: A] :
% 3.49/1.83 ( ( ( M @ A3 )
% 3.49/1.83 = ( some @ A @ B3 ) )
% 3.49/1.83 => ( member @ B @ A3 @ ( dom @ B @ A @ M ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_247_finite__map__freshness,axiom,
% 3.49/1.83 ! [A: $tType,B: $tType,F: A > ( option @ B )] :
% 3.49/1.83 ( ( finite_finite2 @ A @ ( dom @ A @ B @ F ) )
% 3.49/1.83 => ( ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 3.49/1.83 => ? [X4: A] :
% 3.49/1.83 ( ( F @ X4 )
% 3.49/1.83 = ( none @ B ) ) ) ) ).
% 3.49/1.83
% 3.49/1.83 thf(fact_248_dom__def,axiom,
% 3.49/1.83 ! [B: $tType,A: $tType] :
% 3.49/1.84 ( ( dom @ A @ B )
% 3.49/1.84 = ( ^ [M3: A > ( option @ B )] :
% 3.49/1.84 ( collect @ A
% 3.49/1.84 @ ^ [A6: A] :
% 3.49/1.84 ( ( M3 @ A6 )
% 3.49/1.84 != ( none @ B ) ) ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(fact_249_domIff,axiom,
% 3.49/1.84 ! [A: $tType,B: $tType,A3: A,M: A > ( option @ B )] :
% 3.49/1.84 ( ( member @ A @ A3 @ ( dom @ A @ B @ M ) )
% 3.49/1.84 = ( ( M @ A3 )
% 3.49/1.84 != ( none @ B ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(fact_250_substitution_Oset__deterministic,axiom,
% 3.49/1.84 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,L3: 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 ) ) ) )] :
% 3.49/1.84 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.84 => ( ( ( S @ R2 )
% 3.49/1.84 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.49/1.84 => ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S @ S2 )
% 3.49/1.84 = ( ( member @ L @ L3 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma2 @ Tau2 ) ) )
% 3.49/1.84 & ( S2
% 3.49/1.84 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(fact_251_substitution_Orevision__step_Oset,axiom,
% 3.49/1.84 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,L3: L,V2: val @ R @ L @ V] :
% 3.49/1.84 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.84 => ( ( ( S @ R2 )
% 3.49/1.84 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.49/1.84 => ( ( member @ L @ L3 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma2 @ Tau2 ) ) )
% 3.49/1.84 => ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(fact_252_substitution_OSLC__set,axiom,
% 3.49/1.84 ! [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,Sigma2: L > ( option @ ( val @ R @ L @ V ) ),Tau2: L > ( option @ ( val @ R @ L @ V ) ),E3: cntxt @ R @ L @ V,L3: L,V2: val @ 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 ) ) ) ),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 ) ) ) )] :
% 3.49/1.84 ( ( substitution @ R @ L @ V @ Subst )
% 3.49/1.84 => ( ( ( S_1 @ R2 )
% 3.49/1.84 = ( some @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( product_prod @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( 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 @ ( assign @ R @ L @ V @ ( ve @ R @ L @ V @ ( loc @ L @ R @ V @ L3 ) ) @ ( ve @ R @ L @ V @ V2 ) ) ) ) ) ) )
% 3.49/1.84 => ( ( S_2
% 3.49/1.84 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( L > ( option @ ( val @ R @ L @ V ) ) ) @ ( expr @ R @ L @ V ) @ ( fun_upd @ L @ ( option @ ( val @ R @ L @ V ) ) @ Tau2 @ L3 @ ( some @ ( val @ R @ L @ V ) @ V2 ) ) @ ( plug @ R @ L @ V @ E3 @ ( ve @ R @ L @ V @ ( cv @ R @ L @ V @ unit ) ) ) ) ) ) ) )
% 3.49/1.84 => ( ( member @ L @ L3 @ ( dom @ L @ ( val @ R @ L @ V ) @ ( combine @ L @ ( val @ R @ L @ V ) @ Sigma2 @ Tau2 ) ) )
% 3.49/1.84 => ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_1 @ S_22 )
% 3.49/1.84 => ( ( R2 != R3 )
% 3.49/1.84 => ? [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 ) ) ) )] :
% 3.49/1.84 ( ( eq_states @ R @ L @ V @ S_3 @ S_32 )
% 3.49/1.84 & ( ( revision_step @ R @ L @ V @ Subst @ R3 @ S_2 @ S_3 )
% 3.49/1.84 | ( S_2 = S_3 ) )
% 3.49/1.84 & ( ( revision_step @ R @ L @ V @ Subst @ R2 @ S_22 @ S_32 )
% 3.49/1.84 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(fact_253_reachability__closed__under__execution,axiom,
% 3.49/1.84 ! [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 ) ) ) )] :
% 3.49/1.84 ( ( reachable @ r @ l @ v @ subst @ S )
% 3.49/1.84 => ( ( 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 ) ) )
% 3.49/1.84 => ( reachable @ r @ l @ v @ subst @ S2 ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(fact_254_SLC__get,axiom,
% 3.49/1.84 ! [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,Sigma2: l > ( option @ ( val @ r @ l @ v ) ),Tau2: l > ( option @ ( val @ r @ l @ v ) ),E3: cntxt @ r @ l @ v,L3: l,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 ) ) ) )] :
% 3.49/1.84 ( ( ( S_1 @ R2 )
% 3.49/1.84 = ( some @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( product_prod @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( 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 @ ( read @ r @ l @ v @ ( ve @ r @ l @ v @ ( loc @ l @ r @ v @ L3 ) ) ) ) ) ) ) )
% 3.49/1.84 => ( ( S_2
% 3.49/1.84 = ( 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 ) ) @ Sigma2 @ ( product_Pair @ ( l > ( option @ ( val @ r @ l @ v ) ) ) @ ( expr @ r @ l @ v ) @ Tau2 @ ( plug @ r @ l @ v @ E3 @ ( ve @ r @ l @ v @ ( the @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 @ L3 ) ) ) ) ) ) ) ) )
% 3.49/1.84 => ( ( member @ l @ L3 @ ( dom @ l @ ( val @ r @ l @ v ) @ ( combine @ l @ ( val @ r @ l @ v ) @ Sigma2 @ Tau2 ) ) )
% 3.49/1.84 => ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_1 @ S_22 )
% 3.49/1.84 => ( ( R2 != R3 )
% 3.49/1.84 => ? [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 ) ) ) )] :
% 3.49/1.84 ( ( eq_states @ r @ l @ v @ S_3 @ S_32 )
% 3.49/1.84 & ( ( revision_step @ r @ l @ v @ subst @ R3 @ S_2 @ S_3 )
% 3.49/1.84 | ( S_2 = S_3 ) )
% 3.49/1.84 & ( ( revision_step @ r @ l @ v @ subst @ R2 @ S_22 @ S_32 )
% 3.49/1.84 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 3.49/1.84 ! [A7: $tType,A8: $tType] :
% 3.49/1.84 ( ( ( finite_finite @ A7 )
% 3.49/1.84 & ( finite_finite @ A8 ) )
% 3.49/1.84 => ( finite_finite @ ( A7 > A8 ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.49/1.84 ! [A7: $tType,A8: $tType] :
% 3.49/1.84 ( ( order @ A8 )
% 3.49/1.84 => ( order @ ( A7 > A8 ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_Set_Oset___Finite__Set_Ofinite_1,axiom,
% 3.49/1.84 ! [A7: $tType] :
% 3.49/1.84 ( ( finite_finite @ A7 )
% 3.49/1.84 => ( finite_finite @ ( set @ A7 ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 3.49/1.84 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_HOL_Obool___Finite__Set_Ofinite_3,axiom,
% 3.49/1.84 finite_finite @ $o ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_HOL_Obool___Orderings_Oorder_4,axiom,
% 3.49/1.84 order @ $o ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_5,axiom,
% 3.49/1.84 ! [A7: $tType,A8: $tType] :
% 3.49/1.84 ( ( ( finite_finite @ A7 )
% 3.49/1.84 & ( finite_finite @ A8 ) )
% 3.49/1.84 => ( finite_finite @ ( sum_sum @ A7 @ A8 ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_Option_Ooption___Finite__Set_Ofinite_6,axiom,
% 3.49/1.84 ! [A7: $tType] :
% 3.49/1.84 ( ( finite_finite @ A7 )
% 3.49/1.84 => ( finite_finite @ ( option @ A7 ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_7,axiom,
% 3.49/1.84 ! [A7: $tType,A8: $tType] :
% 3.49/1.84 ( ( ( finite_finite @ A7 )
% 3.49/1.84 & ( finite_finite @ A8 ) )
% 3.49/1.84 => ( finite_finite @ ( product_prod @ A7 @ A8 ) ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(help_If_3_1_T,axiom,
% 3.49/1.84 ! [P: $o] :
% 3.49/1.84 ( ( P = $true )
% 3.49/1.84 | ( P = $false ) ) ).
% 3.49/1.84
% 3.49/1.84 thf(help_If_2_1_T,axiom,
% 3.49/1.84 ! [A: $tType,X2: A,Y: A] :
% 3.49/1.84 ( ( if @ A @ $false @ X2 @ Y )
% 3.49/1.84 = Y ) ).
% 3.49/1.84
% 3.49/1.84 thf(help_If_1_1_T,axiom,
% 3.49/1.84 ! [A: $tType,X2: A,Y: A] :
% 3.49/1.84 ( ( if @ A @ $true @ X2 @ Y )
% 3.49/1.84 = X2 ) ).
% 3.49/1.84
% 3.49/1.84 thf(conj_0,conjecture,
% 3.49/1.84 r3 != right_forkee ).
% 3.49/1.84 ------------------------
% 3.62/1.90 % (13179)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12937 for (2999ds/183Mi)
% 3.62/1.90 % (13180)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_12937 for (2999ds/4Mi)
% 3.62/1.90 % (13181)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_12937 for (2999ds/27Mi)
% 3.62/1.90 % (13182)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12937 for (2999ds/2Mi)
% 3.62/1.90 % (13183)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_12937 for (2999ds/2Mi)
% 3.62/1.90 % (13184)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_12937 for (2999ds/275Mi)
% 3.62/1.90 % (13185)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12937 for (2999ds/18Mi)
% 3.62/1.91 % (13182)Instruction limit reached!
% 3.62/1.91 % (13182)------------------------------
% 3.62/1.91 % (13182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.91 % (13182)Termination reason: Unknown
% 3.62/1.91 % (13182)Termination phase: shuffling
% 3.62/1.91
% 3.62/1.91 % (13182)Memory used [KB]: 1407
% 3.62/1.91 % (13182)Time elapsed: 0.004 s
% 3.62/1.91 % (13182)Instructions burned: 3 (million)
% 3.62/1.91 % (13182)------------------------------
% 3.62/1.91 % (13182)------------------------------
% 3.62/1.91 % (13183)Instruction limit reached!
% 3.62/1.91 % (13183)------------------------------
% 3.62/1.91 % (13183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.91 % (13183)Termination reason: Unknown
% 3.62/1.91 % (13183)Termination phase: shuffling
% 3.62/1.91
% 3.62/1.91 % (13183)Memory used [KB]: 1535
% 3.62/1.91 % (13183)Time elapsed: 0.004 s
% 3.62/1.91 % (13183)Instructions burned: 3 (million)
% 3.62/1.91 % (13183)------------------------------
% 3.62/1.91 % (13183)------------------------------
% 3.62/1.91 % (13180)Instruction limit reached!
% 3.62/1.91 % (13180)------------------------------
% 3.62/1.91 % (13180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.91 % (13180)Termination reason: Unknown
% 3.62/1.91 % (13180)Termination phase: shuffling
% 3.62/1.91
% 3.62/1.91 % (13180)Memory used [KB]: 1535
% 3.62/1.91 % (13180)Time elapsed: 0.005 s
% 3.62/1.91 % (13180)Instructions burned: 5 (million)
% 3.62/1.91 % (13180)------------------------------
% 3.62/1.91 % (13180)------------------------------
% 3.62/1.92 % (13185)Instruction limit reached!
% 3.62/1.92 % (13185)------------------------------
% 3.62/1.92 % (13185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.92 % (13185)Termination reason: Unknown
% 3.62/1.92 % (13185)Termination phase: shuffling
% 3.62/1.92
% 3.62/1.92 % (13185)Memory used [KB]: 1663
% 3.62/1.92 % (13185)Time elapsed: 0.013 s
% 3.62/1.92 % (13185)Instructions burned: 18 (million)
% 3.62/1.92 % (13185)------------------------------
% 3.62/1.92 % (13185)------------------------------
% 3.62/1.92 % (13181)Instruction limit reached!
% 3.62/1.92 % (13181)------------------------------
% 3.62/1.92 % (13181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.92 % (13181)Termination reason: Unknown
% 3.62/1.92 % (13181)Termination phase: shuffling
% 3.62/1.92
% 3.62/1.92 % (13181)Memory used [KB]: 1791
% 3.62/1.92 % (13181)Time elapsed: 0.018 s
% 3.62/1.92 % (13181)Instructions burned: 27 (million)
% 3.62/1.92 % (13181)------------------------------
% 3.62/1.92 % (13181)------------------------------
% 3.62/1.92 % (13199)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_12937 for (2999ds/37Mi)
% 3.62/1.92 % (13198)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12937 for (2999ds/3Mi)
% 3.62/1.92 % (13200)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_12937 for (2999ds/15Mi)
% 3.62/1.93 % (13198)Instruction limit reached!
% 3.62/1.93 % (13198)------------------------------
% 3.62/1.93 % (13198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.93 % (13198)Termination reason: Unknown
% 3.62/1.93 % (13198)Termination phase: shuffling
% 3.62/1.93
% 3.62/1.93 % (13198)Memory used [KB]: 1535
% 3.62/1.93 % (13198)Time elapsed: 0.004 s
% 3.62/1.93 % (13198)Instructions burned: 3 (million)
% 3.62/1.93 % (13198)------------------------------
% 3.62/1.93 % (13198)------------------------------
% 3.62/1.93 % (13206)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_12937 for (2999ds/3Mi)
% 3.62/1.93 % (13200)Instruction limit reached!
% 3.62/1.93 % (13200)------------------------------
% 3.62/1.93 % (13200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.93 % (13200)Termination reason: Unknown
% 3.62/1.93 % (13200)Termination phase: shuffling
% 3.62/1.93
% 3.62/1.93 % (13200)Memory used [KB]: 1663
% 3.62/1.93 % (13200)Time elapsed: 0.011 s
% 3.62/1.93 % (13200)Instructions burned: 15 (million)
% 3.62/1.93 % (13200)------------------------------
% 3.62/1.93 % (13200)------------------------------
% 3.62/1.93 % (13206)Instruction limit reached!
% 3.62/1.93 % (13206)------------------------------
% 3.62/1.93 % (13206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.93 % (13206)Termination reason: Unknown
% 3.62/1.93 % (13206)Termination phase: shuffling
% 3.62/1.93
% 3.62/1.93 % (13206)Memory used [KB]: 1535
% 3.62/1.93 % (13206)Time elapsed: 0.004 s
% 3.62/1.93 % (13206)Instructions burned: 3 (million)
% 3.62/1.93 % (13206)------------------------------
% 3.62/1.93 % (13206)------------------------------
% 3.62/1.94 % (13207)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_12937 for (2999ds/1041Mi)
% 3.62/1.94 % (13199)Instruction limit reached!
% 3.62/1.94 % (13199)------------------------------
% 3.62/1.94 % (13199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.94 % (13199)Termination reason: Unknown
% 3.62/1.94 % (13199)Termination phase: shuffling
% 3.62/1.94
% 3.62/1.94 % (13199)Memory used [KB]: 2046
% 3.62/1.94 % (13199)Time elapsed: 0.021 s
% 3.62/1.94 % (13199)Instructions burned: 37 (million)
% 3.62/1.94 % (13199)------------------------------
% 3.62/1.94 % (13199)------------------------------
% 3.62/1.94 % (13211)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12937 for (2999ds/7Mi)
% 3.62/1.95 % (13211)Instruction limit reached!
% 3.62/1.95 % (13211)------------------------------
% 3.62/1.95 % (13211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.95 % (13211)Termination reason: Unknown
% 3.62/1.95 % (13211)Termination phase: shuffling
% 3.62/1.95
% 3.62/1.95 % (13211)Memory used [KB]: 1535
% 3.62/1.95 % (13211)Time elapsed: 0.006 s
% 3.62/1.95 % (13211)Instructions burned: 7 (million)
% 3.62/1.95 % (13211)------------------------------
% 3.62/1.95 % (13211)------------------------------
% 3.62/1.95 % (13215)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12937 for (2999ds/16Mi)
% 3.62/1.95 % (13217)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_12937 for (2999ds/3Mi)
% 3.62/1.95 % (13222)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_12937 for (2998ds/3Mi)
% 3.62/1.95 % (13222)Instruction limit reached!
% 3.62/1.95 % (13222)------------------------------
% 3.62/1.95 % (13222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.95 % (13222)Termination reason: Unknown
% 3.62/1.95 % (13222)Termination phase: shuffling
% 3.62/1.95
% 3.62/1.95 % (13222)Memory used [KB]: 1407
% 3.62/1.95 % (13222)Time elapsed: 0.002 s
% 3.62/1.95 % (13222)Instructions burned: 3 (million)
% 3.62/1.95 % (13222)------------------------------
% 3.62/1.95 % (13222)------------------------------
% 3.62/1.95 % (13217)Instruction limit reached!
% 3.62/1.95 % (13217)------------------------------
% 3.62/1.95 % (13217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.95 % (13217)Termination reason: Unknown
% 3.62/1.95 % (13217)Termination phase: shuffling
% 3.62/1.95
% 3.62/1.95 % (13217)Memory used [KB]: 1407
% 3.62/1.95 % (13217)Time elapsed: 0.004 s
% 3.62/1.95 % (13217)Instructions burned: 3 (million)
% 3.62/1.95 % (13217)------------------------------
% 3.62/1.95 % (13217)------------------------------
% 3.62/1.96 % (13179)Instruction limit reached!
% 3.62/1.96 % (13179)------------------------------
% 3.62/1.96 % (13179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.96 % (13179)Termination reason: Unknown
% 3.62/1.96 % (13179)Termination phase: shuffling
% 3.62/1.96
% 3.62/1.96 % (13179)Memory used [KB]: 3198
% 3.62/1.96 % (13179)Time elapsed: 0.062 s
% 3.62/1.96 % (13179)Instructions burned: 183 (million)
% 3.62/1.96 % (13179)------------------------------
% 3.62/1.96 % (13179)------------------------------
% 3.62/1.96 % (13215)Instruction limit reached!
% 3.62/1.96 % (13215)------------------------------
% 3.62/1.96 % (13215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.96 % (13215)Termination reason: Unknown
% 3.62/1.96 % (13215)Termination phase: shuffling
% 3.62/1.96
% 3.62/1.96 % (13215)Memory used [KB]: 1535
% 3.62/1.96 % (13215)Time elapsed: 0.011 s
% 3.62/1.96 % (13215)Instructions burned: 16 (million)
% 3.62/1.96 % (13215)------------------------------
% 3.62/1.96 % (13215)------------------------------
% 3.62/1.96 % (13224)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/7Mi)
% 3.62/1.96 % (13228)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/3Mi)
% 3.62/1.96 % (13228)Instruction limit reached!
% 3.62/1.96 % (13228)------------------------------
% 3.62/1.96 % (13228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.96 % (13224)Instruction limit reached!
% 3.62/1.96 % (13224)------------------------------
% 3.62/1.96 % (13224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.96 % (13228)Termination reason: Unknown
% 3.62/1.96 % (13224)Termination reason: Unknown
% 3.62/1.96 % (13228)Termination phase: shuffling
% 3.62/1.96 % (13224)Termination phase: shuffling
% 3.62/1.96
% 3.62/1.96
% 3.62/1.96 % (13228)Memory used [KB]: 1535
% 3.62/1.96 % (13224)Memory used [KB]: 1535
% 3.62/1.96 % (13228)Time elapsed: 0.002 s
% 3.62/1.96 % (13224)Time elapsed: 0.005 s
% 3.62/1.96 % (13228)Instructions burned: 4 (million)
% 3.62/1.96 % (13224)Instructions burned: 9 (million)
% 3.62/1.96 % (13228)------------------------------
% 3.62/1.96 % (13228)------------------------------
% 3.62/1.96 % (13224)------------------------------
% 3.62/1.96 % (13224)------------------------------
% 3.62/1.97 % (13231)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/18Mi)
% 3.62/1.97 % (13229)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/4Mi)
% 3.62/1.97 % (13234)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/6Mi)
% 3.62/1.97 % (13235)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_12937 for (2998ds/902Mi)
% 3.62/1.97 % (13229)Instruction limit reached!
% 3.62/1.97 % (13229)------------------------------
% 3.62/1.97 % (13229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.97 % (13229)Termination reason: Unknown
% 3.62/1.97 % (13229)Termination phase: shuffling
% 3.62/1.97
% 3.62/1.97 % (13229)Memory used [KB]: 1535
% 3.62/1.97 % (13229)Time elapsed: 0.004 s
% 3.62/1.97 % (13229)Instructions burned: 4 (million)
% 3.62/1.97 % (13229)------------------------------
% 3.62/1.97 % (13229)------------------------------
% 3.62/1.97 % (13231)Instruction limit reached!
% 3.62/1.97 % (13231)------------------------------
% 3.62/1.97 % (13231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.97 % (13231)Termination reason: Unknown
% 3.62/1.97 % (13231)Termination phase: shuffling
% 3.62/1.97
% 3.62/1.97 % (13231)Memory used [KB]: 1663
% 3.62/1.97 % (13231)Time elapsed: 0.008 s
% 3.62/1.97 % (13231)Instructions burned: 19 (million)
% 3.62/1.97 % (13231)------------------------------
% 3.62/1.97 % (13231)------------------------------
% 3.62/1.98 % (13234)Instruction limit reached!
% 3.62/1.98 % (13234)------------------------------
% 3.62/1.98 % (13234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.98 % (13234)Termination reason: Unknown
% 3.62/1.98 % (13234)Termination phase: shuffling
% 3.62/1.98
% 3.62/1.98 % (13234)Memory used [KB]: 1535
% 3.62/1.98 % (13234)Time elapsed: 0.003 s
% 3.62/1.98 % (13234)Instructions burned: 6 (million)
% 3.62/1.98 % (13234)------------------------------
% 3.62/1.98 % (13234)------------------------------
% 3.62/1.98 % (13233)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/710Mi)
% 3.62/1.98 % (13241)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_12937 for (2998ds/6Mi)
% 3.62/1.98 % (13240)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/5Mi)
% 3.62/1.99 % (13241)Instruction limit reached!
% 3.62/1.99 % (13241)------------------------------
% 3.62/1.99 % (13241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.99 % (13241)Termination reason: Unknown
% 3.62/1.99 % (13241)Termination phase: shuffling
% 3.62/1.99
% 3.62/1.99 % (13241)Memory used [KB]: 1663
% 3.62/1.99 % (13241)Time elapsed: 0.003 s
% 3.62/1.99 % (13241)Instructions burned: 7 (million)
% 3.62/1.99 % (13241)------------------------------
% 3.62/1.99 % (13241)------------------------------
% 3.62/1.99 % (13240)Instruction limit reached!
% 3.62/1.99 % (13240)------------------------------
% 3.62/1.99 % (13240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/1.99 % (13240)Termination reason: Unknown
% 3.62/1.99 % (13240)Termination phase: shuffling
% 3.62/1.99
% 3.62/1.99 % (13240)Memory used [KB]: 1535
% 3.62/1.99 % (13240)Time elapsed: 0.004 s
% 3.62/1.99 % (13240)Instructions burned: 7 (million)
% 3.62/1.99 % (13240)------------------------------
% 3.62/1.99 % (13240)------------------------------
% 3.62/1.99 % (13239)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_12937 for (2998ds/21Mi)
% 3.62/2.00 % (13249)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_12937 for (2998ds/779Mi)
% 3.62/2.00 % (13248)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/377Mi)
% 3.62/2.00 % (13239)Instruction limit reached!
% 3.62/2.00 % (13239)------------------------------
% 3.62/2.00 % (13239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.62/2.00 % (13239)Termination reason: Unknown
% 3.62/2.00 % (13239)Termination phase: shuffling
% 3.62/2.00
% 3.62/2.00 % (13239)Memory used [KB]: 1663
% 3.62/2.00 % (13239)Time elapsed: 0.014 s
% 3.62/2.00 % (13239)Instructions burned: 22 (million)
% 3.62/2.00 % (13239)------------------------------
% 3.62/2.00 % (13239)------------------------------
% 4.46/2.01 % (13184)Refutation not found, incomplete strategy
% 4.46/2.01 % (13184)------------------------------
% 4.46/2.01 % (13184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.01 % (13184)Termination reason: Refutation not found, incomplete strategy
% 4.46/2.01
% 4.46/2.01
% 4.46/2.01 % (13184)Memory used [KB]: 7931
% 4.46/2.01 % (13184)Time elapsed: 0.112 s
% 4.46/2.01 % (13184)Instructions burned: 263 (million)
% 4.46/2.01 % (13184)------------------------------
% 4.46/2.01 % (13184)------------------------------
% 4.46/2.02 % (13258)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_12937 for (2998ds/19Mi)
% 4.46/2.02 % (13258)Instruction limit reached!
% 4.46/2.02 % (13258)------------------------------
% 4.46/2.02 % (13258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.02 % (13258)Termination reason: Unknown
% 4.46/2.02 % (13258)Termination phase: shuffling
% 4.46/2.02
% 4.46/2.02 % (13258)Memory used [KB]: 1791
% 4.46/2.02 % (13258)Time elapsed: 0.007 s
% 4.46/2.02 % (13258)Instructions burned: 20 (million)
% 4.46/2.02 % (13258)------------------------------
% 4.46/2.02 % (13258)------------------------------
% 4.46/2.02 % (13265)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/879Mi)
% 4.46/2.03 % (13272)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/17Mi)
% 4.46/2.04 % (13272)Instruction limit reached!
% 4.46/2.04 % (13272)------------------------------
% 4.46/2.04 % (13272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.04 % (13272)Termination reason: Unknown
% 4.46/2.04 % (13272)Termination phase: shuffling
% 4.46/2.04
% 4.46/2.04 % (13272)Memory used [KB]: 1663
% 4.46/2.04 % (13272)Time elapsed: 0.008 s
% 4.46/2.04 % (13272)Instructions burned: 18 (million)
% 4.46/2.04 % (13272)------------------------------
% 4.46/2.04 % (13272)------------------------------
% 4.46/2.05 % (13274)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/3Mi)
% 4.46/2.05 % (13274)Instruction limit reached!
% 4.46/2.05 % (13274)------------------------------
% 4.46/2.05 % (13274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.05 % (13274)Termination reason: Unknown
% 4.46/2.05 % (13274)Termination phase: shuffling
% 4.46/2.05
% 4.46/2.05 % (13274)Memory used [KB]: 1407
% 4.46/2.05 % (13274)Time elapsed: 0.003 s
% 4.46/2.05 % (13274)Instructions burned: 4 (million)
% 4.46/2.05 % (13274)------------------------------
% 4.46/2.05 % (13274)------------------------------
% 4.46/2.06 % (13286)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12937 for (2998ds/30Mi)
% 4.46/2.06 % (13233)Refutation not found, incomplete strategy
% 4.46/2.06 % (13233)------------------------------
% 4.46/2.06 % (13233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.06 % (13233)Termination reason: Refutation not found, incomplete strategy
% 4.46/2.06
% 4.46/2.06
% 4.46/2.06 % (13233)Memory used [KB]: 7931
% 4.46/2.06 % (13233)Time elapsed: 0.086 s
% 4.46/2.06 % (13233)Instructions burned: 260 (million)
% 4.46/2.06 % (13233)------------------------------
% 4.46/2.06 % (13233)------------------------------
% 4.46/2.07 % (13286)Instruction limit reached!
% 4.46/2.07 % (13286)------------------------------
% 4.46/2.07 % (13286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.07 % (13286)Termination reason: Unknown
% 4.46/2.07 % (13286)Termination phase: shuffling
% 4.46/2.07
% 4.46/2.07 % (13286)Memory used [KB]: 1791
% 4.46/2.07 % (13286)Time elapsed: 0.012 s
% 4.46/2.07 % (13286)Instructions burned: 30 (million)
% 4.46/2.07 % (13286)------------------------------
% 4.46/2.07 % (13286)------------------------------
% 4.46/2.07 % (13294)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_12937 for (2997ds/127Mi)
% 4.46/2.08 % (13300)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_12937 for (2997ds/100Mi)
% 4.46/2.10 % (13265)Refutation not found, incomplete strategy
% 4.46/2.10 % (13265)------------------------------
% 4.46/2.10 % (13265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.10 % (13265)Termination reason: Refutation not found, incomplete strategy
% 4.46/2.10
% 4.46/2.10
% 4.46/2.10 % (13265)Memory used [KB]: 7803
% 4.46/2.10 % (13265)Time elapsed: 0.081 s
% 4.46/2.10 % (13265)Instructions burned: 275 (million)
% 4.46/2.10 % (13265)------------------------------
% 4.46/2.10 % (13265)------------------------------
% 4.46/2.11 % (13300)Instruction limit reached!
% 4.46/2.11 % (13300)------------------------------
% 4.46/2.11 % (13300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.11 % (13300)Termination reason: Unknown
% 4.46/2.11 % (13300)Termination phase: shuffling
% 4.46/2.11
% 4.46/2.11 % (13300)Memory used [KB]: 2814
% 4.46/2.11 % (13300)Time elapsed: 0.031 s
% 4.46/2.11 % (13300)Instructions burned: 101 (million)
% 4.46/2.11 % (13300)------------------------------
% 4.46/2.11 % (13300)------------------------------
% 5.15/2.11 % (13316)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_12937 for (2997ds/3Mi)
% 5.15/2.12 % (13294)Instruction limit reached!
% 5.15/2.12 % (13294)------------------------------
% 5.15/2.12 % (13294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.12 % (13294)Termination reason: Unknown
% 5.15/2.12 % (13294)Termination phase: shuffling
% 5.15/2.12
% 5.15/2.12 % (13294)Memory used [KB]: 2686
% 5.15/2.12 % (13294)Time elapsed: 0.044 s
% 5.15/2.12 % (13294)Instructions burned: 127 (million)
% 5.15/2.12 % (13294)------------------------------
% 5.15/2.12 % (13294)------------------------------
% 5.15/2.12 % (13316)Instruction limit reached!
% 5.15/2.12 % (13316)------------------------------
% 5.15/2.12 % (13316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.12 % (13316)Termination reason: Unknown
% 5.15/2.12 % (13316)Termination phase: shuffling
% 5.15/2.12
% 5.15/2.12 % (13316)Memory used [KB]: 1535
% 5.15/2.12 % (13316)Time elapsed: 0.002 s
% 5.15/2.12 % (13316)Instructions burned: 3 (million)
% 5.15/2.12 % (13316)------------------------------
% 5.15/2.12 % (13316)------------------------------
% 5.15/2.12 % (13318)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_12937 for (2997ds/20Mi)
% 5.15/2.13 % (13322)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_12937 for (2997ds/107Mi)
% 5.15/2.13 % (13321)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_12937 for (2997ds/86Mi)
% 5.15/2.13 % (13318)Instruction limit reached!
% 5.15/2.13 % (13318)------------------------------
% 5.15/2.13 % (13318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.13 % (13318)Termination reason: Unknown
% 5.15/2.13 % (13318)Termination phase: shuffling
% 5.15/2.13
% 5.15/2.13 % (13318)Memory used [KB]: 1663
% 5.15/2.13 % (13318)Time elapsed: 0.009 s
% 5.15/2.13 % (13318)Instructions burned: 21 (million)
% 5.15/2.13 % (13318)------------------------------
% 5.15/2.13 % (13318)------------------------------
% 5.15/2.14 % (13330)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_12937 for (2997ds/39Mi)
% 5.15/2.15 % (13248)Instruction limit reached!
% 5.15/2.15 % (13248)------------------------------
% 5.15/2.15 % (13248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.15 % (13248)Termination reason: Unknown
% 5.15/2.15 % (13248)Termination phase: Property scanning
% 5.15/2.15
% 5.15/2.15 % (13248)Memory used [KB]: 3965
% 5.15/2.15 % (13248)Time elapsed: 0.150 s
% 5.15/2.15 % (13248)Instructions burned: 378 (million)
% 5.15/2.15 % (13248)------------------------------
% 5.15/2.15 % (13248)------------------------------
% 5.15/2.15 % (13330)Instruction limit reached!
% 5.15/2.15 % (13330)------------------------------
% 5.15/2.15 % (13330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.15 % (13330)Termination reason: Unknown
% 5.15/2.15 % (13330)Termination phase: shuffling
% 5.15/2.15
% 5.15/2.15 % (13330)Memory used [KB]: 2046
% 5.15/2.15 % (13330)Time elapsed: 0.015 s
% 5.15/2.15 % (13330)Instructions burned: 41 (million)
% 5.15/2.15 % (13330)------------------------------
% 5.15/2.15 % (13330)------------------------------
% 5.15/2.15 % (13321)Instruction limit reached!
% 5.15/2.15 % (13321)------------------------------
% 5.15/2.15 % (13321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.15 % (13321)Termination reason: Unknown
% 5.15/2.15 % (13321)Termination phase: shuffling
% 5.15/2.15
% 5.15/2.15 % (13321)Memory used [KB]: 2302
% 5.15/2.15 % (13321)Time elapsed: 0.031 s
% 5.15/2.15 % (13321)Instructions burned: 88 (million)
% 5.15/2.15 % (13321)------------------------------
% 5.15/2.15 % (13321)------------------------------
% 5.15/2.16 % (13339)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_12937 for (2996ds/448Mi)
% 5.15/2.16 % (13322)Instruction limit reached!
% 5.15/2.16 % (13322)------------------------------
% 5.15/2.16 % (13322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.16 % (13322)Termination reason: Unknown
% 5.15/2.16 % (13322)Termination phase: shuffling
% 5.15/2.16
% 5.15/2.16 % (13322)Memory used [KB]: 2686
% 5.15/2.16 % (13322)Time elapsed: 0.035 s
% 5.15/2.16 % (13322)Instructions burned: 108 (million)
% 5.15/2.16 % (13322)------------------------------
% 5.15/2.16 % (13322)------------------------------
% 5.15/2.16 % (13342)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_12937 for (2996ds/46Mi)
% 5.15/2.16 % (13345)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_12937 for (2996ds/98Mi)
% 5.15/2.18 % (13347)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_12937 for (2996ds/507Mi)
% 5.15/2.18 % (13342)Instruction limit reached!
% 5.15/2.18 % (13342)------------------------------
% 5.15/2.18 % (13342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.18 % (13342)Termination reason: Unknown
% 5.15/2.18 % (13342)Termination phase: shuffling
% 5.15/2.18
% 5.15/2.18 % (13342)Memory used [KB]: 2046
% 5.15/2.18 % (13342)Time elapsed: 0.018 s
% 5.15/2.18 % (13342)Instructions burned: 48 (million)
% 5.15/2.18 % (13342)------------------------------
% 5.15/2.18 % (13342)------------------------------
% 5.15/2.19 % (13354)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_12937 for (2996ds/149Mi)
% 5.15/2.19 % (13345)Instruction limit reached!
% 5.15/2.19 % (13345)------------------------------
% 5.15/2.19 % (13345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.15/2.19 % (13345)Termination reason: Unknown
% 5.15/2.19 % (13345)Termination phase: shuffling
% 5.15/2.19
% 5.15/2.19 % (13345)Memory used [KB]: 2814
% 5.15/2.19 % (13345)Time elapsed: 0.031 s
% 5.15/2.19 % (13345)Instructions burned: 100 (million)
% 5.15/2.19 % (13345)------------------------------
% 5.15/2.19 % (13345)------------------------------
% 5.68/2.20 % (13249)Instruction limit reached!
% 5.68/2.20 % (13249)------------------------------
% 5.68/2.20 % (13249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.20 % (13249)Termination reason: Unknown
% 5.68/2.20 % (13249)Termination phase: Saturation
% 5.68/2.20
% 5.68/2.20 % (13249)Memory used [KB]: 8955
% 5.68/2.20 % (13249)Time elapsed: 0.208 s
% 5.68/2.20 % (13249)Instructions burned: 782 (million)
% 5.68/2.20 % (13249)------------------------------
% 5.68/2.20 % (13249)------------------------------
% 5.68/2.20 % (13362)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_12937 for (2996ds/39Mi)
% 5.68/2.21 % (13368)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_12937 for (2996ds/6Mi)
% 5.68/2.21 % (13368)Instruction limit reached!
% 5.68/2.21 % (13368)------------------------------
% 5.68/2.21 % (13368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.21 % (13368)Termination reason: Unknown
% 5.68/2.21 % (13368)Termination phase: shuffling
% 5.68/2.21
% 5.68/2.21 % (13368)Memory used [KB]: 1535
% 5.68/2.21 % (13368)Time elapsed: 0.003 s
% 5.68/2.21 % (13368)Instructions burned: 6 (million)
% 5.68/2.21 % (13368)------------------------------
% 5.68/2.21 % (13368)------------------------------
% 5.68/2.22 % (13362)Instruction limit reached!
% 5.68/2.22 % (13362)------------------------------
% 5.68/2.22 % (13362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.22 % (13362)Termination reason: Unknown
% 5.68/2.22 % (13362)Termination phase: shuffling
% 5.68/2.22
% 5.68/2.22 % (13362)Memory used [KB]: 1791
% 5.68/2.22 % (13362)Time elapsed: 0.015 s
% 5.68/2.22 % (13362)Instructions burned: 40 (million)
% 5.68/2.22 % (13362)------------------------------
% 5.68/2.22 % (13362)------------------------------
% 5.68/2.22 % (13235)Instruction limit reached!
% 5.68/2.22 % (13235)------------------------------
% 5.68/2.22 % (13235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.22 % (13235)Termination reason: Unknown
% 5.68/2.22 % (13235)Termination phase: Saturation
% 5.68/2.22
% 5.68/2.22 % (13235)Memory used [KB]: 9850
% 5.68/2.22 % (13235)Time elapsed: 0.250 s
% 5.68/2.22 % (13235)Instructions burned: 903 (million)
% 5.68/2.22 % (13235)------------------------------
% 5.68/2.22 % (13235)------------------------------
% 5.68/2.22 % (13373)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_12937 for (2996ds/1087Mi)
% 5.68/2.23 % (13375)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_12937 for (2996ds/47Mi)
% 5.68/2.23 % (13377)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_12937 for (2996ds/44Mi)
% 5.68/2.24 % (13354)Instruction limit reached!
% 5.68/2.24 % (13354)------------------------------
% 5.68/2.24 % (13354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.24 % (13354)Termination reason: Unknown
% 5.68/2.24 % (13354)Termination phase: shuffling
% 5.68/2.24
% 5.68/2.24 % (13354)Memory used [KB]: 2942
% 5.68/2.24 % (13354)Time elapsed: 0.051 s
% 5.68/2.24 % (13354)Instructions burned: 150 (million)
% 5.68/2.24 % (13354)------------------------------
% 5.68/2.24 % (13354)------------------------------
% 5.68/2.24 % (13375)Instruction limit reached!
% 5.68/2.24 % (13375)------------------------------
% 5.68/2.24 % (13375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.24 % (13375)Termination reason: Unknown
% 5.68/2.24 % (13375)Termination phase: shuffling
% 5.68/2.24
% 5.68/2.24 % (13375)Memory used [KB]: 2046
% 5.68/2.24 % (13375)Time elapsed: 0.016 s
% 5.68/2.24 % (13375)Instructions burned: 47 (million)
% 5.68/2.24 % (13375)------------------------------
% 5.68/2.24 % (13375)------------------------------
% 5.68/2.25 % (13377)Instruction limit reached!
% 5.68/2.25 % (13377)------------------------------
% 5.68/2.25 % (13377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.25 % (13377)Termination reason: Unknown
% 5.68/2.25 % (13377)Termination phase: shuffling
% 5.68/2.25
% 5.68/2.25 % (13377)Memory used [KB]: 2174
% 5.68/2.25 % (13377)Time elapsed: 0.014 s
% 5.68/2.25 % (13377)Instructions burned: 47 (million)
% 5.68/2.25 % (13377)------------------------------
% 5.68/2.25 % (13377)------------------------------
% 5.68/2.25 % (13382)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_12937 for (2996ds/432Mi)
% 5.68/2.25 % (13386)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_12937 for (2995ds/62Mi)
% 5.68/2.25 % (13390)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_12937 for (2995ds/31Mi)
% 5.68/2.26 % (13207)Instruction limit reached!
% 5.68/2.26 % (13207)------------------------------
% 5.68/2.26 % (13207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.26 % (13207)Termination reason: Unknown
% 5.68/2.26 % (13207)Termination phase: Saturation
% 5.68/2.26
% 5.68/2.26 % (13207)Memory used [KB]: 9850
% 5.68/2.26 % (13207)Time elapsed: 0.320 s
% 5.68/2.26 % (13207)Instructions burned: 1041 (million)
% 5.68/2.26 % (13207)------------------------------
% 5.68/2.26 % (13207)------------------------------
% 5.68/2.26 % (13390)Instruction limit reached!
% 5.68/2.26 % (13390)------------------------------
% 5.68/2.26 % (13390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.26 % (13390)Termination reason: Unknown
% 5.68/2.26 % (13390)Termination phase: shuffling
% 5.68/2.26
% 5.68/2.26 % (13390)Memory used [KB]: 1918
% 5.68/2.26 % (13390)Time elapsed: 0.011 s
% 5.68/2.26 % (13390)Instructions burned: 32 (million)
% 5.68/2.26 % (13390)------------------------------
% 5.68/2.26 % (13390)------------------------------
% 5.68/2.27 % (13396)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_12937 for (2995ds/96Mi)
% 5.68/2.27 % (13386)Instruction limit reached!
% 5.68/2.27 % (13386)------------------------------
% 5.68/2.27 % (13386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.27 % (13386)Termination reason: Unknown
% 5.68/2.27 % (13386)Termination phase: shuffling
% 5.68/2.27
% 5.68/2.27 % (13386)Memory used [KB]: 2302
% 5.68/2.27 % (13386)Time elapsed: 0.018 s
% 5.68/2.27 % (13386)Instructions burned: 63 (million)
% 5.68/2.27 % (13386)------------------------------
% 5.68/2.27 % (13386)------------------------------
% 5.68/2.27 % (13339)Instruction limit reached!
% 5.68/2.27 % (13339)------------------------------
% 5.68/2.27 % (13339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.27 % (13339)Termination reason: Unknown
% 5.68/2.27 % (13339)Termination phase: Saturation
% 5.68/2.27
% 5.68/2.27 % (13339)Memory used [KB]: 7675
% 5.68/2.27 % (13339)Time elapsed: 0.116 s
% 5.68/2.27 % (13339)Instructions burned: 448 (million)
% 5.68/2.27 % (13339)------------------------------
% 5.68/2.27 % (13339)------------------------------
% 5.68/2.27 % (13398)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_12937 for (2995ds/453Mi)
% 5.68/2.28 % (13400)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_12937 for (2995ds/71Mi)
% 5.68/2.28 % (13402)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_12937 for (2995ds/83Mi)
% 6.12/2.30 % (13396)Instruction limit reached!
% 6.12/2.30 % (13396)------------------------------
% 6.12/2.30 % (13396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.30 % (13396)Termination reason: Unknown
% 6.12/2.30 % (13396)Termination phase: shuffling
% 6.12/2.30
% 6.12/2.30 % (13396)Memory used [KB]: 2558
% 6.12/2.30 % (13396)Time elapsed: 0.032 s
% 6.12/2.30 % (13396)Instructions burned: 97 (million)
% 6.12/2.30 % (13396)------------------------------
% 6.12/2.30 % (13396)------------------------------
% 6.12/2.30 % (13400)Instruction limit reached!
% 6.12/2.30 % (13400)------------------------------
% 6.12/2.30 % (13400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.30 % (13400)Termination reason: Unknown
% 6.12/2.30 % (13400)Termination phase: shuffling
% 6.12/2.30
% 6.12/2.30 % (13400)Memory used [KB]: 2302
% 6.12/2.30 % (13400)Time elapsed: 0.024 s
% 6.12/2.30 % (13400)Instructions burned: 71 (million)
% 6.12/2.30 % (13400)------------------------------
% 6.12/2.30 % (13400)------------------------------
% 6.12/2.31 % (13416)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_12937 for (2995ds/11Mi)
% 6.12/2.31 % (13402)Instruction limit reached!
% 6.12/2.31 % (13402)------------------------------
% 6.12/2.31 % (13402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.31 % (13402)Termination reason: Unknown
% 6.12/2.31 % (13402)Termination phase: shuffling
% 6.12/2.31
% 6.12/2.31 % (13402)Memory used [KB]: 2302
% 6.12/2.31 % (13402)Time elapsed: 0.028 s
% 6.12/2.31 % (13402)Instructions burned: 84 (million)
% 6.12/2.31 % (13402)------------------------------
% 6.12/2.31 % (13402)------------------------------
% 6.12/2.31 % (13416)Instruction limit reached!
% 6.12/2.31 % (13416)------------------------------
% 6.12/2.31 % (13416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.31 % (13416)Termination reason: Unknown
% 6.12/2.31 % (13416)Termination phase: shuffling
% 6.12/2.31
% 6.12/2.31 % (13416)Memory used [KB]: 1663
% 6.12/2.31 % (13416)Time elapsed: 0.004 s
% 6.12/2.31 % (13416)Instructions burned: 11 (million)
% 6.12/2.31 % (13416)------------------------------
% 6.12/2.31 % (13416)------------------------------
% 6.12/2.31 % (13420)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_12937 for (2995ds/41Mi)
% 6.12/2.32 % (13426)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12937 for (2995ds/6Mi)
% 6.12/2.32 % (13428)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_12937 for (2995ds/150Mi)
% 6.12/2.32 % (13426)Instruction limit reached!
% 6.12/2.32 % (13426)------------------------------
% 6.12/2.32 % (13426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.32 % (13426)Termination reason: Unknown
% 6.12/2.32 % (13426)Termination phase: shuffling
% 6.12/2.32
% 6.12/2.32 % (13426)Memory used [KB]: 1535
% 6.12/2.32 % (13426)Time elapsed: 0.004 s
% 6.12/2.32 % (13426)Instructions burned: 9 (million)
% 6.12/2.32 % (13426)------------------------------
% 6.12/2.32 % (13426)------------------------------
% 6.12/2.32 % (13420)Instruction limit reached!
% 6.12/2.32 % (13420)------------------------------
% 6.12/2.32 % (13420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.32 % (13420)Termination reason: Unknown
% 6.12/2.32 % (13420)Termination phase: shuffling
% 6.12/2.32
% 6.12/2.32 % (13420)Memory used [KB]: 2174
% 6.12/2.32 % (13420)Time elapsed: 0.013 s
% 6.12/2.32 % (13420)Instructions burned: 43 (million)
% 6.12/2.32 % (13420)------------------------------
% 6.12/2.32 % (13420)------------------------------
% 6.12/2.33 % (13436)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_12937 for (2995ds/343Mi)
% 6.12/2.33 % (13347)Instruction limit reached!
% 6.12/2.33 % (13347)------------------------------
% 6.12/2.33 % (13347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.33 % (13347)Termination reason: Unknown
% 6.12/2.33 % (13347)Termination phase: Saturation
% 6.12/2.33
% 6.12/2.33 % (13347)Memory used [KB]: 4221
% 6.12/2.33 % (13347)Time elapsed: 0.156 s
% 6.12/2.33 % (13347)Instructions burned: 508 (million)
% 6.12/2.33 % (13347)------------------------------
% 6.12/2.33 % (13347)------------------------------
% 6.12/2.33 % (13439)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_12937 for (2995ds/109Mi)
% 6.12/2.34 % (13445)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_12937 for (2995ds/253Mi)
% 6.12/2.36 % (13382)Instruction limit reached!
% 6.12/2.36 % (13382)------------------------------
% 6.12/2.36 % (13382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.36 % (13382)Termination reason: Unknown
% 6.12/2.36 % (13382)Termination phase: Saturation
% 6.12/2.36
% 6.12/2.36 % (13382)Memory used [KB]: 3198
% 6.12/2.36 % (13382)Time elapsed: 0.114 s
% 6.12/2.36 % (13382)Instructions burned: 433 (million)
% 6.12/2.36 % (13382)------------------------------
% 6.12/2.36 % (13382)------------------------------
% 6.12/2.37 % (13428)Instruction limit reached!
% 6.12/2.37 % (13428)------------------------------
% 6.12/2.37 % (13428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.37 % (13428)Termination reason: Unknown
% 6.12/2.37 % (13428)Termination phase: shuffling
% 6.12/2.37
% 6.12/2.37 % (13428)Memory used [KB]: 3070
% 6.12/2.37 % (13428)Time elapsed: 0.049 s
% 6.12/2.37 % (13428)Instructions burned: 152 (million)
% 6.12/2.37 % (13428)------------------------------
% 6.12/2.37 % (13428)------------------------------
% 6.12/2.37 % (13439)Instruction limit reached!
% 6.12/2.37 % (13439)------------------------------
% 6.12/2.37 % (13439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.37 % (13439)Termination reason: Unknown
% 6.12/2.37 % (13439)Termination phase: shuffling
% 6.12/2.37
% 6.12/2.37 % (13439)Memory used [KB]: 2558
% 6.12/2.37 % (13439)Time elapsed: 0.036 s
% 6.12/2.37 % (13439)Instructions burned: 111 (million)
% 6.12/2.37 % (13439)------------------------------
% 6.12/2.37 % (13439)------------------------------
% 6.12/2.37 % (13451)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_12937 for (2994ds/140Mi)
% 6.12/2.38 % (13452)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_12937 for (2994ds/614Mi)
% 6.12/2.38 % (13453)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_12937 for (2994ds/202Mi)
% 6.12/2.39 % (13398)Instruction limit reached!
% 6.12/2.39 % (13398)------------------------------
% 6.12/2.39 % (13398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.39 % (13398)Termination reason: Unknown
% 6.12/2.39 % (13398)Termination phase: Saturation
% 6.12/2.39
% 6.12/2.39 % (13398)Memory used [KB]: 7675
% 6.12/2.39 % (13398)Time elapsed: 0.117 s
% 6.12/2.39 % (13398)Instructions burned: 453 (million)
% 6.12/2.39 % (13398)------------------------------
% 6.12/2.39 % (13398)------------------------------
% 6.79/2.40 % (13454)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_12937 for (2994ds/339Mi)
% 6.79/2.41 % (13451)Instruction limit reached!
% 6.79/2.41 % (13451)------------------------------
% 6.79/2.41 % (13451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.41 % (13451)Termination reason: Unknown
% 6.79/2.41 % (13451)Termination phase: shuffling
% 6.79/2.41
% 6.79/2.41 % (13451)Memory used [KB]: 2814
% 6.79/2.41 % (13451)Time elapsed: 0.045 s
% 6.79/2.41 % (13451)Instructions burned: 142 (million)
% 6.79/2.41 % (13451)------------------------------
% 6.79/2.41 % (13451)------------------------------
% 6.79/2.42 % (13445)Instruction limit reached!
% 6.79/2.42 % (13445)------------------------------
% 6.79/2.42 % (13445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.42 % (13445)Termination reason: Unknown
% 6.79/2.42 % (13445)Termination phase: SInE selection
% 6.79/2.42
% 6.79/2.42 % (13445)Memory used [KB]: 3326
% 6.79/2.42 % (13445)Time elapsed: 0.077 s
% 6.79/2.42 % (13445)Instructions burned: 255 (million)
% 6.79/2.42 % (13445)------------------------------
% 6.79/2.42 % (13445)------------------------------
% 6.79/2.42 % (13455)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_12937 for (2994ds/283Mi)
% 6.79/2.43 % (13456)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_12937 for (2994ds/134Mi)
% 6.79/2.43 % (13436)Instruction limit reached!
% 6.79/2.43 % (13436)------------------------------
% 6.79/2.43 % (13436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.43 % (13436)Termination reason: Unknown
% 6.79/2.43 % (13436)Termination phase: Property scanning
% 6.79/2.43
% 6.79/2.43 % (13436)Memory used [KB]: 3709
% 6.79/2.43 % (13436)Time elapsed: 0.099 s
% 6.79/2.43 % (13436)Instructions burned: 346 (million)
% 6.79/2.43 % (13436)------------------------------
% 6.79/2.43 % (13436)------------------------------
% 6.79/2.44 % (13457)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_12937 for (2994ds/298Mi)
% 6.79/2.44 % (13453)Instruction limit reached!
% 6.79/2.44 % (13453)------------------------------
% 6.79/2.44 % (13453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.44 % (13453)Termination reason: Unknown
% 6.79/2.44 % (13453)Termination phase: Property scanning
% 6.79/2.44
% 6.79/2.44 % (13453)Memory used [KB]: 3326
% 6.79/2.44 % (13453)Time elapsed: 0.064 s
% 6.79/2.44 % (13453)Instructions burned: 204 (million)
% 6.79/2.44 % (13453)------------------------------
% 6.79/2.44 % (13453)------------------------------
% 6.79/2.45 % (13458)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_12937 for (2994ds/192Mi)
% 6.79/2.47 % (13456)Instruction limit reached!
% 6.79/2.47 % (13456)------------------------------
% 6.79/2.47 % (13456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.47 % (13456)Termination reason: Unknown
% 6.79/2.47 % (13456)Termination phase: shuffling
% 6.79/2.47
% 6.79/2.47 % (13456)Memory used [KB]: 2686
% 6.79/2.47 % (13456)Time elapsed: 0.043 s
% 6.79/2.47 % (13456)Instructions burned: 135 (million)
% 6.79/2.47 % (13456)------------------------------
% 6.79/2.47 % (13456)------------------------------
% 6.79/2.48 % (13459)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_12937 for (2993ds/258Mi)
% 7.17/2.50 % (13454)Instruction limit reached!
% 7.17/2.50 % (13454)------------------------------
% 7.17/2.50 % (13454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.50 % (13454)Termination reason: Unknown
% 7.17/2.50 % (13454)Termination phase: Property scanning
% 7.17/2.50
% 7.17/2.50 % (13454)Memory used [KB]: 3837
% 7.17/2.50 % (13454)Time elapsed: 0.099 s
% 7.17/2.50 % (13454)Instructions burned: 340 (million)
% 7.17/2.50 % (13454)------------------------------
% 7.17/2.50 % (13454)------------------------------
% 7.17/2.50 % (13455)Instruction limit reached!
% 7.17/2.50 % (13455)------------------------------
% 7.17/2.50 % (13455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.50 % (13455)Termination reason: Unknown
% 7.17/2.50 % (13455)Termination phase: Property scanning
% 7.17/2.50
% 7.17/2.50 % (13455)Memory used [KB]: 3198
% 7.17/2.50 % (13455)Time elapsed: 0.076 s
% 7.17/2.50 % (13455)Instructions burned: 283 (million)
% 7.17/2.50 % (13455)------------------------------
% 7.17/2.50 % (13455)------------------------------
% 7.17/2.51 % (13460)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_12937 for (2993ds/90Mi)
% 7.17/2.51 % (13461)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_12937 for (2993ds/231Mi)
% 7.17/2.51 % (13458)Instruction limit reached!
% 7.17/2.51 % (13458)------------------------------
% 7.17/2.51 % (13458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.51 % (13458)Termination reason: Unknown
% 7.17/2.51 % (13458)Termination phase: Property scanning
% 7.17/2.51
% 7.17/2.51 % (13458)Memory used [KB]: 3326
% 7.17/2.51 % (13458)Time elapsed: 0.061 s
% 7.17/2.51 % (13458)Instructions burned: 193 (million)
% 7.17/2.51 % (13458)------------------------------
% 7.17/2.51 % (13458)------------------------------
% 7.17/2.52 % (13457)Instruction limit reached!
% 7.17/2.52 % (13457)------------------------------
% 7.17/2.52 % (13457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.52 % (13457)Termination reason: Unknown
% 7.17/2.52 % (13457)Termination phase: Property scanning
% 7.17/2.52
% 7.17/2.52 % (13457)Memory used [KB]: 3198
% 7.17/2.52 % (13457)Time elapsed: 0.080 s
% 7.17/2.52 % (13457)Instructions burned: 300 (million)
% 7.17/2.52 % (13457)------------------------------
% 7.17/2.52 % (13457)------------------------------
% 7.17/2.52 % (13462)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_12937 for (2993ds/458Mi)
% 7.17/2.52 % (13463)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_12937 for (2993ds/31Mi)
% 7.17/2.53 % (13463)Instruction limit reached!
% 7.17/2.53 % (13463)------------------------------
% 7.17/2.53 % (13463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.53 % (13460)Instruction limit reached!
% 7.17/2.53 % (13460)------------------------------
% 7.17/2.53 % (13460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.53 % (13463)Termination reason: Unknown
% 7.17/2.53 % (13460)Termination reason: Unknown
% 7.17/2.53 % (13463)Termination phase: shuffling
% 7.17/2.53
% 7.17/2.53 % (13460)Termination phase: shuffling
% 7.17/2.53 % (13463)Memory used [KB]: 1791
% 7.17/2.53
% 7.17/2.53 % (13463)Time elapsed: 0.011 s
% 7.17/2.53 % (13460)Memory used [KB]: 2302
% 7.17/2.53 % (13463)Instructions burned: 33 (million)
% 7.17/2.53 % (13460)Time elapsed: 0.029 s
% 7.17/2.53 % (13463)------------------------------
% 7.17/2.53 % (13463)------------------------------
% 7.17/2.53 % (13460)Instructions burned: 92 (million)
% 7.17/2.53 % (13460)------------------------------
% 7.17/2.53 % (13460)------------------------------
% 7.17/2.54 % (13452)Instruction limit reached!
% 7.17/2.54 % (13452)------------------------------
% 7.17/2.54 % (13452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.54 % (13452)Termination reason: Unknown
% 7.17/2.54 % (13452)Termination phase: Saturation
% 7.17/2.54
% 7.17/2.54 % (13452)Memory used [KB]: 8827
% 7.17/2.54 % (13452)Time elapsed: 0.168 s
% 7.17/2.54 % (13452)Instructions burned: 617 (million)
% 7.17/2.54 % (13452)------------------------------
% 7.17/2.54 % (13452)------------------------------
% 7.17/2.54 % (13464)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_12937 for (2993ds/297Mi)
% 7.17/2.54 % (13465)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_12937 for (2993ds/987Mi)
% 7.17/2.55 % (13373)Instruction limit reached!
% 7.17/2.55 % (13373)------------------------------
% 7.17/2.55 % (13373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.55 % (13373)Termination reason: Unknown
% 7.17/2.55 % (13373)Termination phase: Saturation
% 7.17/2.55
% 7.17/2.55 % (13373)Memory used [KB]: 8571
% 7.17/2.55 % (13373)Time elapsed: 0.323 s
% 7.17/2.55 % (13373)Instructions burned: 1087 (million)
% 7.17/2.55 % (13373)------------------------------
% 7.17/2.55 % (13373)------------------------------
% 7.17/2.55 % (13466)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_12937 for (2992ds/182Mi)
% 7.17/2.55 % (13459)Instruction limit reached!
% 7.17/2.55 % (13459)------------------------------
% 7.17/2.55 % (13459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.55 % (13459)Termination reason: Unknown
% 7.17/2.55 % (13459)Termination phase: Preprocessing 3
% 7.17/2.55
% 7.17/2.55 % (13459)Memory used [KB]: 3454
% 7.17/2.55 % (13459)Time elapsed: 0.078 s
% 7.17/2.55 % (13459)Instructions burned: 260 (million)
% 7.17/2.55 % (13459)------------------------------
% 7.17/2.55 % (13459)------------------------------
% 7.17/2.56 % (13467)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_12937 for (2992ds/182Mi)
% 7.17/2.56 % (13468)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_12937 for (2992ds/154Mi)
% 7.17/2.57 % (13461)Instruction limit reached!
% 7.17/2.57 % (13461)------------------------------
% 7.17/2.57 % (13461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.57 % (13461)Termination reason: Unknown
% 7.17/2.57 % (13461)Termination phase: Preprocessing 3
% 7.17/2.57
% 7.17/2.57 % (13461)Memory used [KB]: 3198
% 7.17/2.57 % (13461)Time elapsed: 0.062 s
% 7.17/2.57 % (13461)Instructions burned: 231 (million)
% 7.17/2.57 % (13461)------------------------------
% 7.17/2.57 % (13461)------------------------------
% 7.17/2.58 % (13469)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_12937 for (2992ds/79Mi)
% 8.24/2.60 % (13469)Instruction limit reached!
% 8.24/2.60 % (13469)------------------------------
% 8.24/2.60 % (13469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.60 % (13469)Termination reason: Unknown
% 8.24/2.60 % (13469)Termination phase: shuffling
% 8.24/2.60
% 8.24/2.60 % (13469)Memory used [KB]: 2430
% 8.24/2.60 % (13469)Time elapsed: 0.026 s
% 8.24/2.60 % (13469)Instructions burned: 81 (million)
% 8.24/2.60 % (13469)------------------------------
% 8.24/2.60 % (13469)------------------------------
% 8.24/2.60 % (13468)Instruction limit reached!
% 8.24/2.60 % (13468)------------------------------
% 8.24/2.60 % (13468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.60 % (13468)Termination reason: Unknown
% 8.24/2.60 % (13468)Termination phase: Property scanning
% 8.24/2.60
% 8.24/2.60 % (13468)Memory used [KB]: 2814
% 8.24/2.60 % (13468)Time elapsed: 0.041 s
% 8.24/2.60 % (13468)Instructions burned: 155 (million)
% 8.24/2.60 % (13468)------------------------------
% 8.24/2.60 % (13468)------------------------------
% 8.24/2.61 % (13466)Instruction limit reached!
% 8.24/2.61 % (13466)------------------------------
% 8.24/2.61 % (13466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.61 % (13466)Termination reason: Unknown
% 8.24/2.61 % (13466)Termination phase: shuffling
% 8.24/2.61
% 8.24/2.61 % (13466)Memory used [KB]: 3198
% 8.24/2.61 % (13466)Time elapsed: 0.057 s
% 8.24/2.61 % (13466)Instructions burned: 182 (million)
% 8.24/2.61 % (13466)------------------------------
% 8.24/2.61 % (13466)------------------------------
% 8.24/2.61 % (13467)Instruction limit reached!
% 8.24/2.61 % (13467)------------------------------
% 8.24/2.61 % (13467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.61 % (13467)Termination reason: Unknown
% 8.24/2.61 % (13467)Termination phase: shuffling
% 8.24/2.61
% 8.24/2.61 % (13467)Memory used [KB]: 3198
% 8.24/2.61 % (13467)Time elapsed: 0.057 s
% 8.24/2.61 % (13467)Instructions burned: 182 (million)
% 8.24/2.61 % (13467)------------------------------
% 8.24/2.61 % (13467)------------------------------
% 8.24/2.61 % (13470)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_12937 for (2992ds/216Mi)
% 8.24/2.61 % (13471)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_12937 for (2992ds/114Mi)
% 8.24/2.62 % (13472)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_12937 for (2992ds/922Mi)
% 8.24/2.62 % (13464)Instruction limit reached!
% 8.24/2.62 % (13464)------------------------------
% 8.24/2.62 % (13464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.62 % (13464)Termination reason: Unknown
% 8.24/2.62 % (13464)Termination phase: Saturation
% 8.24/2.62
% 8.24/2.62 % (13464)Memory used [KB]: 7547
% 8.24/2.62 % (13464)Time elapsed: 0.077 s
% 8.24/2.62 % (13464)Instructions burned: 298 (million)
% 8.24/2.62 % (13464)------------------------------
% 8.24/2.62 % (13464)------------------------------
% 8.24/2.62 % (13473)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_12937 for (2992ds/182Mi)
% 8.24/2.63 % (13474)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_12937 for (2992ds/164Mi)
% 8.24/2.64 % (13462)Instruction limit reached!
% 8.24/2.64 % (13462)------------------------------
% 8.24/2.64 % (13462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.64 % (13462)Termination reason: Unknown
% 8.24/2.64 % (13462)Termination phase: Property scanning
% 8.24/2.64
% 8.24/2.64 % (13462)Memory used [KB]: 3965
% 8.24/2.64 % (13462)Time elapsed: 0.126 s
% 8.24/2.64 % (13462)Instructions burned: 461 (million)
% 8.24/2.64 % (13462)------------------------------
% 8.24/2.64 % (13462)------------------------------
% 8.24/2.65 % (13471)Instruction limit reached!
% 8.24/2.65 % (13471)------------------------------
% 8.24/2.65 % (13471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.65 % (13471)Termination reason: Unknown
% 8.24/2.65 % (13471)Termination phase: shuffling
% 8.24/2.65
% 8.24/2.65 % (13471)Memory used [KB]: 2686
% 8.24/2.65 % (13471)Time elapsed: 0.037 s
% 8.24/2.65 % (13471)Instructions burned: 117 (million)
% 8.24/2.65 % (13471)------------------------------
% 8.24/2.65 % (13471)------------------------------
% 8.24/2.65 % (13475)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_12937 for (2991ds/50Mi)
% 8.24/2.66 % (13476)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_12937 for (2991ds/368Mi)
% 8.24/2.67 % (13475)Instruction limit reached!
% 8.24/2.67 % (13475)------------------------------
% 8.24/2.67 % (13475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.67 % (13475)Termination reason: Unknown
% 8.24/2.67 % (13475)Termination phase: shuffling
% 8.24/2.67
% 8.24/2.67 % (13475)Memory used [KB]: 2174
% 8.24/2.67 % (13475)Time elapsed: 0.015 s
% 8.24/2.67 % (13475)Instructions burned: 52 (million)
% 8.24/2.67 % (13475)------------------------------
% 8.24/2.67 % (13475)------------------------------
% 8.24/2.67 % (13470)Instruction limit reached!
% 8.24/2.67 % (13470)------------------------------
% 8.24/2.67 % (13470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.67 % (13470)Termination reason: Unknown
% 8.24/2.67 % (13470)Termination phase: SInE selection
% 8.24/2.67
% 8.24/2.67 % (13470)Memory used [KB]: 2814
% 8.24/2.67 % (13470)Time elapsed: 0.056 s
% 8.24/2.67 % (13470)Instructions burned: 219 (million)
% 8.24/2.67 % (13470)------------------------------
% 8.24/2.67 % (13470)------------------------------
% 8.24/2.67 % (13473)Instruction limit reached!
% 8.24/2.67 % (13473)------------------------------
% 8.24/2.67 % (13473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.67 % (13473)Termination reason: Unknown
% 8.24/2.67 % (13473)Termination phase: Preprocessing 1
% 8.24/2.67
% 8.24/2.67 % (13473)Memory used [KB]: 2942
% 8.24/2.67 % (13473)Time elapsed: 0.048 s
% 8.24/2.67 % (13473)Instructions burned: 182 (million)
% 8.24/2.67 % (13473)------------------------------
% 8.24/2.67 % (13473)------------------------------
% 8.24/2.67 % (13474)Instruction limit reached!
% 8.24/2.67 % (13474)------------------------------
% 8.24/2.67 % (13474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.67 % (13474)Termination reason: Unknown
% 8.24/2.67 % (13474)Termination phase: Property scanning
% 8.24/2.67
% 8.24/2.67 % (13474)Memory used [KB]: 2814
% 8.24/2.67 % (13474)Time elapsed: 0.043 s
% 8.24/2.67 % (13474)Instructions burned: 164 (million)
% 8.24/2.67 % (13474)------------------------------
% 8.24/2.67 % (13474)------------------------------
% 8.24/2.68 % (13477)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_12937 for (2991ds/1021Mi)
% 8.24/2.68 % (13478)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_12937 for (2991ds/267Mi)
% 8.24/2.68 % (13479)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_12937 for (2991ds/204Mi)
% 8.24/2.68 % (13480)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_12937 for (2991ds/26Mi)
% 8.24/2.69 % (13480)Instruction limit reached!
% 8.24/2.69 % (13480)------------------------------
% 8.24/2.69 % (13480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.69 % (13480)Termination reason: Unknown
% 8.24/2.69 % (13480)Termination phase: shuffling
% 8.24/2.69
% 8.24/2.69 % (13480)Memory used [KB]: 1918
% 8.24/2.69 % (13480)Time elapsed: 0.009 s
% 8.24/2.69 % (13480)Instructions burned: 28 (million)
% 8.24/2.69 % (13480)------------------------------
% 8.24/2.69 % (13480)------------------------------
% 8.95/2.70 % (13481)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_12937 for (2991ds/53Mi)
% 8.95/2.71 % (13481)Instruction limit reached!
% 8.95/2.71 % (13481)------------------------------
% 8.95/2.71 % (13481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.71 % (13481)Termination reason: Unknown
% 8.95/2.71 % (13481)Termination phase: shuffling
% 8.95/2.71
% 8.95/2.71 % (13481)Memory used [KB]: 2174
% 8.95/2.71 % (13481)Time elapsed: 0.015 s
% 8.95/2.71 % (13481)Instructions burned: 53 (million)
% 8.95/2.71 % (13481)------------------------------
% 8.95/2.71 % (13481)------------------------------
% 8.95/2.72 % (13482)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_12937 for (2991ds/4436Mi)
% 8.95/2.74 % (13479)Instruction limit reached!
% 8.95/2.74 % (13479)------------------------------
% 8.95/2.74 % (13479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.74 % (13479)Termination reason: Unknown
% 8.95/2.74 % (13479)Termination phase: Property scanning
% 8.95/2.74
% 8.95/2.74 % (13479)Memory used [KB]: 3198
% 8.95/2.74 % (13479)Time elapsed: 0.063 s
% 8.95/2.74 % (13479)Instructions burned: 205 (million)
% 8.95/2.74 % (13479)------------------------------
% 8.95/2.74 % (13479)------------------------------
% 8.95/2.75 % (13478)Instruction limit reached!
% 8.95/2.75 % (13478)------------------------------
% 8.95/2.75 % (13478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.75 % (13478)Termination reason: Unknown
% 8.95/2.75 % (13478)Termination phase: Property scanning
% 8.95/2.75
% 8.95/2.75 % (13478)Memory used [KB]: 3198
% 8.95/2.75 % (13478)Time elapsed: 0.071 s
% 8.95/2.75 % (13478)Instructions burned: 267 (million)
% 8.95/2.75 % (13478)------------------------------
% 8.95/2.75 % (13478)------------------------------
% 8.95/2.75 % (13483)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_12937 for (2991ds/1539Mi)
% 8.95/2.76 % (13484)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_12937 for (2990ds/408Mi)
% 8.95/2.76 % (13476)Instruction limit reached!
% 8.95/2.76 % (13476)------------------------------
% 8.95/2.76 % (13476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.76 % (13476)Termination reason: Unknown
% 8.95/2.76 % (13476)Termination phase: Equality resolution with deletion
% 8.95/2.76
% 8.95/2.76 % (13476)Memory used [KB]: 3965
% 8.95/2.76 % (13476)Time elapsed: 0.105 s
% 8.95/2.76 % (13476)Instructions burned: 369 (million)
% 8.95/2.76 % (13476)------------------------------
% 8.95/2.76 % (13476)------------------------------
% 8.95/2.77 % (13485)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_12937 for (2990ds/5205Mi)
% 9.24/2.83 % (13465)Instruction limit reached!
% 9.24/2.83 % (13465)------------------------------
% 9.24/2.83 % (13465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.83 % (13465)Termination reason: Unknown
% 9.24/2.83 % (13465)Termination phase: Saturation
% 9.24/2.83
% 9.24/2.83 % (13465)Memory used [KB]: 11001
% 9.24/2.83 % (13465)Time elapsed: 0.315 s
% 9.24/2.83 % (13465)Instructions burned: 987 (million)
% 9.24/2.83 % (13465)------------------------------
% 9.24/2.83 % (13465)------------------------------
% 9.24/2.84 % (13486)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_12937 for (2990ds/1913Mi)
% 9.24/2.87 % (13484)Instruction limit reached!
% 9.24/2.87 % (13484)------------------------------
% 9.24/2.87 % (13484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.87 % (13484)Termination reason: Unknown
% 9.24/2.87 % (13484)Termination phase: Property scanning
% 9.24/2.87
% 9.24/2.87 % (13484)Memory used [KB]: 4093
% 9.24/2.87 % (13484)Time elapsed: 0.118 s
% 9.24/2.87 % (13484)Instructions burned: 411 (million)
% 9.24/2.87 % (13484)------------------------------
% 9.24/2.87 % (13484)------------------------------
% 9.24/2.88 % (13487)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_12937 for (2989ds/4350Mi)
% 9.24/2.90 % (13472)Instruction limit reached!
% 9.24/2.90 % (13472)------------------------------
% 9.24/2.90 % (13472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.90 % (13472)Termination reason: Unknown
% 9.24/2.90 % (13472)Termination phase: Saturation
% 9.24/2.90
% 9.24/2.90 % (13472)Memory used [KB]: 9210
% 9.66/2.90 % (13472)Time elapsed: 0.279 s
% 9.66/2.90 % (13472)Instructions burned: 924 (million)
% 9.66/2.90 % (13472)------------------------------
% 9.66/2.90 % (13472)------------------------------
% 9.66/2.91 % (13488)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_12937 for (2989ds/68Mi)
% 9.66/2.93 % (13488)Instruction limit reached!
% 9.66/2.93 % (13488)------------------------------
% 9.66/2.93 % (13488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.93 % (13488)Termination reason: Unknown
% 9.66/2.93 % (13488)Termination phase: shuffling
% 9.66/2.93
% 9.66/2.93 % (13488)Memory used [KB]: 2302
% 9.66/2.93 % (13488)Time elapsed: 0.022 s
% 9.66/2.93 % (13488)Instructions burned: 69 (million)
% 9.66/2.93 % (13488)------------------------------
% 9.66/2.93 % (13488)------------------------------
% 9.66/2.94 % (13489)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_12937 for (2989ds/358Mi)
% 9.66/2.96 % (13487)Refutation not found, incomplete strategy
% 9.66/2.96 % (13487)------------------------------
% 9.66/2.96 % (13487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.96 % (13487)Termination reason: Refutation not found, incomplete strategy
% 9.66/2.96
% 9.66/2.96
% 9.66/2.96 % (13487)Memory used [KB]: 7803
% 9.66/2.96 % (13487)Time elapsed: 0.073 s
% 9.66/2.96 % (13487)Instructions burned: 248 (million)
% 9.66/2.96 % (13487)------------------------------
% 9.66/2.96 % (13487)------------------------------
% 9.66/2.96 % (13477)Instruction limit reached!
% 9.66/2.96 % (13477)------------------------------
% 9.66/2.96 % (13477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.96 % (13477)Termination reason: Unknown
% 9.66/2.96 % (13477)Termination phase: Saturation
% 9.66/2.96
% 9.66/2.96 % (13477)Memory used [KB]: 10746
% 9.66/2.96 % (13477)Time elapsed: 0.287 s
% 9.66/2.96 % (13477)Instructions burned: 1021 (million)
% 9.66/2.96 % (13477)------------------------------
% 9.66/2.96 % (13477)------------------------------
% 9.66/2.97 % (13490)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_12937 for (2988ds/31Mi)
% 9.66/2.97 % (13491)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_12937 for (2988ds/279Mi)
% 9.66/2.98 % (13490)Instruction limit reached!
% 9.66/2.98 % (13490)------------------------------
% 9.66/2.98 % (13490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.98 % (13490)Termination reason: Unknown
% 9.66/2.98 % (13490)Termination phase: shuffling
% 9.66/2.98
% 9.66/2.98 % (13490)Memory used [KB]: 1791
% 9.66/2.98 % (13490)Time elapsed: 0.011 s
% 9.66/2.98 % (13490)Instructions burned: 33 (million)
% 9.66/2.98 % (13490)------------------------------
% 9.66/2.98 % (13490)------------------------------
% 9.66/2.98 % (13492)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_12937 for (2988ds/258Mi)
% 11.49/3.04 % (13489)Instruction limit reached!
% 11.49/3.04 % (13489)------------------------------
% 11.49/3.04 % (13489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.49/3.04 % (13489)Termination reason: Unknown
% 11.49/3.04 % (13489)Termination phase: Preprocessing 3
% 11.49/3.04
% 11.49/3.04 % (13489)Memory used [KB]: 3709
% 11.49/3.04 % (13489)Time elapsed: 0.101 s
% 11.49/3.04 % (13489)Instructions burned: 359 (million)
% 11.49/3.04 % (13489)------------------------------
% 11.49/3.04 % (13489)------------------------------
% 11.49/3.04 % (13491)Instruction limit reached!
% 11.49/3.04 % (13491)------------------------------
% 11.49/3.04 % (13491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.49/3.04 % (13491)Termination reason: Unknown
% 11.49/3.04 % (13491)Termination phase: Saturation
% 11.49/3.04
% 11.49/3.04 % (13491)Memory used [KB]: 3198
% 11.49/3.04 % (13491)Time elapsed: 0.072 s
% 11.49/3.04 % (13491)Instructions burned: 280 (million)
% 11.49/3.04 % (13491)------------------------------
% 11.49/3.04 % (13491)------------------------------
% 11.49/3.05 % (13493)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_12937 for (2988ds/26Mi)
% 11.49/3.05 % (13494)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_12937 for (2987ds/995Mi)
% 11.49/3.05 % (13493)Instruction limit reached!
% 11.49/3.05 % (13493)------------------------------
% 11.49/3.05 % (13493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.49/3.05 % (13493)Termination reason: Unknown
% 11.49/3.05 % (13493)Termination phase: shuffling
% 11.49/3.05
% 11.49/3.05 % (13493)Memory used [KB]: 1918
% 11.49/3.05 % (13493)Time elapsed: 0.009 s
% 11.49/3.05 % (13493)Instructions burned: 28 (million)
% 11.49/3.05 % (13493)------------------------------
% 11.49/3.05 % (13493)------------------------------
% 11.49/3.06 % (13492)Instruction limit reached!
% 11.49/3.06 % (13492)------------------------------
% 11.49/3.06 % (13492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.49/3.06 % (13492)Termination reason: Unknown
% 11.49/3.06 % (13492)Termination phase: Naming
% 11.49/3.06
% 11.49/3.06 % (13492)Memory used [KB]: 3454
% 11.49/3.06 % (13492)Time elapsed: 0.077 s
% 11.49/3.06 % (13492)Instructions burned: 260 (million)
% 11.49/3.06 % (13492)------------------------------
% 11.49/3.06 % (13492)------------------------------
% 11.49/3.06 % (13495)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_12937 for (2987ds/373Mi)
% 11.49/3.07 % (13496)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_12937 for (2987ds/253Mi)
% 12.02/3.14 % (13496)Instruction limit reached!
% 12.02/3.14 % (13496)------------------------------
% 12.02/3.14 % (13496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.14 % (13496)Termination reason: Unknown
% 12.02/3.14 % (13496)Termination phase: Property scanning
% 12.02/3.14
% 12.02/3.14 % (13496)Memory used [KB]: 3198
% 12.02/3.14 % (13496)Time elapsed: 0.068 s
% 12.02/3.14 % (13496)Instructions burned: 256 (million)
% 12.02/3.14 % (13496)------------------------------
% 12.02/3.14 % (13496)------------------------------
% 12.02/3.15 % (13497)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_12937 for (2987ds/832Mi)
% 12.02/3.17 % (13495)Instruction limit reached!
% 12.02/3.17 % (13495)------------------------------
% 12.02/3.17 % (13495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.17 % (13495)Termination reason: Unknown
% 12.02/3.17 % (13495)Termination phase: Property scanning
% 12.02/3.17
% 12.02/3.17 % (13495)Memory used [KB]: 4093
% 12.02/3.17 % (13495)Time elapsed: 0.106 s
% 12.02/3.17 % (13495)Instructions burned: 377 (million)
% 12.02/3.17 % (13495)------------------------------
% 12.02/3.17 % (13495)------------------------------
% 12.02/3.18 % (13498)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_12937 for (2986ds/668Mi)
% 12.02/3.19 % (13483)Instruction limit reached!
% 12.02/3.19 % (13483)------------------------------
% 12.02/3.19 % (13483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.19 % (13483)Termination reason: Unknown
% 12.02/3.19 % (13483)Termination phase: Saturation
% 12.02/3.19
% 12.02/3.19 % (13483)Memory used [KB]: 11769
% 12.02/3.19 % (13483)Time elapsed: 0.444 s
% 12.02/3.19 % (13483)Instructions burned: 1542 (million)
% 12.02/3.19 % (13483)------------------------------
% 12.02/3.19 % (13483)------------------------------
% 12.55/3.20 % (13499)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_12937 for (2986ds/40Mi)
% 12.55/3.21 % (13499)Instruction limit reached!
% 12.55/3.21 % (13499)------------------------------
% 12.55/3.21 % (13499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.55/3.21 % (13499)Termination reason: Unknown
% 12.55/3.21 % (13499)Termination phase: shuffling
% 12.55/3.21
% 12.55/3.21 % (13499)Memory used [KB]: 2046
% 12.55/3.21 % (13499)Time elapsed: 0.013 s
% 12.55/3.21 % (13499)Instructions burned: 42 (million)
% 12.55/3.21 % (13499)------------------------------
% 12.55/3.21 % (13499)------------------------------
% 12.55/3.22 % (13500)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_12937 for (2986ds/294Mi)
% 12.55/3.28 % (13500)Refutation not found, incomplete strategy
% 12.55/3.28 % (13500)------------------------------
% 12.55/3.28 % (13500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.55/3.28 % (13500)Termination reason: Refutation not found, incomplete strategy
% 12.55/3.28
% 12.55/3.28
% 12.55/3.28 % (13500)Memory used [KB]: 7419
% 12.55/3.28 % (13500)Time elapsed: 0.054 s
% 12.55/3.28 % (13500)Instructions burned: 210 (million)
% 12.55/3.28 % (13500)------------------------------
% 12.55/3.28 % (13500)------------------------------
% 12.55/3.29 % (13501)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_12937 for (2985ds/187Mi)
% 12.94/3.32 % (13494)Instruction limit reached!
% 12.94/3.32 % (13494)------------------------------
% 12.94/3.32 % (13494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.32 % (13494)Termination reason: Unknown
% 12.94/3.32 % (13494)Termination phase: Saturation
% 12.94/3.32
% 12.94/3.32 % (13494)Memory used [KB]: 9594
% 12.94/3.32 % (13494)Time elapsed: 0.264 s
% 12.94/3.32 % (13494)Instructions burned: 995 (million)
% 12.94/3.32 % (13494)------------------------------
% 12.94/3.32 % (13494)------------------------------
% 12.94/3.33 % (13502)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_12937 for (2985ds/371Mi)
% 12.94/3.35 % (13501)Instruction limit reached!
% 12.94/3.35 % (13501)------------------------------
% 12.94/3.35 % (13501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.35 % (13501)Termination reason: Unknown
% 12.94/3.35 % (13501)Termination phase: Property scanning
% 12.94/3.35
% 12.94/3.35 % (13501)Memory used [KB]: 3326
% 12.94/3.35 % (13501)Time elapsed: 0.059 s
% 12.94/3.35 % (13501)Instructions burned: 190 (million)
% 12.94/3.35 % (13501)------------------------------
% 12.94/3.35 % (13501)------------------------------
% 12.94/3.35 % (13498)Instruction limit reached!
% 12.94/3.35 % (13498)------------------------------
% 12.94/3.35 % (13498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.35 % (13498)Termination reason: Unknown
% 12.94/3.35 % (13498)Termination phase: Saturation
% 12.94/3.35
% 12.94/3.35 % (13498)Memory used [KB]: 13560
% 12.94/3.35 % (13498)Time elapsed: 0.176 s
% 12.94/3.35 % (13498)Instructions burned: 668 (million)
% 12.94/3.35 % (13498)------------------------------
% 12.94/3.35 % (13498)------------------------------
% 12.94/3.35 % (13503)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_12937 for (2984ds/1827Mi)
% 12.94/3.36 % (13504)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_12937 for (2984ds/70Mi)
% 12.94/3.37 % (13497)Instruction limit reached!
% 12.94/3.37 % (13497)------------------------------
% 12.94/3.37 % (13497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.37 % (13497)Termination reason: Unknown
% 12.94/3.37 % (13497)Termination phase: Saturation
% 12.94/3.37
% 12.94/3.37 % (13497)Memory used [KB]: 11769
% 12.94/3.37 % (13497)Time elapsed: 0.227 s
% 12.94/3.37 % (13497)Instructions burned: 835 (million)
% 12.94/3.37 % (13497)------------------------------
% 12.94/3.37 % (13497)------------------------------
% 12.94/3.38 % (13504)Instruction limit reached!
% 12.94/3.38 % (13504)------------------------------
% 12.94/3.38 % (13504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.38 % (13504)Termination reason: Unknown
% 12.94/3.38 % (13504)Termination phase: shuffling
% 12.94/3.38
% 12.94/3.38 % (13504)Memory used [KB]: 2430
% 12.94/3.38 % (13504)Time elapsed: 0.021 s
% 12.94/3.38 % (13504)Instructions burned: 73 (million)
% 12.94/3.38 % (13504)------------------------------
% 12.94/3.38 % (13504)------------------------------
% 12.94/3.38 % (13505)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_12937 for (2984ds/316Mi)
% 14.05/3.40 % (13506)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_12937 for (2984ds/932Mi)
% 14.05/3.42 % (13486)Instruction limit reached!
% 14.05/3.42 % (13486)------------------------------
% 14.05/3.42 % (13486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.42 % (13486)Termination reason: Unknown
% 14.05/3.42 % (13486)Termination phase: Saturation
% 14.05/3.42
% 14.05/3.42 % (13486)Memory used [KB]: 5245
% 14.05/3.42 % (13486)Time elapsed: 0.572 s
% 14.05/3.42 % (13486)Instructions burned: 1915 (million)
% 14.05/3.42 % (13486)------------------------------
% 14.05/3.42 % (13486)------------------------------
% 14.05/3.43 % (13507)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_12937 for (2984ds/4714Mi)
% 14.05/3.43 % (13502)Instruction limit reached!
% 14.05/3.43 % (13502)------------------------------
% 14.05/3.43 % (13502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.43 % (13502)Termination reason: Unknown
% 14.05/3.43 % (13502)Termination phase: Saturation
% 14.05/3.43
% 14.05/3.43 % (13502)Memory used [KB]: 8827
% 14.05/3.43 % (13502)Time elapsed: 0.109 s
% 14.05/3.43 % (13502)Instructions burned: 373 (million)
% 14.05/3.43 % (13502)------------------------------
% 14.05/3.43 % (13502)------------------------------
% 14.05/3.44 % (13508)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_12937 for (2984ds/8250Mi)
% 14.05/3.46 % (13505)Instruction limit reached!
% 14.05/3.46 % (13505)------------------------------
% 14.05/3.46 % (13505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.46 % (13505)Termination reason: Unknown
% 14.05/3.46 % (13505)Termination phase: Function definition elimination
% 14.05/3.46
% 14.05/3.46 % (13505)Memory used [KB]: 3198
% 14.05/3.46 % (13505)Time elapsed: 0.083 s
% 14.05/3.46 % (13505)Instructions burned: 319 (million)
% 14.05/3.46 % (13505)------------------------------
% 14.05/3.46 % (13505)------------------------------
% 14.05/3.47 % (13509)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_12937 for (2983ds/770Mi)
% 14.48/3.55 % (13509)Refutation not found, incomplete strategy
% 14.48/3.55 % (13509)------------------------------
% 14.48/3.55 % (13509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.48/3.55 % (13509)Termination reason: Refutation not found, incomplete strategy
% 14.48/3.55
% 14.48/3.55
% 14.48/3.55 % (13509)Memory used [KB]: 7803
% 14.48/3.55 % (13509)Time elapsed: 0.074 s
% 14.48/3.55 % (13509)Instructions burned: 252 (million)
% 14.48/3.55 % (13509)------------------------------
% 14.48/3.55 % (13509)------------------------------
% 14.48/3.56 % (13510)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_12937 for (2982ds/794Mi)
% 14.77/3.60 % (13507)Refutation not found, incomplete strategy
% 14.77/3.60 % (13507)------------------------------
% 14.77/3.60 % (13507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.77/3.60 % (13507)Termination reason: Refutation not found, incomplete strategy
% 14.77/3.60
% 14.77/3.60
% 14.77/3.60 % (13507)Memory used [KB]: 9083
% 14.77/3.60 % (13507)Time elapsed: 0.172 s
% 14.77/3.60 % (13507)Instructions burned: 666 (million)
% 14.77/3.60 % (13507)------------------------------
% 14.77/3.60 % (13507)------------------------------
% 14.77/3.61 % (13511)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_12937 for (2982ds/464Mi)
% 14.77/3.68 % (13506)Instruction limit reached!
% 14.77/3.68 % (13506)------------------------------
% 14.77/3.68 % (13506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.77/3.68 % (13506)Termination reason: Unknown
% 14.77/3.68 % (13506)Termination phase: Saturation
% 14.77/3.68
% 14.77/3.68 % (13506)Memory used [KB]: 9083
% 14.77/3.68 % (13506)Time elapsed: 0.278 s
% 14.77/3.68 % (13506)Instructions burned: 935 (million)
% 14.77/3.68 % (13506)------------------------------
% 14.77/3.68 % (13506)------------------------------
% 14.77/3.69 % (13512)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_12937 for (2981ds/1376Mi)
% 15.44/3.73 % (13511)Instruction limit reached!
% 15.44/3.73 % (13511)------------------------------
% 15.44/3.73 % (13511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.44/3.73 % (13511)Termination reason: Unknown
% 15.44/3.73 % (13511)Termination phase: Property scanning
% 15.44/3.73
% 15.44/3.73 % (13511)Memory used [KB]: 3965
% 15.44/3.73 % (13511)Time elapsed: 0.126 s
% 15.44/3.73 % (13511)Instructions burned: 468 (million)
% 15.44/3.73 % (13511)------------------------------
% 15.44/3.73 % (13511)------------------------------
% 15.44/3.74 % (13513)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_12937 for (2981ds/906Mi)
% 15.44/3.77 % (13510)Instruction limit reached!
% 15.44/3.77 % (13510)------------------------------
% 15.44/3.77 % (13510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.44/3.77 % (13510)Termination reason: Unknown
% 15.44/3.77 % (13510)Termination phase: Saturation
% 15.44/3.77
% 15.44/3.77 % (13510)Memory used [KB]: 5628
% 15.44/3.77 % (13510)Time elapsed: 0.216 s
% 15.44/3.77 % (13510)Instructions burned: 794 (million)
% 15.44/3.77 % (13510)------------------------------
% 15.44/3.77 % (13510)------------------------------
% 15.44/3.78 % (13514)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_12937 for (2980ds/434Mi)
% 16.22/3.90 % (13503)Instruction limit reached!
% 16.22/3.90 % (13503)------------------------------
% 16.22/3.90 % (13503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.22/3.90 % (13503)Termination reason: Unknown
% 16.22/3.90 % (13503)Termination phase: Saturation
% 16.22/3.90
% 16.22/3.90 % (13503)Memory used [KB]: 12153
% 16.22/3.90 % (13503)Time elapsed: 0.551 s
% 16.22/3.90 % (13503)Instructions burned: 1827 (million)
% 16.22/3.90 % (13503)------------------------------
% 16.22/3.90 % (13503)------------------------------
% 16.22/3.91 % (13514)Instruction limit reached!
% 16.22/3.91 % (13514)------------------------------
% 16.22/3.91 % (13514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.22/3.91 % (13514)Termination reason: Unknown
% 16.22/3.91 % (13514)Termination phase: Saturation
% 16.22/3.91
% 16.22/3.91 % (13514)Memory used [KB]: 8699
% 16.22/3.91 % (13514)Time elapsed: 0.130 s
% 16.22/3.91 % (13514)Instructions burned: 434 (million)
% 16.22/3.91 % (13514)------------------------------
% 16.22/3.91 % (13514)------------------------------
% 16.22/3.91 % (13515)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_12937 for (2979ds/865Mi)
% 16.22/3.92 % (13516)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_12937 for (2979ds/593Mi)
% 16.22/4.00 % (13482)Instruction limit reached!
% 16.22/4.00 % (13482)------------------------------
% 16.22/4.00 % (13482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.22/4.00 % (13482)Termination reason: Unknown
% 16.22/4.00 % (13482)Termination phase: Saturation
% 16.22/4.00
% 16.22/4.00 % (13482)Memory used [KB]: 9338
% 16.22/4.00 % (13482)Time elapsed: 1.280 s
% 16.22/4.00 % (13482)Instructions burned: 4438 (million)
% 16.22/4.00 % (13482)------------------------------
% 16.22/4.00 % (13482)------------------------------
% 18.48/4.01 % (13517)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_12937 for (2978ds/443Mi)
% 18.48/4.02 % (13513)Instruction limit reached!
% 18.48/4.02 % (13513)------------------------------
% 18.48/4.02 % (13513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.48/4.02 % (13513)Termination reason: Unknown
% 18.48/4.02 % (13513)Termination phase: Saturation
% 18.48/4.02
% 18.48/4.02 % (13513)Memory used [KB]: 13560
% 18.48/4.02 % (13513)Time elapsed: 0.277 s
% 18.48/4.02 % (13513)Instructions burned: 908 (million)
% 18.48/4.02 % (13513)------------------------------
% 18.48/4.02 % (13513)------------------------------
% 18.48/4.03 % (13518)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_12937 for (2978ds/594Mi)
% 18.48/4.07 % (13516)Instruction limit reached!
% 18.48/4.07 % (13516)------------------------------
% 18.48/4.07 % (13516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.48/4.07 % (13516)Termination reason: Unknown
% 18.48/4.07 % (13516)Termination phase: Saturation
% 18.48/4.07
% 18.48/4.07 % (13516)Memory used [KB]: 8699
% 18.48/4.07 % (13516)Time elapsed: 0.153 s
% 18.48/4.07 % (13516)Instructions burned: 594 (million)
% 18.48/4.07 % (13516)------------------------------
% 18.48/4.07 % (13516)------------------------------
% 18.48/4.08 % (13519)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_12937 for (2977ds/327Mi)
% 18.98/4.13 % (13517)Instruction limit reached!
% 18.98/4.13 % (13517)------------------------------
% 18.98/4.13 % (13517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.98/4.13 % (13517)Termination reason: Unknown
% 18.98/4.13 % (13517)Termination phase: Property scanning
% 18.98/4.13
% 18.98/4.13 % (13517)Memory used [KB]: 3837
% 18.98/4.13 % (13517)Time elapsed: 0.123 s
% 18.98/4.13 % (13517)Instructions burned: 445 (million)
% 18.98/4.13 % (13517)------------------------------
% 18.98/4.13 % (13517)------------------------------
% 18.98/4.14 % (13512)Instruction limit reached!
% 18.98/4.14 % (13512)------------------------------
% 18.98/4.14 % (13512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.98/4.14 % (13512)Termination reason: Unknown
% 18.98/4.14 % (13512)Termination phase: Saturation
% 18.98/4.14
% 18.98/4.14 % (13512)Memory used [KB]: 13304
% 18.98/4.14 % (13512)Time elapsed: 0.456 s
% 18.98/4.14 % (13512)Instructions burned: 1376 (million)
% 18.98/4.14 % (13512)------------------------------
% 18.98/4.14 % (13512)------------------------------
% 18.98/4.14 % (13520)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_12937 for (2977ds/5411Mi)
% 18.98/4.15 % (13515)Instruction limit reached!
% 18.98/4.15 % (13515)------------------------------
% 18.98/4.15 % (13515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.98/4.15 % (13515)Termination reason: Unknown
% 18.98/4.15 % (13515)Termination phase: Saturation
% 18.98/4.15
% 18.98/4.15 % (13515)Memory used [KB]: 9338
% 18.98/4.15 % (13515)Time elapsed: 0.237 s
% 18.98/4.15 % (13515)Instructions burned: 865 (million)
% 18.98/4.15 % (13515)------------------------------
% 18.98/4.15 % (13515)------------------------------
% 18.98/4.15 % (13521)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_12937 for (2976ds/1762Mi)
% 18.98/4.16 % (13522)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_12937 for (2976ds/96Mi)
% 18.98/4.18 % (13519)Instruction limit reached!
% 18.98/4.18 % (13519)------------------------------
% 18.98/4.18 % (13519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.98/4.18 % (13519)Termination reason: Unknown
% 18.98/4.18 % (13519)Termination phase: Property scanning
% 18.98/4.18
% 18.98/4.18 % (13519)Memory used [KB]: 3965
% 18.98/4.18 % (13519)Time elapsed: 0.099 s
% 18.98/4.18 % (13519)Instructions burned: 329 (million)
% 18.98/4.18 % (13519)------------------------------
% 18.98/4.18 % (13519)------------------------------
% 18.98/4.19 % (13522)Instruction limit reached!
% 18.98/4.19 % (13522)------------------------------
% 18.98/4.19 % (13522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.98/4.19 % (13522)Termination reason: Unknown
% 18.98/4.19 % (13522)Termination phase: shuffling
% 18.98/4.19
% 18.98/4.19 % (13522)Memory used [KB]: 2686
% 18.98/4.19 % (13522)Time elapsed: 0.028 s
% 18.98/4.19 % (13522)Instructions burned: 97 (million)
% 18.98/4.19 % (13522)------------------------------
% 18.98/4.19 % (13522)------------------------------
% 18.98/4.19 % (13523)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_12937 for (2976ds/503Mi)
% 19.51/4.20 % (13524)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_12937 for (2976ds/90Mi)
% 19.51/4.20 % (13518)Instruction limit reached!
% 19.51/4.20 % (13518)------------------------------
% 19.51/4.20 % (13518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.51/4.20 % (13518)Termination reason: Unknown
% 19.51/4.20 % (13518)Termination phase: Saturation
% 19.51/4.20
% 19.51/4.20 % (13518)Memory used [KB]: 8571
% 19.51/4.20 % (13518)Time elapsed: 0.171 s
% 19.51/4.20 % (13518)Instructions burned: 594 (million)
% 19.51/4.20 % (13518)------------------------------
% 19.51/4.20 % (13518)------------------------------
% 19.51/4.21 % (13525)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_12937 for (2976ds/593Mi)
% 19.51/4.22 % (13520)Refutation not found, incomplete strategy
% 19.51/4.22 % (13520)------------------------------
% 19.51/4.22 % (13520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.51/4.22 % (13520)Termination reason: Refutation not found, incomplete strategy
% 19.51/4.22
% 19.51/4.22
% 19.51/4.22 % (13520)Memory used [KB]: 7931
% 19.51/4.22 % (13520)Time elapsed: 0.080 s
% 19.51/4.22 % (13520)Instructions burned: 263 (million)
% 19.51/4.22 % (13520)------------------------------
% 19.51/4.22 % (13520)------------------------------
% 19.51/4.23 % (13524)Instruction limit reached!
% 19.51/4.23 % (13524)------------------------------
% 19.51/4.23 % (13524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.51/4.23 % (13524)Termination reason: Unknown
% 19.51/4.23 % (13524)Termination phase: shuffling
% 19.51/4.23
% 19.51/4.23 % (13524)Memory used [KB]: 2558
% 19.51/4.23 % (13524)Time elapsed: 0.030 s
% 19.51/4.23 % (13524)Instructions burned: 92 (million)
% 19.51/4.23 % (13524)------------------------------
% 19.51/4.23 % (13524)------------------------------
% 19.51/4.23 % (13526)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_12937 for (2976ds/1512Mi)
% 19.51/4.24 % (13527)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_12937 for (2976ds/569Mi)
% 20.03/4.34 % (13523)Instruction limit reached!
% 20.03/4.34 % (13523)------------------------------
% 20.03/4.34 % (13523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.34 % (13523)Termination reason: Unknown
% 20.03/4.34 % (13523)Termination phase: Saturation
% 20.03/4.34
% 20.03/4.34 % (13523)Memory used [KB]: 8699
% 20.03/4.34 % (13523)Time elapsed: 0.147 s
% 20.03/4.34 % (13523)Instructions burned: 503 (million)
% 20.03/4.34 % (13523)------------------------------
% 20.03/4.34 % (13523)------------------------------
% 20.03/4.35 % (13528)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_12937 for (2975ds/501Mi)
% 20.03/4.37 % (13525)Instruction limit reached!
% 20.03/4.37 % (13525)------------------------------
% 20.03/4.37 % (13525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.37 % (13525)Termination reason: Unknown
% 20.03/4.37 % (13525)Termination phase: Saturation
% 20.03/4.37
% 20.03/4.37 % (13525)Memory used [KB]: 8827
% 20.03/4.37 % (13525)Time elapsed: 0.162 s
% 20.03/4.37 % (13525)Instructions burned: 595 (million)
% 20.03/4.37 % (13525)------------------------------
% 20.03/4.37 % (13525)------------------------------
% 20.03/4.38 % (13529)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_12937 for (2974ds/562Mi)
% 20.03/4.38 % (13527)Instruction limit reached!
% 20.03/4.38 % (13527)------------------------------
% 20.03/4.38 % (13527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.38 % (13527)Termination reason: Unknown
% 20.03/4.38 % (13527)Termination phase: Saturation
% 20.03/4.38
% 20.03/4.38 % (13527)Memory used [KB]: 8571
% 20.03/4.38 % (13527)Time elapsed: 0.149 s
% 20.03/4.38 % (13527)Instructions burned: 569 (million)
% 20.03/4.38 % (13527)------------------------------
% 20.03/4.38 % (13527)------------------------------
% 20.03/4.39 % (13485)Instruction limit reached!
% 20.03/4.39 % (13485)------------------------------
% 20.03/4.39 % (13485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.39 % (13485)Termination reason: Unknown
% 20.03/4.39 % (13485)Termination phase: Saturation
% 20.03/4.39
% 20.03/4.39 % (13485)Memory used [KB]: 20340
% 20.03/4.39 % (13485)Time elapsed: 1.620 s
% 20.03/4.39 % (13485)Instructions burned: 5205 (million)
% 20.03/4.39 % (13485)------------------------------
% 20.03/4.39 % (13485)------------------------------
% 20.03/4.39 % (13530)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12937 for (2974ds/406Mi)
% 20.73/4.40 % (13531)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_12937 for (2974ds/582Mi)
% 20.73/4.48 % (13528)Instruction limit reached!
% 20.73/4.48 % (13528)------------------------------
% 20.73/4.48 % (13528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.73/4.48 % (13528)Termination reason: Unknown
% 20.73/4.48 % (13528)Termination phase: Property scanning
% 20.73/4.48
% 20.73/4.48 % (13528)Memory used [KB]: 4221
% 20.73/4.48 % (13528)Time elapsed: 0.135 s
% 20.73/4.48 % (13528)Instructions burned: 501 (million)
% 20.73/4.48 % (13528)------------------------------
% 20.73/4.48 % (13528)------------------------------
% 20.73/4.49 % (13532)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_12937 for (2973ds/456Mi)
% 20.96/4.50 % (13530)Instruction limit reached!
% 20.96/4.50 % (13530)------------------------------
% 20.96/4.50 % (13530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.96/4.50 % (13530)Termination reason: Unknown
% 20.96/4.50 % (13530)Termination phase: Property scanning
% 20.96/4.50
% 20.96/4.50 % (13530)Memory used [KB]: 3965
% 20.96/4.50 % (13530)Time elapsed: 0.113 s
% 20.96/4.50 % (13530)Instructions burned: 409 (million)
% 20.96/4.50 % (13530)------------------------------
% 20.96/4.50 % (13530)------------------------------
% 20.96/4.51 % (13533)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_12937 for (2973ds/393Mi)
% 20.96/4.53 % (13529)Instruction limit reached!
% 20.96/4.53 % (13529)------------------------------
% 20.96/4.53 % (13529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.96/4.53 % (13529)Termination reason: Unknown
% 20.96/4.53 % (13529)Termination phase: Saturation
% 20.96/4.53
% 20.96/4.53 % (13529)Memory used [KB]: 9083
% 20.96/4.53 % (13529)Time elapsed: 0.152 s
% 20.96/4.53 % (13529)Instructions burned: 562 (million)
% 20.96/4.53 % (13529)------------------------------
% 20.96/4.53 % (13529)------------------------------
% 20.96/4.54 % (13534)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_12937 for (2973ds/1335Mi)
% 20.96/4.56 % (13531)Instruction limit reached!
% 20.96/4.56 % (13531)------------------------------
% 20.96/4.56 % (13531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.96/4.56 % (13531)Termination reason: Unknown
% 20.96/4.56 % (13531)Termination phase: Saturation
% 20.96/4.56
% 20.96/4.56 % (13531)Memory used [KB]: 8955
% 20.96/4.56 % (13531)Time elapsed: 0.158 s
% 20.96/4.56 % (13531)Instructions burned: 584 (million)
% 20.96/4.56 % (13531)------------------------------
% 20.96/4.56 % (13531)------------------------------
% 20.96/4.57 % (13535)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_12937 for (2972ds/3373Mi)
% 21.51/4.62 % (13533)Instruction limit reached!
% 21.51/4.62 % (13533)------------------------------
% 21.51/4.62 % (13533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.51/4.62 % (13533)Termination reason: Unknown
% 21.51/4.62 % (13533)Termination phase: Saturation
% 21.51/4.62
% 21.51/4.62 % (13533)Memory used [KB]: 7675
% 21.51/4.62 % (13533)Time elapsed: 0.103 s
% 21.51/4.62 % (13533)Instructions burned: 396 (million)
% 21.51/4.62 % (13533)------------------------------
% 21.51/4.62 % (13533)------------------------------
% 21.51/4.62 % (13532)Instruction limit reached!
% 21.51/4.62 % (13532)------------------------------
% 21.51/4.62 % (13532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.51/4.62 % (13532)Termination reason: Unknown
% 21.51/4.62 % (13532)Termination phase: Saturation
% 21.51/4.62
% 21.51/4.62 % (13532)Memory used [KB]: 4605
% 21.51/4.62 % (13532)Time elapsed: 0.129 s
% 21.51/4.62 % (13532)Instructions burned: 458 (million)
% 21.51/4.62 % (13532)------------------------------
% 21.51/4.62 % (13532)------------------------------
% 21.51/4.63 % (13536)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_12937 for (2972ds/474Mi)
% 21.51/4.63 % (13537)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_12937 for (2972ds/157Mi)
% 21.51/4.65 % (13526)Instruction limit reached!
% 21.51/4.65 % (13526)------------------------------
% 21.51/4.65 % (13526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.51/4.65 % (13526)Termination reason: Unknown
% 21.51/4.65 % (13526)Termination phase: Saturation
% 21.51/4.65
% 21.51/4.65 % (13526)Memory used [KB]: 11769
% 21.51/4.65 % (13526)Time elapsed: 0.420 s
% 21.51/4.65 % (13526)Instructions burned: 1512 (million)
% 21.51/4.65 % (13526)------------------------------
% 21.51/4.65 % (13526)------------------------------
% 21.51/4.66 % (13521)Instruction limit reached!
% 21.51/4.66 % (13521)------------------------------
% 21.51/4.66 % (13521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.51/4.66 % (13521)Termination reason: Unknown
% 21.51/4.66 % (13521)Termination phase: Saturation
% 21.51/4.66
% 21.51/4.66 % (13521)Memory used [KB]: 12792
% 21.51/4.66 % (13521)Time elapsed: 0.505 s
% 21.51/4.66 % (13521)Instructions burned: 1762 (million)
% 21.51/4.66 % (13521)------------------------------
% 21.51/4.66 % (13521)------------------------------
% 21.51/4.66 % (13538)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_12937 for (2971ds/590Mi)
% 21.51/4.67 % (13539)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_12937 for (2971ds/104Mi)
% 21.51/4.67 % (13537)Instruction limit reached!
% 21.51/4.67 % (13537)------------------------------
% 21.51/4.67 % (13537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.51/4.67 % (13537)Termination reason: Unknown
% 21.51/4.67 % (13537)Termination phase: Property scanning
% 21.51/4.67
% 21.51/4.67 % (13537)Memory used [KB]: 2814
% 21.51/4.67 % (13537)Time elapsed: 0.042 s
% 21.51/4.67 % (13537)Instructions burned: 160 (million)
% 21.51/4.67 % (13537)------------------------------
% 21.51/4.67 % (13537)------------------------------
% 21.51/4.68 % (13540)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_12937 for (2971ds/414Mi)
% 22.86/4.70 % (13539)Instruction limit reached!
% 22.86/4.70 % (13539)------------------------------
% 22.86/4.70 % (13539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.86/4.70 % (13539)Termination reason: Unknown
% 22.86/4.70 % (13539)Termination phase: shuffling
% 22.86/4.70
% 22.86/4.70 % (13539)Memory used [KB]: 2558
% 22.86/4.70 % (13539)Time elapsed: 0.033 s
% 22.86/4.70 % (13539)Instructions burned: 104 (million)
% 22.86/4.70 % (13539)------------------------------
% 22.86/4.70 % (13539)------------------------------
% 22.86/4.71 % (13541)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_12937 for (2971ds/715Mi)
% 22.86/4.75 % (13536)Instruction limit reached!
% 22.86/4.75 % (13536)------------------------------
% 22.86/4.75 % (13536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.86/4.75 % (13536)Termination reason: Unknown
% 22.86/4.75 % (13536)Termination phase: Saturation
% 22.86/4.75
% 22.86/4.75 % (13536)Memory used [KB]: 7931
% 22.86/4.75 % (13536)Time elapsed: 0.124 s
% 22.86/4.75 % (13536)Instructions burned: 475 (million)
% 22.86/4.75 % (13536)------------------------------
% 22.86/4.75 % (13536)------------------------------
% 22.86/4.76 % (13542)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_12937 for (2970ds/961Mi)
% 22.86/4.78 % (13540)Instruction limit reached!
% 22.86/4.78 % (13540)------------------------------
% 22.86/4.78 % (13540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.86/4.78 % (13540)Termination reason: Unknown
% 22.86/4.78 % (13540)Termination phase: Saturation
% 22.86/4.78
% 22.86/4.78 % (13540)Memory used [KB]: 7675
% 22.86/4.78 % (13540)Time elapsed: 0.106 s
% 22.86/4.78 % (13540)Instructions burned: 417 (million)
% 22.86/4.78 % (13540)------------------------------
% 22.86/4.78 % (13540)------------------------------
% 22.86/4.79 % (13543)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_12937 for (2970ds/1213Mi)
% 23.25/4.82 % (13538)Instruction limit reached!
% 23.25/4.82 % (13538)------------------------------
% 23.25/4.82 % (13538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.25/4.82 % (13538)Termination reason: Unknown
% 23.25/4.82 % (13538)Termination phase: Saturation
% 23.25/4.82
% 23.25/4.82 % (13538)Memory used [KB]: 8571
% 23.25/4.82 % (13538)Time elapsed: 0.157 s
% 23.25/4.82 % (13538)Instructions burned: 593 (million)
% 23.25/4.82 % (13538)------------------------------
% 23.25/4.82 % (13538)------------------------------
% 23.25/4.83 % (13544)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_12937 for (2970ds/1979Mi)
% 23.25/4.89 % (13534)Instruction limit reached!
% 23.25/4.89 % (13534)------------------------------
% 23.25/4.89 % (13534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.25/4.89 % (13534)Termination reason: Unknown
% 23.25/4.89 % (13534)Termination phase: Saturation
% 23.25/4.89
% 23.25/4.89 % (13534)Memory used [KB]: 9466
% 23.25/4.89 % (13534)Time elapsed: 0.353 s
% 23.25/4.89 % (13534)Instructions burned: 1336 (million)
% 23.25/4.89 % (13534)------------------------------
% 23.25/4.89 % (13534)------------------------------
% 23.88/4.90 % (13545)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_12937 for (2969ds/481Mi)
% 23.88/4.91 % (13541)Instruction limit reached!
% 23.88/4.91 % (13541)------------------------------
% 23.88/4.91 % (13541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.88/4.91 % (13541)Termination reason: Unknown
% 23.88/4.91 % (13541)Termination phase: Saturation
% 23.88/4.91
% 23.88/4.91 % (13541)Memory used [KB]: 4861
% 23.88/4.91 % (13541)Time elapsed: 0.199 s
% 23.88/4.91 % (13541)Instructions burned: 715 (million)
% 23.88/4.91 % (13541)------------------------------
% 23.88/4.91 % (13541)------------------------------
% 23.88/4.92 % (13546)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_12937 for (2969ds/783Mi)
% 25.57/5.02 % (13542)Instruction limit reached!
% 25.57/5.02 % (13542)------------------------------
% 25.57/5.02 % (13542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.57/5.02 % (13542)Termination reason: Unknown
% 25.57/5.02 % (13542)Termination phase: Saturation
% 25.57/5.02
% 25.57/5.02 % (13542)Memory used [KB]: 9594
% 25.57/5.02 % (13542)Time elapsed: 0.267 s
% 25.57/5.02 % (13542)Instructions burned: 963 (million)
% 25.57/5.02 % (13542)------------------------------
% 25.57/5.02 % (13542)------------------------------
% 25.57/5.03 % (13545)Instruction limit reached!
% 25.57/5.03 % (13545)------------------------------
% 25.57/5.03 % (13545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.57/5.03 % (13545)Termination reason: Unknown
% 25.57/5.03 % (13545)Termination phase: Saturation
% 25.57/5.03
% 25.57/5.03 % (13545)Memory used [KB]: 8059
% 25.57/5.03 % (13545)Time elapsed: 0.126 s
% 25.57/5.03 % (13545)Instructions burned: 481 (million)
% 25.57/5.03 % (13545)------------------------------
% 25.57/5.03 % (13545)------------------------------
% 25.57/5.03 % (13547)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_12937 for (2968ds/432Mi)
% 25.57/5.03 % (13548)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_12937 for (2968ds/1670Mi)
% 25.57/5.11 % (13547)Refutation not found, incomplete strategy
% 25.57/5.11 % (13547)------------------------------
% 25.57/5.11 % (13547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.57/5.11 % (13547)Termination reason: Refutation not found, incomplete strategy
% 25.57/5.11
% 25.57/5.11
% 25.57/5.11 % (13547)Memory used [KB]: 7803
% 25.57/5.11 % (13547)Time elapsed: 0.073 s
% 25.57/5.11 % (13547)Instructions burned: 247 (million)
% 25.57/5.11 % (13547)------------------------------
% 25.57/5.11 % (13547)------------------------------
% 25.57/5.12 % (13549)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_12937 for (2967ds/90Mi)
% 26.20/5.13 % (13543)Instruction limit reached!
% 26.20/5.13 % (13543)------------------------------
% 26.20/5.13 % (13543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.20/5.13 % (13543)Termination reason: Unknown
% 26.20/5.13 % (13543)Termination phase: Saturation
% 26.20/5.13
% 26.20/5.13 % (13543)Memory used [KB]: 11513
% 26.20/5.13 % (13543)Time elapsed: 0.335 s
% 26.20/5.13 % (13543)Instructions burned: 1213 (million)
% 26.20/5.13 % (13543)------------------------------
% 26.20/5.13 % (13543)------------------------------
% 26.20/5.14 % (13550)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_12937 for (2967ds/346Mi)
% 26.20/5.14 % (13549)Instruction limit reached!
% 26.20/5.14 % (13549)------------------------------
% 26.20/5.14 % (13549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.20/5.14 % (13549)Termination reason: Unknown
% 26.20/5.14 % (13549)Termination phase: shuffling
% 26.20/5.14
% 26.20/5.14 % (13549)Memory used [KB]: 2302
% 26.20/5.14 % (13549)Time elapsed: 0.029 s
% 26.20/5.14 % (13549)Instructions burned: 93 (million)
% 26.20/5.14 % (13549)------------------------------
% 26.20/5.14 % (13549)------------------------------
% 26.20/5.15 % (13546)Instruction limit reached!
% 26.20/5.15 % (13546)------------------------------
% 26.20/5.15 % (13546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.20/5.15 % (13546)Termination reason: Unknown
% 26.20/5.15 % (13546)Termination phase: Saturation
% 26.20/5.15
% 26.20/5.15 % (13546)Memory used [KB]: 9594
% 26.20/5.15 % (13546)Time elapsed: 0.233 s
% 26.20/5.15 % (13546)Instructions burned: 785 (million)
% 26.20/5.15 % (13546)------------------------------
% 26.20/5.15 % (13546)------------------------------
% 26.20/5.15 % (13551)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_12937 for (2966ds/401Mi)
% 26.20/5.16 % (13552)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_12937 for (2966ds/6454Mi)
% 26.53/5.23 % (13550)Instruction limit reached!
% 26.53/5.23 % (13550)------------------------------
% 26.53/5.23 % (13550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.53/5.23 % (13550)Termination reason: Unknown
% 26.53/5.23 % (13550)Termination phase: Property scanning
% 26.53/5.23
% 26.53/5.23 % (13550)Memory used [KB]: 3198
% 26.53/5.23 % (13550)Time elapsed: 0.092 s
% 26.53/5.23 % (13550)Instructions burned: 349 (million)
% 26.53/5.23 % (13550)------------------------------
% 26.53/5.23 % (13550)------------------------------
% 26.53/5.24 % (13553)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_12937 for (2966ds/283Mi)
% 26.53/5.24 % (13552)Refutation not found, incomplete strategy
% 26.53/5.24 % (13552)------------------------------
% 26.53/5.24 % (13552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.53/5.24 % (13552)Termination reason: Refutation not found, incomplete strategy
% 26.53/5.24
% 26.53/5.24
% 26.53/5.24 % (13552)Memory used [KB]: 7803
% 26.53/5.24 % (13552)Time elapsed: 0.082 s
% 26.53/5.24 % (13552)Instructions burned: 274 (million)
% 26.53/5.24 % (13552)------------------------------
% 26.53/5.24 % (13552)------------------------------
% 26.53/5.25 % (13554)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_12937 for (2965ds/865Mi)
% 26.53/5.26 % (13551)Instruction limit reached!
% 26.53/5.26 % (13551)------------------------------
% 26.53/5.26 % (13551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.53/5.26 % (13551)Termination reason: Unknown
% 26.53/5.26 % (13551)Termination phase: Saturation
% 26.53/5.26
% 26.53/5.26 % (13551)Memory used [KB]: 7675
% 26.53/5.26 % (13551)Time elapsed: 0.105 s
% 26.53/5.26 % (13551)Instructions burned: 403 (million)
% 26.53/5.26 % (13551)------------------------------
% 26.53/5.26 % (13551)------------------------------
% 26.53/5.27 % (13555)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_12937 for (2965ds/4528Mi)
% 27.12/5.32 % (13553)Instruction limit reached!
% 27.12/5.32 % (13553)------------------------------
% 27.12/5.32 % (13553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.12/5.32 % (13553)Termination reason: Unknown
% 27.12/5.32 % (13553)Termination phase: Property scanning
% 27.12/5.32
% 27.12/5.32 % (13553)Memory used [KB]: 3837
% 27.12/5.32 % (13553)Time elapsed: 0.084 s
% 27.12/5.32 % (13553)Instructions burned: 286 (million)
% 27.12/5.32 % (13553)------------------------------
% 27.12/5.32 % (13553)------------------------------
% 27.12/5.33 % (13556)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_12937 for (2965ds/1001Mi)
% 27.12/5.34 % (13555)Refutation not found, incomplete strategy
% 27.12/5.34 % (13555)------------------------------
% 27.12/5.34 % (13555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.12/5.34 % (13555)Termination reason: Refutation not found, incomplete strategy
% 27.12/5.34
% 27.12/5.34
% 27.12/5.34 % (13555)Memory used [KB]: 3326
% 27.12/5.34 % (13555)Time elapsed: 0.074 s
% 27.12/5.34 % (13555)Instructions burned: 251 (million)
% 27.12/5.34 % (13555)------------------------------
% 27.12/5.34 % (13555)------------------------------
% 27.12/5.35 % (13557)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_12937 for (2964ds/102Mi)
% 27.12/5.38 % (13557)Instruction limit reached!
% 27.12/5.38 % (13557)------------------------------
% 27.12/5.38 % (13557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.12/5.38 % (13557)Termination reason: Unknown
% 27.12/5.38 % (13557)Termination phase: Property scanning
% 27.12/5.38
% 27.12/5.38 % (13557)Memory used [KB]: 2814
% 27.12/5.38 % (13557)Time elapsed: 0.029 s
% 27.12/5.38 % (13557)Instructions burned: 105 (million)
% 27.12/5.38 % (13557)------------------------------
% 27.12/5.38 % (13557)------------------------------
% 27.12/5.39 % (13558)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_12937 for (2964ds/952Mi)
% 27.12/5.39 % (13544)Instruction limit reached!
% 27.12/5.39 % (13544)------------------------------
% 27.12/5.39 % (13544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.12/5.39 % (13544)Termination reason: Unknown
% 27.12/5.39 % (13544)Termination phase: Saturation
% 27.12/5.39
% 27.12/5.39 % (13544)Memory used [KB]: 11257
% 27.12/5.39 % (13544)Time elapsed: 0.567 s
% 27.12/5.39 % (13544)Instructions burned: 1980 (million)
% 27.12/5.39 % (13544)------------------------------
% 27.12/5.39 % (13544)------------------------------
% 27.64/5.40 % (13559)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_12937 for (2964ds/578Mi)
% 27.64/5.48 % (13554)Instruction limit reached!
% 27.64/5.48 % (13554)------------------------------
% 27.64/5.48 % (13554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.64/5.48 % (13554)Termination reason: Unknown
% 27.64/5.48 % (13554)Termination phase: Saturation
% 27.64/5.48
% 27.64/5.48 % (13554)Memory used [KB]: 11257
% 27.64/5.48 % (13554)Time elapsed: 0.234 s
% 27.64/5.48 % (13554)Instructions burned: 867 (million)
% 27.64/5.48 % (13554)------------------------------
% 27.64/5.48 % (13554)------------------------------
% 27.64/5.49 % (13548)Instruction limit reached!
% 27.64/5.49 % (13548)------------------------------
% 27.64/5.49 % (13548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.64/5.49 % (13548)Termination reason: Unknown
% 27.64/5.49 % (13548)Termination phase: Saturation
% 27.64/5.49
% 27.64/5.49 % (13548)Memory used [KB]: 10106
% 27.64/5.49 % (13548)Time elapsed: 0.452 s
% 27.64/5.49 % (13548)Instructions burned: 1673 (million)
% 27.64/5.49 % (13548)------------------------------
% 27.64/5.49 % (13548)------------------------------
% 27.64/5.49 % (13560)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_12937 for (2963ds/643Mi)
% 27.64/5.50 % (13561)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_12937 for (2963ds/865Mi)
% 28.56/5.50 % (13535)Instruction limit reached!
% 28.56/5.50 % (13535)------------------------------
% 28.56/5.50 % (13535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.56/5.50 % (13535)Termination reason: Unknown
% 28.56/5.50 % (13535)Termination phase: Saturation
% 28.56/5.50
% 28.56/5.50 % (13535)Memory used [KB]: 13560
% 28.56/5.50 % (13535)Time elapsed: 0.936 s
% 28.56/5.50 % (13535)Instructions burned: 3374 (million)
% 28.56/5.50 % (13535)------------------------------
% 28.56/5.50 % (13535)------------------------------
% 28.56/5.51 % (13562)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_12937 for (2963ds/1174Mi)
% 28.56/5.55 % (13559)Instruction limit reached!
% 28.56/5.55 % (13559)------------------------------
% 28.56/5.55 % (13559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.56/5.55 % (13559)Termination reason: Unknown
% 28.56/5.55 % (13559)Termination phase: Saturation
% 28.56/5.55
% 28.56/5.55 % (13559)Memory used [KB]: 8699
% 28.56/5.55 % (13559)Time elapsed: 0.151 s
% 28.56/5.55 % (13559)Instructions burned: 579 (million)
% 28.56/5.55 % (13559)------------------------------
% 28.56/5.55 % (13559)------------------------------
% 28.56/5.56 % (13563)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_12937 for (2962ds/644Mi)
% 28.83/5.61 % (13556)Instruction limit reached!
% 28.83/5.61 % (13556)------------------------------
% 28.83/5.61 % (13556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.61 % (13556)Termination reason: Unknown
% 28.83/5.61 % (13556)Termination phase: Saturation
% 28.83/5.61
% 28.83/5.61 % (13556)Memory used [KB]: 10106
% 28.83/5.61 % (13556)Time elapsed: 0.285 s
% 28.83/5.61 % (13556)Instructions burned: 1002 (million)
% 28.83/5.61 % (13556)------------------------------
% 28.83/5.61 % (13556)------------------------------
% 28.83/5.62 % (13564)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_12937 for (2962ds/1201Mi)
% 28.83/5.64 % (13558)Instruction limit reached!
% 28.83/5.64 % (13558)------------------------------
% 28.83/5.64 % (13558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.64 % (13558)Termination reason: Unknown
% 28.83/5.64 % (13558)Termination phase: Saturation
% 28.83/5.64
% 28.83/5.64 % (13558)Memory used [KB]: 9594
% 28.83/5.64 % (13558)Time elapsed: 0.257 s
% 28.83/5.64 % (13558)Instructions burned: 955 (million)
% 28.83/5.64 % (13558)------------------------------
% 28.83/5.64 % (13558)------------------------------
% 28.83/5.65 % (13565)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_12937 for (2961ds/1046Mi)
% 28.83/5.66 % (13560)Instruction limit reached!
% 28.83/5.66 % (13560)------------------------------
% 28.83/5.66 % (13560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.66 % (13560)Termination reason: Unknown
% 28.83/5.66 % (13560)Termination phase: Saturation
% 28.83/5.66
% 28.83/5.66 % (13560)Memory used [KB]: 8955
% 28.83/5.66 % (13560)Time elapsed: 0.166 s
% 28.83/5.66 % (13560)Instructions burned: 643 (million)
% 28.83/5.66 % (13560)------------------------------
% 28.83/5.66 % (13560)------------------------------
% 28.83/5.67 % (13566)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_12937 for (2961ds/222Mi)
% 29.67/5.73 % (13566)Instruction limit reached!
% 29.67/5.73 % (13566)------------------------------
% 29.67/5.73 % (13566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.67/5.73 % (13566)Termination reason: Unknown
% 29.67/5.73 % (13566)Termination phase: Preprocessing 3
% 29.67/5.73
% 29.67/5.73 % (13566)Memory used [KB]: 3070
% 29.67/5.73 % (13566)Time elapsed: 0.062 s
% 29.67/5.73 % (13566)Instructions burned: 224 (million)
% 29.67/5.73 % (13566)------------------------------
% 29.67/5.73 % (13566)------------------------------
% 29.67/5.73 % (13561)Instruction limit reached!
% 29.67/5.73 % (13561)------------------------------
% 29.67/5.73 % (13561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.67/5.73 % (13561)Termination reason: Unknown
% 29.67/5.73 % (13561)Termination phase: Saturation
% 29.67/5.73
% 29.67/5.73 % (13561)Memory used [KB]: 9722
% 29.67/5.73 % (13561)Time elapsed: 0.235 s
% 29.67/5.73 % (13561)Instructions burned: 865 (million)
% 29.67/5.73 % (13561)------------------------------
% 29.67/5.73 % (13561)------------------------------
% 29.67/5.74 % (13563)Instruction limit reached!
% 29.67/5.74 % (13563)------------------------------
% 29.67/5.74 % (13563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.67/5.74 % (13563)Termination reason: Unknown
% 29.67/5.74 % (13563)Termination phase: Saturation
% 29.67/5.74
% 29.67/5.74 % (13563)Memory used [KB]: 5500
% 29.67/5.74 % (13563)Time elapsed: 0.176 s
% 29.67/5.74 % (13563)Instructions burned: 646 (million)
% 29.67/5.74 % (13563)------------------------------
% 29.67/5.74 % (13563)------------------------------
% 29.67/5.74 % (13567)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_12937 for (2961ds/68Mi)
% 29.67/5.74 % (13568)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=454:si=on:rtra=on_0 on DTF2THF_12937 for (2961ds/454Mi)
% 29.67/5.75 % (13569)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_12937 for (2961ds/360Mi)
% 29.67/5.76 % (13567)Instruction limit reached!
% 29.67/5.76 % (13567)------------------------------
% 29.67/5.76 % (13567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.67/5.76 % (13567)Termination reason: Unknown
% 29.67/5.76 % (13567)Termination phase: shuffling
% 29.67/5.76
% 29.67/5.76 % (13567)Memory used [KB]: 2302
% 29.67/5.76 % (13567)Time elapsed: 0.022 s
% 29.67/5.76 % (13567)Instructions burned: 68 (million)
% 29.67/5.76 % (13567)------------------------------
% 29.67/5.76 % (13567)------------------------------
% 29.67/5.76 % (13508)Instruction limit reached!
% 29.67/5.76 % (13508)------------------------------
% 29.67/5.76 % (13508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.67/5.76 % (13508)Termination reason: Unknown
% 29.67/5.76 % (13508)Termination phase: Saturation
% 29.67/5.76
% 29.67/5.76 % (13508)Memory used [KB]: 13816
% 29.67/5.76 % (13508)Time elapsed: 2.320 s
% 29.67/5.76 % (13508)Instructions burned: 8251 (million)
% 29.67/5.76 % (13508)------------------------------
% 29.67/5.76 % (13508)------------------------------
% 29.67/5.77 % (13570)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_12937 for (2960ds/157Mi)
% 29.67/5.77 % (13571)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_12937 for (2960ds/5061Mi)
% 30.26/5.81 % (13570)Instruction limit reached!
% 30.26/5.81 % (13570)------------------------------
% 30.26/5.81 % (13570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.81 % (13570)Termination reason: Unknown
% 30.26/5.81 % (13570)Termination phase: Property scanning
% 30.26/5.81
% 30.26/5.81 % (13570)Memory used [KB]: 2814
% 30.26/5.81 % (13570)Time elapsed: 0.042 s
% 30.26/5.81 % (13570)Instructions burned: 160 (million)
% 30.26/5.81 % (13570)------------------------------
% 30.26/5.81 % (13570)------------------------------
% 30.26/5.82 % (13572)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_12937 for (2960ds/2401Mi)
% 30.26/5.83 % (13562)Instruction limit reached!
% 30.26/5.83 % (13562)------------------------------
% 30.26/5.83 % (13562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.83 % (13562)Termination reason: Unknown
% 30.26/5.83 % (13562)Termination phase: Saturation
% 30.26/5.83
% 30.26/5.83 % (13562)Memory used [KB]: 11641
% 30.26/5.83 % (13562)Time elapsed: 0.321 s
% 30.26/5.83 % (13562)Instructions burned: 1174 (million)
% 30.26/5.83 % (13562)------------------------------
% 30.26/5.83 % (13562)------------------------------
% 30.26/5.84 % (13569)Instruction limit reached!
% 30.26/5.84 % (13569)------------------------------
% 30.26/5.84 % (13569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.84 % (13569)Termination reason: Unknown
% 30.26/5.84 % (13569)Termination phase: Property scanning
% 30.26/5.84
% 30.26/5.84 % (13569)Memory used [KB]: 3198
% 30.26/5.84 % (13569)Time elapsed: 0.092 s
% 30.26/5.84 % (13569)Instructions burned: 361 (million)
% 30.26/5.84 % (13569)------------------------------
% 30.26/5.84 % (13569)------------------------------
% 30.26/5.84 % (13573)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_12937 for (2960ds/5798Mi)
% 30.26/5.85 % (13574)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_12937 for (2960ds/346Mi)
% 30.26/5.86 % (13568)Instruction limit reached!
% 30.26/5.86 % (13568)------------------------------
% 30.26/5.86 % (13568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.86 % (13568)Termination reason: Unknown
% 30.26/5.86 % (13568)Termination phase: Saturation
% 30.26/5.86
% 30.26/5.86 % (13568)Memory used [KB]: 12281
% 30.26/5.86 % (13568)Time elapsed: 0.117 s
% 30.26/5.86 % (13568)Instructions burned: 455 (million)
% 30.26/5.86 % (13568)------------------------------
% 30.26/5.86 % (13568)------------------------------
% 30.26/5.87 % (13575)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_12937 for (2959ds/1321Mi)
% 30.88/5.93 % (13565)Instruction limit reached!
% 30.88/5.93 % (13565)------------------------------
% 30.88/5.93 % (13565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.88/5.93 % (13565)Termination reason: Unknown
% 30.88/5.93 % (13565)Termination phase: Saturation
% 30.88/5.93
% 30.88/5.93 % (13565)Memory used [KB]: 8955
% 30.88/5.93 % (13565)Time elapsed: 0.280 s
% 30.88/5.93 % (13565)Instructions burned: 1047 (million)
% 30.88/5.93 % (13565)------------------------------
% 30.88/5.93 % (13565)------------------------------
% 30.88/5.94 % (13574)Instruction limit reached!
% 30.88/5.94 % (13574)------------------------------
% 30.88/5.94 % (13574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.88/5.94 % (13574)Termination reason: Unknown
% 30.88/5.94 % (13574)Termination phase: Property scanning
% 30.88/5.94
% 30.88/5.94 % (13574)Memory used [KB]: 3198
% 30.88/5.94 % (13574)Time elapsed: 0.091 s
% 30.88/5.94 % (13574)Instructions burned: 346 (million)
% 30.88/5.94 % (13574)------------------------------
% 30.88/5.94 % (13574)------------------------------
% 30.88/5.94 % (13576)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_12937 for (2959ds/1312Mi)
% 30.88/5.95 % (13577)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_12937 for (2959ds/672Mi)
% 30.88/5.96 % (13564)Instruction limit reached!
% 30.88/5.96 % (13564)------------------------------
% 30.88/5.96 % (13564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.88/5.96 % (13564)Termination reason: Unknown
% 30.88/5.96 % (13564)Termination phase: Saturation
% 30.88/5.96
% 30.88/5.96 % (13564)Memory used [KB]: 10106
% 30.88/5.96 % (13564)Time elapsed: 0.335 s
% 30.88/5.96 % (13564)Instructions burned: 1201 (million)
% 30.88/5.96 % (13564)------------------------------
% 30.88/5.96 % (13564)------------------------------
% 30.88/5.97 % (13578)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_12937 for (2958ds/1897Mi)
% 33.34/6.15 % (13577)Instruction limit reached!
% 33.34/6.15 % (13577)------------------------------
% 33.34/6.15 % (13577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.34/6.15 % (13577)Termination reason: Unknown
% 33.34/6.15 % (13577)Termination phase: Saturation
% 33.34/6.15
% 33.34/6.15 % (13577)Memory used [KB]: 9594
% 33.34/6.15 % (13577)Time elapsed: 0.204 s
% 33.34/6.15 % (13577)Instructions burned: 672 (million)
% 33.34/6.15 % (13577)------------------------------
% 33.34/6.15 % (13577)------------------------------
% 33.34/6.16 % (13579)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_12937 for (2956ds/1202Mi)
% 33.81/6.23 % (13575)Instruction limit reached!
% 33.81/6.23 % (13575)------------------------------
% 33.81/6.23 % (13575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.81/6.23 % (13575)Termination reason: Unknown
% 33.81/6.23 % (13575)Termination phase: Saturation
% 33.81/6.23
% 33.81/6.23 % (13575)Memory used [KB]: 9083
% 33.81/6.23 % (13575)Time elapsed: 0.366 s
% 33.81/6.23 % (13575)Instructions burned: 1323 (million)
% 33.81/6.23 % (13575)------------------------------
% 33.81/6.23 % (13575)------------------------------
% 33.81/6.24 % (13580)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_12937 for (2956ds/1493Mi)
% 34.36/6.30 % (13576)Instruction limit reached!
% 34.36/6.30 % (13576)------------------------------
% 34.36/6.30 % (13576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.36/6.30 % (13576)Termination reason: Unknown
% 34.36/6.30 % (13576)Termination phase: Saturation
% 34.36/6.30
% 34.36/6.30 % (13576)Memory used [KB]: 10234
% 34.36/6.30 % (13576)Time elapsed: 0.362 s
% 34.36/6.30 % (13576)Instructions burned: 1314 (million)
% 34.36/6.30 % (13576)------------------------------
% 34.36/6.30 % (13576)------------------------------
% 34.36/6.31 % (13580)Refutation not found, incomplete strategy
% 34.36/6.31 % (13580)------------------------------
% 34.36/6.31 % (13580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.36/6.31 % (13580)Termination reason: Refutation not found, incomplete strategy
% 34.36/6.31
% 34.36/6.31
% 34.36/6.31 % (13580)Memory used [KB]: 7547
% 34.36/6.31 % (13580)Time elapsed: 0.066 s
% 34.36/6.31 % (13580)Instructions burned: 246 (million)
% 34.36/6.31 % (13580)------------------------------
% 34.36/6.31 % (13580)------------------------------
% 34.36/6.31 % (13581)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_12937 for (2955ds/7679Mi)
% 34.36/6.32 % (13582)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_12937 for (2955ds/340Mi)
% 34.84/6.42 % (13582)Instruction limit reached!
% 34.84/6.42 % (13582)------------------------------
% 34.84/6.42 % (13582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.84/6.42 % (13582)Termination reason: Unknown
% 34.84/6.42 % (13582)Termination phase: Property scanning
% 34.84/6.42
% 34.84/6.42 % (13582)Memory used [KB]: 4093
% 34.84/6.42 % (13582)Time elapsed: 0.100 s
% 34.84/6.42 % (13582)Instructions burned: 343 (million)
% 34.84/6.42 % (13582)------------------------------
% 34.84/6.42 % (13582)------------------------------
% 34.84/6.42 % (13583)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_12937 for (2954ds/3672Mi)
% 34.84/6.49 % (13572)Instruction limit reached!
% 34.84/6.49 % (13572)------------------------------
% 34.84/6.49 % (13572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.84/6.49 % (13572)Termination reason: Unknown
% 34.84/6.49 % (13572)Termination phase: Saturation
% 34.84/6.49
% 34.84/6.49 % (13572)Memory used [KB]: 8059
% 34.84/6.49 % (13572)Time elapsed: 0.670 s
% 34.84/6.49 % (13572)Instructions burned: 2403 (million)
% 34.84/6.49 % (13572)------------------------------
% 34.84/6.49 % (13572)------------------------------
% 34.84/6.49 % (13579)Instruction limit reached!
% 34.84/6.49 % (13579)------------------------------
% 34.84/6.49 % (13579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.84/6.49 % (13579)Termination reason: Unknown
% 34.84/6.49 % (13579)Termination phase: Saturation
% 34.84/6.49
% 34.84/6.49 % (13579)Memory used [KB]: 7419
% 34.84/6.49 % (13579)Time elapsed: 0.335 s
% 34.84/6.49 % (13579)Instructions burned: 1205 (million)
% 34.84/6.49 % (13579)------------------------------
% 34.84/6.49 % (13579)------------------------------
% 35.69/6.50 % (13584)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_12937 for (2953ds/1535Mi)
% 35.69/6.50 % (13585)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_12937 for (2953ds/4637Mi)
% 35.69/6.52 % (13578)Instruction limit reached!
% 35.69/6.52 % (13578)------------------------------
% 35.69/6.52 % (13578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.69/6.52 % (13578)Termination reason: Unknown
% 35.69/6.52 % (13578)Termination phase: Saturation
% 35.69/6.52
% 35.69/6.52 % (13578)Memory used [KB]: 10362
% 35.69/6.52 % (13578)Time elapsed: 0.555 s
% 35.69/6.52 % (13578)Instructions burned: 1898 (million)
% 35.69/6.52 % (13578)------------------------------
% 35.69/6.52 % (13578)------------------------------
% 35.69/6.53 % (13586)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_12937 for (2953ds/3174Mi)
% 35.69/6.58 % (13585)Refutation not found, incomplete strategy
% 35.69/6.58 % (13585)------------------------------
% 35.69/6.58 % (13585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.69/6.58 % (13585)Termination reason: Refutation not found, incomplete strategy
% 35.69/6.58
% 35.69/6.58
% 35.69/6.58 % (13585)Memory used [KB]: 7803
% 35.69/6.58 % (13585)Time elapsed: 0.073 s
% 35.69/6.58 % (13585)Instructions burned: 248 (million)
% 35.69/6.58 % (13585)------------------------------
% 35.69/6.58 % (13585)------------------------------
% 35.69/6.59 % (13587)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_12937 for (2952ds/307Mi)
% 36.01/6.67 % (13587)Instruction limit reached!
% 36.01/6.67 % (13587)------------------------------
% 36.01/6.67 % (13587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.01/6.67 % (13587)Termination reason: Unknown
% 36.01/6.67 % (13587)Termination phase: Property scanning
% 36.01/6.67
% 36.01/6.67 % (13587)Memory used [KB]: 3198
% 36.01/6.67 % (13587)Time elapsed: 0.080 s
% 36.01/6.67 % (13587)Instructions burned: 310 (million)
% 36.01/6.67 % (13587)------------------------------
% 36.01/6.67 % (13587)------------------------------
% 36.01/6.68 % (13588)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_12937 for (2951ds/3619Mi)
% 36.70/6.90 % (13584)Instruction limit reached!
% 36.70/6.90 % (13584)------------------------------
% 36.70/6.90 % (13584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.70/6.90 % (13584)Termination reason: Unknown
% 36.70/6.90 % (13584)Termination phase: Saturation
% 36.70/6.90
% 36.70/6.90 % (13584)Memory used [KB]: 12409
% 36.70/6.90 % (13584)Time elapsed: 0.405 s
% 36.70/6.90 % (13584)Instructions burned: 1536 (million)
% 36.70/6.90 % (13584)------------------------------
% 36.70/6.90 % (13584)------------------------------
% 36.70/6.91 % (13589)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_12937 for (2949ds/2325Mi)
% 40.36/7.16 % (13571)Instruction limit reached!
% 40.36/7.16 % (13571)------------------------------
% 40.36/7.16 % (13571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.36/7.16 % (13571)Termination reason: Unknown
% 40.36/7.16 % (13571)Termination phase: Saturation
% 40.36/7.16
% 40.36/7.16 % (13571)Memory used [KB]: 13432
% 40.36/7.16 % (13571)Time elapsed: 1.390 s
% 40.36/7.16 % (13571)Instructions burned: 5061 (million)
% 40.36/7.16 % (13571)------------------------------
% 40.36/7.16 % (13571)------------------------------
% 40.36/7.17 % (13590)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_12937 for (2946ds/2341Mi)
% 40.84/7.20 % (13586)Refutation not found, non-redundant clauses discarded% (13586)------------------------------
% 40.84/7.20 % (13586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.84/7.20 % (13586)Termination reason: Refutation not found, non-redundant clauses discarded
% 40.84/7.20
% 40.84/7.20 % (13586)Memory used [KB]: 11001
% 40.84/7.20 % (13586)Time elapsed: 0.671 s
% 40.84/7.20 % (13586)Instructions burned: 2433 (million)
% 40.84/7.20 % (13586)------------------------------
% 40.84/7.20 % (13586)------------------------------
% 40.84/7.21 % (13591)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_12937 for (2946ds/7257Mi)
% 42.35/7.50 % (13583)Instruction limit reached!
% 42.35/7.50 % (13583)------------------------------
% 42.35/7.50 % (13583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.35/7.50 % (13583)Termination reason: Unknown
% 42.35/7.50 % (13583)Termination phase: Saturation
% 42.35/7.50
% 42.35/7.50 % (13583)Memory used [KB]: 13176
% 42.35/7.50 % (13583)Time elapsed: 1.076 s
% 42.35/7.50 % (13583)Instructions burned: 3672 (million)
% 42.35/7.50 % (13583)------------------------------
% 42.35/7.50 % (13583)------------------------------
% 42.35/7.51 % (13592)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_12937 for (2943ds/3710Mi)
% 42.35/7.54 % (13573)Instruction limit reached!
% 42.35/7.54 % (13573)------------------------------
% 42.35/7.54 % (13573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.35/7.54 % (13573)Termination reason: Unknown
% 42.35/7.54 % (13573)Termination phase: Saturation
% 42.35/7.54
% 42.35/7.54 % (13573)Memory used [KB]: 11641
% 42.35/7.54 % (13573)Time elapsed: 1.699 s
% 42.35/7.54 % (13573)Instructions burned: 5799 (million)
% 42.35/7.54 % (13573)------------------------------
% 42.35/7.54 % (13573)------------------------------
% 42.35/7.54 % (13589)Refutation not found, non-redundant clauses discarded% (13589)------------------------------
% 42.35/7.54 % (13589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.35/7.54 % (13589)Termination reason: Refutation not found, non-redundant clauses discarded
% 42.35/7.54
% 42.35/7.54 % (13589)Memory used [KB]: 13944
% 42.35/7.54 % (13589)Time elapsed: 0.633 s
% 42.35/7.54 % (13589)Instructions burned: 2276 (million)
% 42.35/7.54 % (13589)------------------------------
% 42.35/7.54 % (13589)------------------------------
% 42.35/7.55 % (13593)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_12937 for (2942ds/326Mi)
% 42.35/7.55 % (13594)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_12937 for (2942ds/1100Mi)
% 42.69/7.63 % (13593)Refutation not found, incomplete strategy
% 42.69/7.63 % (13593)------------------------------
% 42.69/7.63 % (13593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.69/7.63 % (13593)Termination reason: Refutation not found, incomplete strategy
% 42.69/7.63
% 42.69/7.63
% 42.69/7.63 % (13593)Memory used [KB]: 7803
% 42.69/7.63 % (13593)Time elapsed: 0.073 s
% 42.69/7.63 % (13593)Instructions burned: 246 (million)
% 42.69/7.63 % (13593)------------------------------
% 42.69/7.63 % (13593)------------------------------
% 42.69/7.64 % (13595)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12937 for (2942ds/406Mi)
% 42.69/7.66 % (13588)Instruction limit reached!
% 42.69/7.66 % (13588)------------------------------
% 42.69/7.66 % (13588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.69/7.66 % (13588)Termination reason: Unknown
% 42.69/7.66 % (13588)Termination phase: Saturation
% 42.69/7.66
% 42.69/7.66 % (13588)Memory used [KB]: 12153
% 42.69/7.66 % (13588)Time elapsed: 0.982 s
% 42.69/7.66 % (13588)Instructions burned: 3619 (million)
% 42.69/7.66 % (13588)------------------------------
% 42.69/7.66 % (13588)------------------------------
% 42.69/7.67 % (13596)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_12937 for (2941ds/1871Mi)
% 42.95/7.75 % (13595)Instruction limit reached!
% 42.95/7.75 % (13595)------------------------------
% 42.95/7.75 % (13595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.95/7.75 % (13595)Termination reason: Unknown
% 42.95/7.75 % (13595)Termination phase: Property scanning
% 42.95/7.75
% 42.95/7.75 % (13595)Memory used [KB]: 3965
% 42.95/7.75 % (13595)Time elapsed: 0.116 s
% 42.95/7.75 % (13595)Instructions burned: 407 (million)
% 42.95/7.75 % (13595)------------------------------
% 42.95/7.75 % (13595)------------------------------
% 42.95/7.76 % (13597)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_12937 for (2940ds/1194Mi)
% 43.16/7.86 % (13594)Instruction limit reached!
% 43.16/7.86 % (13594)------------------------------
% 43.16/7.86 % (13594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.16/7.86 % (13594)Termination reason: Unknown
% 43.16/7.86 % (13594)Termination phase: Saturation
% 43.16/7.86
% 43.16/7.86 % (13594)Memory used [KB]: 11769
% 43.16/7.86 % (13594)Time elapsed: 0.306 s
% 43.16/7.86 % (13594)Instructions burned: 1100 (million)
% 43.16/7.86 % (13594)------------------------------
% 43.16/7.86 % (13594)------------------------------
% 43.16/7.86 % (13590)Instruction limit reached!
% 43.16/7.86 % (13590)------------------------------
% 43.16/7.86 % (13590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.16/7.86 % (13590)Termination reason: Unknown
% 43.16/7.86 % (13590)Termination phase: Saturation
% 43.16/7.86
% 43.16/7.86 % (13590)Memory used [KB]: 10362
% 43.16/7.86 % (13590)Time elapsed: 0.690 s
% 43.16/7.86 % (13590)Instructions burned: 2344 (million)
% 43.16/7.86 % (13590)------------------------------
% 43.16/7.86 % (13590)------------------------------
% 43.16/7.87 % (13598)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_12937 for (2939ds/474Mi)
% 43.16/7.87 % (13599)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_12937 for (2939ds/3115Mi)
% 44.28/7.99 % (13598)Instruction limit reached!
% 44.28/7.99 % (13598)------------------------------
% 44.28/7.99 % (13598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.28/7.99 % (13598)Termination reason: Unknown
% 44.28/7.99 % (13598)Termination phase: Saturation
% 44.28/7.99
% 44.28/7.99 % (13598)Memory used [KB]: 7931
% 44.28/7.99 % (13598)Time elapsed: 0.124 s
% 44.28/7.99 % (13598)Instructions burned: 476 (million)
% 44.28/7.99 % (13598)------------------------------
% 44.28/7.99 % (13598)------------------------------
% 44.28/8.00 % (13600)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_12937 for (2938ds/831Mi)
% 46.65/8.09 % (13597)Instruction limit reached!
% 46.65/8.09 % (13597)------------------------------
% 46.65/8.09 % (13597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.65/8.09 % (13597)Termination reason: Unknown
% 46.65/8.09 % (13597)Termination phase: Saturation
% 46.65/8.09
% 46.65/8.09 % (13597)Memory used [KB]: 10874
% 46.65/8.09 % (13597)Time elapsed: 0.332 s
% 46.65/8.09 % (13597)Instructions burned: 1195 (million)
% 46.65/8.09 % (13597)------------------------------
% 46.65/8.09 % (13597)------------------------------
% 46.65/8.10 % (13601)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_12937 for (2937ds/1188Mi)
% 47.80/8.22 % (13600)Instruction limit reached!
% 47.80/8.22 % (13600)------------------------------
% 47.80/8.22 % (13600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.80/8.22 % (13600)Termination reason: Unknown
% 47.80/8.22 % (13600)Termination phase: Saturation
% 47.80/8.22
% 47.80/8.22 % (13600)Memory used [KB]: 6908
% 47.80/8.22 % (13600)Time elapsed: 0.223 s
% 47.80/8.22 % (13600)Instructions burned: 832 (million)
% 47.80/8.22 % (13600)------------------------------
% 47.80/8.22 % (13600)------------------------------
% 47.80/8.23 % (13596)Instruction limit reached!
% 47.80/8.23 % (13596)------------------------------
% 47.80/8.23 % (13596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.80/8.23 % (13596)Termination reason: Unknown
% 47.80/8.23 % (13596)Termination phase: Saturation
% 47.80/8.23
% 47.80/8.23 % (13596)Memory used [KB]: 13816
% 47.80/8.23 % (13596)Time elapsed: 0.563 s
% 47.80/8.23 % (13596)Instructions burned: 1873 (million)
% 47.80/8.23 % (13596)------------------------------
% 47.80/8.23 % (13596)------------------------------
% 47.80/8.23 % (13602)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_12937 for (2936ds/2868Mi)
% 47.80/8.24 % (13603)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_12937 for (2936ds/1516Mi)
% 48.27/8.31 % (13603)Refutation not found, incomplete strategy
% 48.27/8.31 % (13603)------------------------------
% 48.27/8.31 % (13603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.27/8.31 % (13603)Termination reason: Refutation not found, incomplete strategy
% 48.27/8.31
% 48.27/8.31
% 48.27/8.31 % (13603)Memory used [KB]: 7931
% 48.27/8.31 % (13603)Time elapsed: 0.077 s
% 48.27/8.31 % (13603)Instructions burned: 257 (million)
% 48.27/8.31 % (13603)------------------------------
% 48.27/8.31 % (13603)------------------------------
% 48.27/8.32 % (13604)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_12937 for (2935ds/2321Mi)
% 48.75/8.41 % (13602)Refutation not found, incomplete strategy
% 48.75/8.41 % (13602)------------------------------
% 48.75/8.41 % (13602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.75/8.41 % (13602)Termination reason: Refutation not found, incomplete strategy
% 48.75/8.41
% 48.75/8.41
% 48.75/8.41 % (13602)Memory used [KB]: 9083
% 48.75/8.41 % (13602)Time elapsed: 0.172 s
% 48.75/8.41 % (13602)Instructions burned: 666 (million)
% 48.75/8.41 % (13602)------------------------------
% 48.75/8.41 % (13602)------------------------------
% 48.75/8.42 % (13605)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_12937 for (2934ds/2812Mi)
% 48.75/8.45 % (13601)Instruction limit reached!
% 48.75/8.45 % (13601)------------------------------
% 48.75/8.45 % (13601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.75/8.45 % (13601)Termination reason: Unknown
% 48.75/8.45 % (13601)Termination phase: Saturation
% 48.75/8.45
% 48.75/8.45 % (13601)Memory used [KB]: 11257
% 48.75/8.45 % (13601)Time elapsed: 0.368 s
% 48.75/8.45 % (13601)Instructions burned: 1188 (million)
% 48.75/8.45 % (13601)------------------------------
% 48.75/8.45 % (13601)------------------------------
% 48.75/8.46 % (13606)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_12937 for (2934ds/4604Mi)
% 49.69/8.50 % (13604)Refutation not found, incomplete strategy
% 49.69/8.50 % (13604)------------------------------
% 49.69/8.50 % (13604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.50 % (13604)Termination reason: Refutation not found, incomplete strategy
% 49.69/8.50
% 49.69/8.50
% 49.69/8.50 % (13604)Memory used [KB]: 9083
% 49.69/8.50 % (13604)Time elapsed: 0.181 s
% 49.69/8.50 % (13604)Instructions burned: 701 (million)
% 49.69/8.50 % (13604)------------------------------
% 49.69/8.50 % (13604)------------------------------
% 49.69/8.52 % (13607)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_12937 for (2933ds/2678Mi)
% 49.69/8.52 % (13592)Instruction limit reached!
% 49.69/8.52 % (13592)------------------------------
% 49.69/8.52 % (13592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.52 % (13592)Termination reason: Unknown
% 49.69/8.52 % (13592)Termination phase: Saturation
% 49.69/8.52
% 49.69/8.53 % (13592)Memory used [KB]: 17654
% 49.69/8.53 % (13592)Time elapsed: 1.016 s
% 49.69/8.53 % (13592)Instructions burned: 3712 (million)
% 49.69/8.53 % (13592)------------------------------
% 49.69/8.53 % (13592)------------------------------
% 49.69/8.53 % (13606)Refutation not found, incomplete strategy
% 49.69/8.53 % (13606)------------------------------
% 49.69/8.53 % (13606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.53 % (13606)Termination reason: Refutation not found, incomplete strategy
% 49.69/8.53
% 49.69/8.53
% 49.69/8.53 % (13606)Memory used [KB]: 7803
% 49.69/8.53 % (13606)Time elapsed: 0.073 s
% 49.69/8.53 % (13606)Instructions burned: 248 (million)
% 49.69/8.53 % (13606)------------------------------
% 49.69/8.53 % (13606)------------------------------
% 49.69/8.54 % (13608)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_12937 for (2933ds/643Mi)
% 49.69/8.54 % (13609)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_12937 for (2933ds/458Mi)
% 49.69/8.56 % (13581)Instruction limit reached!
% 49.69/8.56 % (13581)------------------------------
% 49.69/8.56 % (13581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.56 % (13581)Termination reason: Unknown
% 49.69/8.56 % (13581)Termination phase: Saturation
% 49.69/8.56
% 49.69/8.56 % (13581)Memory used [KB]: 15991
% 49.69/8.56 % (13581)Time elapsed: 2.242 s
% 49.69/8.56 % (13581)Instructions burned: 7680 (million)
% 49.69/8.56 % (13581)------------------------------
% 49.69/8.56 % (13581)------------------------------
% 49.69/8.57 % (13610)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_12937 for (2932ds/2546Mi)
% 50.28/8.66 % (13609)Instruction limit reached!
% 50.28/8.66 % (13609)------------------------------
% 50.28/8.66 % (13609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.28/8.66 % (13609)Termination reason: Unknown
% 50.28/8.66 % (13609)Termination phase: Saturation
% 50.28/8.66
% 50.28/8.66 % (13609)Memory used [KB]: 7803
% 50.28/8.66 % (13609)Time elapsed: 0.118 s
% 50.28/8.66 % (13609)Instructions burned: 460 (million)
% 50.28/8.66 % (13609)------------------------------
% 50.28/8.66 % (13609)------------------------------
% 50.28/8.67 % (13611)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_12937 for (2931ds/1432Mi)
% 50.61/8.70 % (13608)Instruction limit reached!
% 50.61/8.70 % (13608)------------------------------
% 50.61/8.70 % (13608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.61/8.70 % (13608)Termination reason: Unknown
% 50.61/8.70 % (13608)Termination phase: Saturation
% 50.61/8.70
% 50.61/8.70 % (13608)Memory used [KB]: 8827
% 50.61/8.70 % (13608)Time elapsed: 0.167 s
% 50.61/8.70 % (13608)Instructions burned: 643 (million)
% 50.61/8.70 % (13608)------------------------------
% 50.61/8.70 % (13608)------------------------------
% 50.61/8.71 % (13612)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_12937 for (2931ds/386Mi)
% 50.61/8.79 % (13599)Instruction limit reached!
% 50.61/8.79 % (13599)------------------------------
% 50.61/8.79 % (13599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.61/8.79 % (13599)Termination reason: Unknown
% 50.61/8.79 % (13599)Termination phase: Saturation
% 50.61/8.79
% 50.61/8.79 % (13599)Memory used [KB]: 14839
% 50.61/8.79 % (13599)Time elapsed: 0.922 s
% 50.61/8.79 % (13599)Instructions burned: 3117 (million)
% 50.61/8.79 % (13599)------------------------------
% 50.61/8.79 % (13599)------------------------------
% 50.98/8.80 % (13613)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_12937 for (2930ds/360Mi)
% 50.98/8.81 % (13612)Instruction limit reached!
% 50.98/8.81 % (13612)------------------------------
% 50.98/8.81 % (13612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.98/8.81 % (13612)Termination reason: Unknown
% 50.98/8.81 % (13612)Termination phase: Property scanning
% 50.98/8.81
% 50.98/8.81 % (13612)Memory used [KB]: 3198
% 50.98/8.81 % (13612)Time elapsed: 0.099 s
% 50.98/8.81 % (13612)Instructions burned: 388 (million)
% 50.98/8.81 % (13612)------------------------------
% 50.98/8.81 % (13612)------------------------------
% 50.98/8.82 % (13614)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_12937 for (2930ds/5446Mi)
% 50.98/8.89 % (13613)Instruction limit reached!
% 50.98/8.89 % (13613)------------------------------
% 50.98/8.89 % (13613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.98/8.89 % (13613)Termination reason: Unknown
% 50.98/8.89 % (13613)Termination phase: Property scanning
% 50.98/8.89
% 50.98/8.89 % (13613)Memory used [KB]: 3198
% 50.98/8.89 % (13613)Time elapsed: 0.093 s
% 50.98/8.89 % (13613)Instructions burned: 362 (million)
% 50.98/8.89 % (13613)------------------------------
% 50.98/8.89 % (13613)------------------------------
% 51.29/8.90 % (13615)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_12937 for (2929ds/2573Mi)
% 53.67/9.03 % (13611)Instruction limit reached!
% 53.67/9.03 % (13611)------------------------------
% 53.67/9.03 % (13611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.67/9.03 % (13611)Termination reason: Unknown
% 53.67/9.03 % (13611)Termination phase: Saturation
% 53.67/9.03
% 53.67/9.03 % (13611)Memory used [KB]: 11129
% 53.67/9.03 % (13611)Time elapsed: 0.365 s
% 53.67/9.03 % (13611)Instructions burned: 1432 (million)
% 53.67/9.03 % (13611)------------------------------
% 53.67/9.03 % (13611)------------------------------
% 53.67/9.04 % (13616)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=2655:si=on:rtra=on_0 on DTF2THF_12937 for (2928ds/2655Mi)
% 54.75/9.25 % (13607)Instruction limit reached!
% 54.75/9.25 % (13607)------------------------------
% 54.75/9.25 % (13607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.75/9.25 % (13607)Termination reason: Unknown
% 54.75/9.25 % (13607)Termination phase: Saturation
% 54.75/9.25
% 54.75/9.25 % (13607)Memory used [KB]: 12281
% 54.75/9.25 % (13607)Time elapsed: 0.736 s
% 54.75/9.25 % (13607)Instructions burned: 2680 (million)
% 54.75/9.25 % (13607)------------------------------
% 54.75/9.25 % (13607)------------------------------
% 54.75/9.25 % (13605)Instruction limit reached!
% 54.75/9.25 % (13605)------------------------------
% 54.75/9.25 % (13605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.75/9.25 % (13605)Termination reason: Unknown
% 54.75/9.25 % (13605)Termination phase: Saturation
% 54.75/9.25
% 54.75/9.25 % (13605)Memory used [KB]: 13432
% 54.75/9.25 % (13605)Time elapsed: 0.861 s
% 54.75/9.25 % (13605)Instructions burned: 2814 (million)
% 54.75/9.25 % (13605)------------------------------
% 54.75/9.25 % (13605)------------------------------
% 54.75/9.26 % (13617)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_12937 for (2925ds/2781Mi)
% 54.75/9.26 % (13618)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_12937 for (2925ds/307Mi)
% 55.29/9.30 % (13610)Instruction limit reached!
% 55.29/9.30 % (13610)------------------------------
% 55.29/9.30 % (13610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.29/9.30 % (13610)Termination reason: Unknown
% 55.29/9.30 % (13610)Termination phase: Saturation
% 55.29/9.30
% 55.29/9.30 % (13610)Memory used [KB]: 12025
% 55.29/9.30 % (13610)Time elapsed: 0.759 s
% 55.29/9.30 % (13610)Instructions burned: 2546 (million)
% 55.29/9.30 % (13610)------------------------------
% 55.29/9.30 % (13610)------------------------------
% 55.29/9.31 % (13619)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_12937 for (2925ds/1548Mi)
% 55.29/9.34 % (13618)Instruction limit reached!
% 55.29/9.34 % (13618)------------------------------
% 55.29/9.34 % (13618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.29/9.34 % (13618)Termination reason: Unknown
% 55.29/9.34 % (13618)Termination phase: Property scanning
% 55.29/9.34
% 55.29/9.34 % (13618)Memory used [KB]: 3198
% 55.29/9.34 % (13618)Time elapsed: 0.081 s
% 55.29/9.34 % (13618)Instructions burned: 310 (million)
% 55.29/9.34 % (13618)------------------------------
% 55.29/9.34 % (13618)------------------------------
% 55.29/9.35 % (13620)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_12937 for (2925ds/5214Mi)
% 55.29/9.38 % (13591)Instruction limit reached!
% 55.29/9.38 % (13591)------------------------------
% 55.29/9.38 % (13591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.29/9.38 % (13591)Termination reason: Unknown
% 55.29/9.38 % (13591)Termination phase: Saturation
% 55.29/9.38
% 55.29/9.38 % (13591)Memory used [KB]: 15095
% 55.29/9.38 % (13591)Time elapsed: 2.168 s
% 55.29/9.38 % (13591)Instructions burned: 7257 (million)
% 55.29/9.38 % (13591)------------------------------
% 55.29/9.38 % (13591)------------------------------
% 55.29/9.38 % (13619)Refutation not found, incomplete strategy
% 55.29/9.38 % (13619)------------------------------
% 55.29/9.38 % (13619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.29/9.38 % (13619)Termination reason: Refutation not found, incomplete strategy
% 55.29/9.38
% 55.29/9.38
% 55.29/9.38 % (13619)Memory used [KB]: 7803
% 55.29/9.38 % (13619)Time elapsed: 0.074 s
% 55.29/9.38 % (13619)Instructions burned: 247 (million)
% 55.29/9.38 % (13619)------------------------------
% 55.29/9.38 % (13619)------------------------------
% 55.29/9.39 % (13621)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_12937 for (2924ds/3201Mi)
% 55.29/9.39 % (13622)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=454:si=on:rtra=on_0 on DTF2THF_12937 for (2924ds/454Mi)
% 55.95/9.51 % (13622)Instruction limit reached!
% 55.95/9.51 % (13622)------------------------------
% 55.95/9.51 % (13622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.95/9.51 % (13622)Termination reason: Unknown
% 55.95/9.51 % (13622)Termination phase: Saturation
% 55.95/9.51
% 55.95/9.51 % (13622)Memory used [KB]: 12281
% 55.95/9.51 % (13622)Time elapsed: 0.117 s
% 55.95/9.51 % (13622)Instructions burned: 455 (million)
% 55.95/9.51 % (13622)------------------------------
% 55.95/9.51 % (13622)------------------------------
% 55.95/9.52 % (13623)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_12937 for (2923ds/3049Mi)
% 56.28/9.67 % (13615)Instruction limit reached!
% 56.28/9.67 % (13615)------------------------------
% 56.28/9.67 % (13615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.28/9.67 % (13615)Termination reason: Unknown
% 56.28/9.67 % (13615)Termination phase: Saturation
% 56.28/9.67
% 56.28/9.67 % (13615)Memory used [KB]: 17654
% 56.28/9.67 % (13615)Time elapsed: 0.772 s
% 56.28/9.67 % (13615)Instructions burned: 2575 (million)
% 56.28/9.67 % (13615)------------------------------
% 56.28/9.67 % (13615)------------------------------
% 56.28/9.68 % (13624)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_12937 for (2921ds/7311Mi)
% 56.57/9.80 % (13616)Instruction limit reached!
% 56.57/9.80 % (13616)------------------------------
% 56.57/9.80 % (13616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.57/9.80 % (13616)Termination reason: Unknown
% 56.57/9.80 % (13616)Termination phase: Saturation
% 56.57/9.80
% 56.57/9.80 % (13616)Memory used [KB]: 19445
% 56.57/9.80 % (13616)Time elapsed: 0.758 s
% 56.57/9.80 % (13616)Instructions burned: 2655 (million)
% 56.57/9.80 % (13616)------------------------------
% 56.57/9.80 % (13616)------------------------------
% 56.57/9.81 % (13625)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_12937 for (2920ds/6804Mi)
% 60.68/10.08 % (13617)Instruction limit reached!
% 60.68/10.08 % (13617)------------------------------
% 60.68/10.08 % (13617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.68/10.08 % (13617)Termination reason: Unknown
% 60.68/10.08 % (13617)Termination phase: Saturation
% 60.68/10.08
% 60.68/10.08 % (13617)Memory used [KB]: 7164
% 60.68/10.08 % (13617)Time elapsed: 0.824 s
% 60.68/10.08 % (13617)Instructions burned: 2781 (million)
% 60.68/10.08 % (13617)------------------------------
% 60.68/10.08 % (13617)------------------------------
% 60.68/10.09 % (13626)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_12937 for (2917ds/1683Mi)
% 62.41/10.31 % (13621)Instruction limit reached!
% 62.41/10.31 % (13621)------------------------------
% 62.41/10.31 % (13621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.41/10.31 % (13621)Termination reason: Unknown
% 62.41/10.31 % (13621)Termination phase: Saturation
% 62.41/10.31
% 62.41/10.31 % (13621)Memory used [KB]: 13816
% 62.41/10.31 % (13621)Time elapsed: 0.923 s
% 62.41/10.31 % (13621)Instructions burned: 3202 (million)
% 62.41/10.31 % (13621)------------------------------
% 62.41/10.31 % (13621)------------------------------
% 62.41/10.32 % (13627)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_12937 for (2915ds/4688Mi)
% 62.94/10.42 % (13623)Instruction limit reached!
% 62.94/10.42 % (13623)------------------------------
% 62.94/10.42 % (13623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.94/10.42 % (13623)Termination reason: Unknown
% 62.94/10.42 % (13623)Termination phase: Saturation
% 62.94/10.42
% 62.94/10.42 % (13623)Memory used [KB]: 12792
% 62.94/10.42 % (13623)Time elapsed: 0.922 s
% 62.94/10.42 % (13623)Instructions burned: 3049 (million)
% 62.94/10.42 % (13623)------------------------------
% 62.94/10.42 % (13623)------------------------------
% 62.94/10.43 % (13628)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_12937 for (2914ds/2207Mi)
% 62.94/10.46 % (13614)Instruction limit reached!
% 62.94/10.46 % (13614)------------------------------
% 62.94/10.46 % (13614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.94/10.46 % (13614)Termination reason: Unknown
% 62.94/10.46 % (13614)Termination phase: Saturation
% 62.94/10.46
% 62.94/10.46 % (13614)Memory used [KB]: 17782
% 62.94/10.46 % (13614)Time elapsed: 1.643 s
% 62.94/10.46 % (13614)Instructions burned: 5448 (million)
% 62.94/10.46 % (13614)------------------------------
% 62.94/10.46 % (13614)------------------------------
% 62.94/10.47 % (13629)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=8216:si=on:rtra=on_0 on DTF2THF_12937 for (2913ds/8216Mi)
% 63.66/10.61 % (13626)Instruction limit reached!
% 63.66/10.61 % (13626)------------------------------
% 63.66/10.61 % (13626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.66/10.61 % (13626)Termination reason: Unknown
% 63.66/10.61 % (13626)Termination phase: Saturation
% 63.66/10.61
% 63.66/10.61 % (13626)Memory used [KB]: 12025
% 63.66/10.61 % (13626)Time elapsed: 0.516 s
% 63.66/10.61 % (13626)Instructions burned: 1684 (million)
% 63.66/10.61 % (13626)------------------------------
% 63.66/10.61 % (13626)------------------------------
% 63.66/10.62 % (13630)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_12937 for (2912ds/430Mi)
% 64.50/10.73 % (13630)Instruction limit reached!
% 64.50/10.73 % (13630)------------------------------
% 64.50/10.73 % (13630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.50/10.73 % (13630)Termination reason: Unknown
% 64.50/10.73 % (13630)Termination phase: Saturation
% 64.50/10.73
% 64.50/10.73 % (13630)Memory used [KB]: 7675
% 64.50/10.73 % (13630)Time elapsed: 0.114 s
% 64.50/10.73 % (13630)Instructions burned: 430 (million)
% 64.50/10.73 % (13630)------------------------------
% 64.50/10.73 % (13630)------------------------------
% 64.50/10.74 % (13631)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_12937 for (2911ds/2012Mi)
% 64.92/10.86 % (13620)Instruction limit reached!
% 64.92/10.86 % (13620)------------------------------
% 64.92/10.86 % (13620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.92/10.86 % (13620)Termination reason: Unknown
% 64.92/10.86 % (13620)Termination phase: Saturation
% 64.92/10.86
% 64.92/10.86 % (13620)Memory used [KB]: 20212
% 64.92/10.86 % (13620)Time elapsed: 1.509 s
% 64.92/10.86 % (13620)Instructions burned: 5215 (million)
% 64.92/10.86 % (13620)------------------------------
% 64.92/10.86 % (13620)------------------------------
% 64.92/10.87 % (13632)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_12937 for (2909ds/631Mi)
% 67.71/11.04 % (13632)Instruction limit reached!
% 67.71/11.04 % (13632)------------------------------
% 67.71/11.04 % (13632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.71/11.04 % (13632)Termination reason: Unknown
% 67.71/11.04 % (13632)Termination phase: Saturation
% 67.71/11.04
% 67.71/11.04 % (13632)Memory used [KB]: 5245
% 67.71/11.04 % (13632)Time elapsed: 0.169 s
% 67.71/11.04 % (13632)Instructions burned: 633 (million)
% 67.71/11.04 % (13632)------------------------------
% 67.71/11.04 % (13632)------------------------------
% 67.71/11.05 % (13633)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_12937 for (2908ds/8785Mi)
% 67.71/11.09 % (13628)Instruction limit reached!
% 67.71/11.09 % (13628)------------------------------
% 67.71/11.09 % (13628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.71/11.09 % (13628)Termination reason: Unknown
% 67.71/11.09 % (13628)Termination phase: Saturation
% 67.71/11.09
% 67.71/11.09 % (13628)Memory used [KB]: 13048
% 67.71/11.09 % (13628)Time elapsed: 0.658 s
% 67.71/11.09 % (13628)Instructions burned: 2207 (million)
% 67.71/11.09 % (13628)------------------------------
% 67.71/11.09 % (13628)------------------------------
% 67.71/11.10 % (13634)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_12937 for (2907ds/739Mi)
% 69.21/11.30 % (13634)Instruction limit reached!
% 69.21/11.30 % (13634)------------------------------
% 69.21/11.30 % (13634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.21/11.30 % (13634)Termination reason: Unknown
% 69.21/11.30 % (13634)Termination phase: Saturation
% 69.21/11.30
% 69.21/11.30 % (13634)Memory used [KB]: 10234
% 69.21/11.30 % (13634)Time elapsed: 0.204 s
% 69.21/11.30 % (13634)Instructions burned: 739 (million)
% 69.21/11.30 % (13634)------------------------------
% 69.21/11.30 % (13634)------------------------------
% 69.21/11.30 % (13631)Instruction limit reached!
% 69.21/11.30 % (13631)------------------------------
% 69.21/11.30 % (13631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.21/11.30 % (13631)Termination reason: Unknown
% 69.21/11.30 % (13631)Termination phase: Saturation
% 69.21/11.30
% 69.21/11.30 % (13631)Memory used [KB]: 18933
% 69.21/11.30 % (13631)Time elapsed: 0.564 s
% 69.21/11.30 % (13631)Instructions burned: 2013 (million)
% 69.21/11.30 % (13631)------------------------------
% 69.21/11.30 % (13631)------------------------------
% 69.21/11.31 % (13635)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_12937 for (2905ds/5473Mi)
% 69.21/11.31 % (13636)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_12937 for (2905ds/43570Mi)
% 69.21/11.35 % (13624)Refutation not found, non-redundant clauses discarded% (13624)------------------------------
% 69.21/11.35 % (13624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.21/11.35 % (13624)Termination reason: Refutation not found, non-redundant clauses discarded
% 69.21/11.35
% 69.21/11.35 % (13624)Memory used [KB]: 13304
% 69.21/11.35 % (13624)Time elapsed: 1.689 s
% 69.21/11.35 % (13624)Instructions burned: 5624 (million)
% 69.21/11.35 % (13624)------------------------------
% 69.21/11.35 % (13624)------------------------------
% 69.21/11.36 % (13637)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_12937 for (2904ds/8382Mi)
% 69.21/11.39 % (13636)Refutation not found, incomplete strategy
% 69.21/11.39 % (13636)------------------------------
% 69.21/11.39 % (13636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.21/11.39 % (13636)Termination reason: Refutation not found, incomplete strategy
% 69.21/11.39
% 69.21/11.39
% 69.21/11.39 % (13636)Memory used [KB]: 7931
% 69.21/11.39 % (13636)Time elapsed: 0.100 s
% 69.21/11.39 % (13636)Instructions burned: 262 (million)
% 69.21/11.39 % (13636)------------------------------
% 69.21/11.39 % (13636)------------------------------
% 69.89/11.40 % (13638)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_12937 for (2904ds/407Mi)
% 70.19/11.51 % (13638)Instruction limit reached!
% 70.19/11.51 % (13638)------------------------------
% 70.19/11.51 % (13638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.19/11.51 % (13638)Termination reason: Unknown
% 70.19/11.51 % (13638)Termination phase: Property scanning
% 70.19/11.51
% 70.19/11.51 % (13638)Memory used [KB]: 3965
% 70.19/11.51 % (13638)Time elapsed: 0.112 s
% 70.19/11.51 % (13638)Instructions burned: 407 (million)
% 70.19/11.51 % (13638)------------------------------
% 70.19/11.51 % (13638)------------------------------
% 70.19/11.52 % (13639)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_12937 for (2903ds/2971Mi)
% 70.91/11.70 % (13639)Refutation not found, incomplete strategy
% 70.91/11.70 % (13639)------------------------------
% 70.91/11.70 % (13639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.91/11.70 % (13639)Termination reason: Refutation not found, incomplete strategy
% 70.91/11.70
% 70.91/11.70
% 70.91/11.70 % (13639)Memory used [KB]: 9083
% 70.91/11.70 % (13639)Time elapsed: 0.175 s
% 70.91/11.70 % (13639)Instructions burned: 662 (million)
% 70.91/11.70 % (13639)------------------------------
% 70.91/11.70 % (13639)------------------------------
% 70.91/11.71 % (13641)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_12937 for (2901ds/9822Mi)
% 70.91/11.72 % (13627)Instruction limit reached!
% 70.91/11.72 % (13627)------------------------------
% 70.91/11.72 % (13627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.91/11.72 % (13627)Termination reason: Unknown
% 70.91/11.72 % (13627)Termination phase: Saturation
% 70.91/11.72
% 70.91/11.72 % (13627)Memory used [KB]: 8315
% 70.91/11.72 % (13627)Time elapsed: 1.398 s
% 70.91/11.72 % (13627)Instructions burned: 4689 (million)
% 70.91/11.72 % (13627)------------------------------
% 70.91/11.72 % (13627)------------------------------
% 70.91/11.73 % (13642)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_12937 for (2901ds/8425Mi)
% 70.91/11.75 % (13625)Instruction limit reached!
% 70.91/11.75 % (13625)------------------------------
% 70.91/11.75 % (13625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.91/11.75 % (13625)Termination reason: Unknown
% 70.91/11.75 % (13625)Termination phase: Saturation
% 70.91/11.75
% 70.91/11.75 % (13625)Memory used [KB]: 15223
% 70.91/11.75 % (13625)Time elapsed: 1.963 s
% 70.91/11.75 % (13625)Instructions burned: 6805 (million)
% 70.91/11.75 % (13625)------------------------------
% 70.91/11.75 % (13625)------------------------------
% 70.91/11.76 % (13643)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_12937 for (2900ds/3107Mi)
% 78.76/12.64 % (13643)Instruction limit reached!
% 78.76/12.64 % (13643)------------------------------
% 78.76/12.64 % (13643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.76/12.64 % (13643)Termination reason: Unknown
% 78.76/12.64 % (13643)Termination phase: Saturation
% 78.76/12.64
% 78.76/12.64 % (13643)Memory used [KB]: 14200
% 78.76/12.64 % (13643)Time elapsed: 0.882 s
% 78.76/12.64 % (13643)Instructions burned: 3110 (million)
% 78.76/12.64 % (13643)------------------------------
% 78.76/12.64 % (13643)------------------------------
% 78.76/12.65 % (13644)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_12937 for (2892ds/7967Mi)
% 80.04/12.82 % (13644)Refutation not found, incomplete strategy
% 80.04/12.82 % (13644)------------------------------
% 80.04/12.82 % (13644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.04/12.82 % (13644)Termination reason: Refutation not found, incomplete strategy
% 80.04/12.82
% 80.04/12.82
% 80.04/12.82 % (13644)Memory used [KB]: 9083
% 80.04/12.82 % (13644)Time elapsed: 0.171 s
% 80.04/12.82 % (13644)Instructions burned: 661 (million)
% 80.04/12.82 % (13644)------------------------------
% 80.04/12.82 % (13644)------------------------------
% 80.04/12.83 % (13645)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_12937 for (2890ds/3629Mi)
% 80.04/12.84 % (13629)Instruction limit reached!
% 80.04/12.84 % (13629)------------------------------
% 80.04/12.84 % (13629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.04/12.84 % (13629)Termination reason: Unknown
% 80.04/12.84 % (13629)Termination phase: Saturation
% 80.04/12.84
% 80.04/12.84 % (13629)Memory used [KB]: 14456
% 80.04/12.84 % (13629)Time elapsed: 2.372 s
% 80.04/12.84 % (13629)Instructions burned: 8219 (million)
% 80.04/12.84 % (13629)------------------------------
% 80.04/12.84 % (13629)------------------------------
% 80.04/12.85 % (13646)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_12937 for (2890ds/939Mi)
% 80.78/12.99 % (13635)Instruction limit reached!
% 80.78/12.99 % (13635)------------------------------
% 80.78/12.99 % (13635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.78/12.99 % (13635)Termination reason: Unknown
% 80.78/12.99 % (13635)Termination phase: Saturation
% 80.78/12.99
% 80.78/12.99 % (13635)Memory used [KB]: 13304
% 80.78/12.99 % (13635)Time elapsed: 1.701 s
% 80.78/12.99 % (13635)Instructions burned: 5474 (million)
% 80.78/12.99 % (13635)------------------------------
% 80.78/12.99 % (13635)------------------------------
% 80.78/13.00 % (13647)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_12937 for (2888ds/1188Mi)
% 81.76/13.11 % (13646)Instruction limit reached!
% 81.76/13.11 % (13646)------------------------------
% 81.76/13.11 % (13646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.76/13.11 % (13646)Termination reason: Unknown
% 81.76/13.11 % (13646)Termination phase: Saturation
% 81.76/13.11
% 81.76/13.11 % (13646)Memory used [KB]: 9978
% 81.76/13.11 % (13646)Time elapsed: 0.259 s
% 81.76/13.11 % (13646)Instructions burned: 940 (million)
% 81.76/13.11 % (13646)------------------------------
% 81.76/13.11 % (13646)------------------------------
% 81.76/13.12 % (13648)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_12937 for (2887ds/3205Mi)
% 83.53/13.35 % (13647)Instruction limit reached!
% 83.53/13.35 % (13647)------------------------------
% 83.53/13.35 % (13647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.53/13.35 % (13647)Termination reason: Unknown
% 83.53/13.35 % (13647)Termination phase: Saturation
% 83.53/13.35
% 83.53/13.35 % (13647)Memory used [KB]: 11257
% 83.53/13.35 % (13647)Time elapsed: 0.354 s
% 83.53/13.35 % (13647)Instructions burned: 1190 (million)
% 83.53/13.35 % (13647)------------------------------
% 83.53/13.35 % (13647)------------------------------
% 83.53/13.36 % (13649)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_12937 for (2884ds/865Mi)
% 84.59/13.60 % (13649)Instruction limit reached!
% 84.59/13.60 % (13649)------------------------------
% 84.59/13.60 % (13649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.59/13.60 % (13649)Termination reason: Unknown
% 84.59/13.60 % (13649)Termination phase: Saturation
% 84.59/13.60
% 84.59/13.60 % (13649)Memory used [KB]: 9722
% 84.59/13.60 % (13649)Time elapsed: 0.236 s
% 84.59/13.60 % (13649)Instructions burned: 868 (million)
% 84.59/13.60 % (13649)------------------------------
% 84.59/13.60 % (13649)------------------------------
% 85.34/13.61 % (13650)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_12937 for (2882ds/7469Mi)
% 85.34/13.69 % (13633)Instruction limit reached!
% 85.34/13.69 % (13633)------------------------------
% 85.34/13.69 % (13633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.34/13.69 % (13633)Termination reason: Unknown
% 85.34/13.69 % (13633)Termination phase: Saturation
% 85.34/13.69
% 85.34/13.69 % (13633)Memory used [KB]: 18038
% 85.34/13.69 % (13633)Time elapsed: 2.666 s
% 85.34/13.69 % (13633)Instructions burned: 8785 (million)
% 85.34/13.69 % (13633)------------------------------
% 85.34/13.69 % (13633)------------------------------
% 85.84/13.70 % (13651)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_12937 for (2881ds/4165Mi)
% 86.24/13.83 % (13645)Instruction limit reached!
% 86.24/13.83 % (13645)------------------------------
% 86.24/13.83 % (13645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.24/13.83 % (13645)Termination reason: Unknown
% 86.24/13.83 % (13645)Termination phase: Saturation
% 86.24/13.83
% 86.24/13.83 % (13645)Memory used [KB]: 12153
% 86.24/13.83 % (13645)Time elapsed: 0.999 s
% 86.24/13.83 % (13645)Instructions burned: 3631 (million)
% 86.24/13.83 % (13645)------------------------------
% 86.24/13.83 % (13645)------------------------------
% 86.24/13.84 % (13652)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_12937 for (2880ds/13468Mi)
% 86.24/13.86 % (13637)Instruction limit reached!
% 86.24/13.86 % (13637)------------------------------
% 86.24/13.86 % (13637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.24/13.86 % (13637)Termination reason: Unknown
% 86.24/13.86 % (13637)Termination phase: Saturation
% 86.24/13.86
% 86.24/13.86 % (13637)Memory used [KB]: 23794
% 86.24/13.86 % (13637)Time elapsed: 2.498 s
% 86.24/13.86 % (13637)Instructions burned: 8382 (million)
% 86.24/13.86 % (13637)------------------------------
% 86.24/13.86 % (13637)------------------------------
% 86.24/13.87 % (13653)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_12937 for (2879ds/2635Mi)
% 88.76/14.08 % (13642)Instruction limit reached!
% 88.76/14.08 % (13642)------------------------------
% 88.76/14.08 % (13642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.76/14.08 % (13642)Termination reason: Unknown
% 88.76/14.08 % (13642)Termination phase: Saturation
% 88.76/14.08
% 88.76/14.08 % (13642)Memory used [KB]: 11001
% 88.76/14.08 % (13642)Time elapsed: 2.352 s
% 88.76/14.08 % (13642)Instructions burned: 8428 (million)
% 88.76/14.08 % (13642)------------------------------
% 88.76/14.08 % (13642)------------------------------
% 88.76/14.09 % (13648)Instruction limit reached!
% 88.76/14.09 % (13648)------------------------------
% 88.76/14.09 % (13648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.76/14.09 % (13648)Termination reason: Unknown
% 88.76/14.09 % (13648)Termination phase: Saturation
% 88.76/14.09
% 88.76/14.09 % (13648)Memory used [KB]: 14200
% 88.76/14.09 % (13648)Time elapsed: 0.970 s
% 88.76/14.09 % (13648)Instructions burned: 3205 (million)
% 88.76/14.09 % (13648)------------------------------
% 88.76/14.09 % (13648)------------------------------
% 88.76/14.09 % (13654)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_12937 for (2877ds/631Mi)
% 88.76/14.10 % (13655)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_12937 for (2877ds/15557Mi)
% 89.80/14.25 % (13654)Instruction limit reached!
% 89.80/14.25 % (13654)------------------------------
% 89.80/14.25 % (13654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.80/14.25 % (13654)Termination reason: Unknown
% 89.80/14.25 % (13654)Termination phase: Saturation
% 89.80/14.25
% 89.80/14.25 % (13654)Memory used [KB]: 8827
% 89.80/14.25 % (13654)Time elapsed: 0.164 s
% 89.80/14.25 % (13654)Instructions burned: 633 (million)
% 89.80/14.25 % (13654)------------------------------
% 89.80/14.25 % (13654)------------------------------
% 89.80/14.26 % (13658)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_12937 for (2875ds/2142Mi)
% 91.49/14.55 % (13653)First to succeed.
% 91.49/14.56 % (13653)Refutation found. Thanks to Tanya!
% 91.49/14.56 % SZS status Theorem for DTF2THF_12937
% 91.49/14.56 % SZS output start Proof for DTF2THF_12937
% 91.49/14.56 thf(type_def_5, type, option: ($tType) > $tType).
% 91.49/14.56 thf(type_def_7, type, const: $tType).
% 91.49/14.56 thf(type_def_8, type, val: ($tType * $tType * $tType) > $tType).
% 91.49/14.56 thf(type_def_9, type, expr: ($tType * $tType * $tType) > $tType).
% 91.49/14.56 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 91.49/14.56 thf(type_def_11, type, set: ($tType) > $tType).
% 91.49/14.56 thf(type_def_12, type, cntxt: ($tType * $tType * $tType) > $tType).
% 91.49/14.56 thf(type_def_13, type, r: $tType).
% 91.49/14.56 thf(type_def_14, type, l: $tType).
% 91.49/14.56 thf(type_def_15, type, v: $tType).
% 91.49/14.56 thf(type_def_16, type, sum_sum: ($tType * $tType) > $tType).
% 91.49/14.56 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 91.49/14.56 thf(func_def_1, type, sum_sum: ($tType * $tType) > $tType).
% 91.49/14.56 thf(func_def_2, type, option: ($tType) > $tType).
% 91.49/14.56 thf(func_def_3, type, const: $tType).
% 91.49/14.56 thf(func_def_4, type, cntxt: ($tType * $tType * $tType) > $tType).
% 91.49/14.56 thf(func_def_5, type, expr: ($tType * $tType * $tType) > $tType).
% 91.49/14.56 thf(func_def_6, type, val: ($tType * $tType * $tType) > $tType).
% 91.49/14.56 thf(func_def_7, type, set: ($tType) > $tType).
% 91.49/14.56 thf(func_def_8, type, v: $tType).
% 91.49/14.56 thf(func_def_9, type, r: $tType).
% 91.49/14.56 thf(func_def_10, type, l: $tType).
% 91.49/14.56 thf(func_def_11, type, type: !>[X0: $tType]:($o)).
% 91.49/14.56 thf(func_def_12, type, order: !>[X0: $tType]:($o)).
% 91.49/14.56 thf(func_def_13, type, finite_finite: !>[X0: $tType]:($o)).
% 91.49/14.56 thf(func_def_14, type, semiring_char_0: !>[X0: $tType]:($o)).
% 91.49/14.56 thf(func_def_15, type, combine: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > (X0 > option @ X1) > X0 > option @ X1)).
% 91.49/14.56 thf(func_def_16, type, f: const).
% 91.49/14.56 thf(func_def_17, type, t: const).
% 91.49/14.56 thf(func_def_18, type, unit: const).
% 91.49/14.56 thf(func_def_19, 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)).
% 91.49/14.56 thf(func_def_20, type, assign: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_21, type, ite: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_22, type, read: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_23, type, ref: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_24, type, rfork: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_25, type, rjoin: !>[X0: $tType, X1: $tType, X2: $tType]:(expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_26, type, ve: !>[X0: $tType, X1: $tType, X2: $tType]:(val @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_27, type, plug: !>[X0: $tType, X1: $tType, X2: $tType]:(cntxt @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_28, type, cv: !>[X0: $tType, X1: $tType, X2: $tType]:(const > val @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_29, type, loc: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > val @ X1 @ X0 @ X2)).
% 91.49/14.56 thf(func_def_30, type, rid: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > val @ X0 @ X1 @ X2)).
% 91.49/14.56 thf(func_def_31, 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)).
% 91.49/14.56 thf(func_def_32, 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)).
% 91.49/14.56 thf(func_def_33, 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)).
% 91.49/14.56 thf(func_def_34, 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)).
% 91.49/14.56 thf(func_def_35, 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))).
% 91.49/14.56 thf(func_def_36, 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)).
% 91.49/14.56 thf(func_def_37, type, finite_finite2: !>[X0: $tType]:(set @ X0 > $o)).
% 91.49/14.56 thf(func_def_38, type, fun_upd: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0 > X1 > X0 > X1)).
% 91.49/14.56 thf(func_def_39, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 91.49/14.56 thf(func_def_40, type, dom: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > set @ X0)).
% 91.49/14.56 thf(func_def_41, 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)).
% 91.49/14.56 thf(func_def_42, 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)).
% 91.49/14.56 thf(func_def_43, 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)).
% 91.49/14.56 thf(func_def_44, 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)).
% 91.49/14.56 thf(func_def_45, 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)).
% 91.49/14.56 thf(func_def_46, 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)).
% 91.49/14.56 thf(func_def_47, 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)).
% 91.49/14.56 thf(func_def_48, 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)).
% 91.49/14.56 thf(func_def_49, 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)).
% 91.49/14.56 thf(func_def_50, 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)).
% 91.49/14.56 thf(func_def_51, type, none: !>[X0: $tType]:(option @ X0)).
% 91.49/14.56 thf(func_def_52, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 91.49/14.56 thf(func_def_53, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 91.49/14.56 thf(func_def_54, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 91.49/14.56 thf(func_def_55, type, top_top: !>[X0: $tType]:(X0)).
% 91.49/14.56 thf(func_def_56, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 91.49/14.56 thf(func_def_57, 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)).
% 91.49/14.56 thf(func_def_58, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 91.49/14.56 thf(func_def_59, type, substitution: !>[X0: $tType, X1: $tType, X2: $tType]:((expr @ X0 @ X1 @ X2 > X2 > expr @ X0 @ X1 @ X2 > expr @ X0 @ X1 @ X2) > $o)).
% 91.49/14.56 thf(func_def_60, type, transitive_rtrancl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0)).
% 91.49/14.56 thf(func_def_61, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 91.49/14.56 thf(func_def_62, type, e: cntxt @ r @ l @ v).
% 91.49/14.56 thf(func_def_63, type, e2: cntxt @ r @ l @ v).
% 91.49/14.56 thf(func_def_64, type, sigma: l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_65, type, sigma2: l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_66, type, tau: l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_67, type, tau2: l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_68, type, e3: expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_69, type, e4: expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_70, type, left_forkee: r).
% 91.49/14.56 thf(func_def_71, type, r2: r).
% 91.49/14.56 thf(func_def_72, type, r3: r).
% 91.49/14.56 thf(func_def_73, type, right_forkee: r).
% 91.49/14.56 thf(func_def_74, 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).
% 91.49/14.56 thf(func_def_75, 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).
% 91.49/14.56 thf(func_def_76, 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).
% 91.49/14.56 thf(func_def_77, type, subst: expr @ r @ l @ v > v > expr @ r @ l @ v > expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_93, type, sP0: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > $o)).
% 91.49/14.56 thf(func_def_94, type, sP1: r > (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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) > $o).
% 91.49/14.56 thf(func_def_95, type, sP2: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > $o)).
% 91.49/14.56 thf(func_def_96, type, sK3: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > X0 > X1)).
% 91.49/14.56 thf(func_def_97, type, sK4: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_98, type, sK5: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_99, type, sK6: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > cntxt @ r @ l @ v).
% 91.49/14.56 thf(func_def_100, type, sK7: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > val @ r @ l @ v).
% 91.49/14.56 thf(func_def_101, type, sK8: !>[X0: $tType]:(X0 > set @ X0 > X0)).
% 91.49/14.56 thf(func_def_102, type, sK9: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_103, type, sK10: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_104, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_105, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_106, type, sK13: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_107, type, sK14: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_108, type, sK15: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > cntxt @ r @ l @ v).
% 91.49/14.56 thf(func_def_109, type, sK16: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > val @ r @ l @ v).
% 91.49/14.56 thf(func_def_110, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > X1 > option @ val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_111, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > X1 > option @ val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_112, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > cntxt @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_113, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_114, type, sK21: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_115, type, sK22: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_116, type, sK23: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > l).
% 91.49/14.56 thf(func_def_117, type, sK24: !>[X0: $tType]:(X0 > set @ X0 > X0)).
% 91.49/14.56 thf(func_def_118, type, sK25: !>[X0: $tType]:(set @ X0 > X0)).
% 91.49/14.56 thf(func_def_119, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > X1 > option @ val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_120, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > X1 > option @ val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_121, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > cntxt @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_122, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_123, type, sK30: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_124, type, sK31: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_125, type, sK32: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > cntxt @ r @ l @ v).
% 91.49/14.56 thf(func_def_126, type, sK33: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_127, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_128, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_129, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > X1 > option @ val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_130, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > X1 > option @ val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_131, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > cntxt @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_132, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_133, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > X1 > option @ val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_134, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > X1 > option @ val @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_135, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > cntxt @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_136, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_137, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_138, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_139, type, sK46: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_140, type, sK47: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_141, type, sK48: (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) > r).
% 91.49/14.56 thf(func_def_142, type, sK49: !>[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)).
% 91.49/14.56 thf(func_def_143, type, sK50: !>[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)).
% 91.49/14.56 thf(func_def_144, type, sK51: !>[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)).
% 91.49/14.56 thf(func_def_145, type, sK52: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_146, type, sK53: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_147, type, sK54: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 91.49/14.56 thf(func_def_148, type, sK55: !>[X0: $tType]:((option @ X0 > $o) > X0)).
% 91.49/14.56 thf(func_def_149, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_150, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_151, type, sK58: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_152, type, sK59: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_153, type, sK60: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > cntxt @ r @ l @ v).
% 91.49/14.56 thf(func_def_154, type, sK61: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r > expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_155, type, sK62: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r).
% 91.49/14.56 thf(func_def_156, type, sK63: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_157, type, sK64: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_158, type, sK65: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_159, type, sK66: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r).
% 91.49/14.56 thf(func_def_160, type, sK67: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_161, type, sK68: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_162, type, sK69: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_163, type, sK70: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X1)).
% 91.49/14.56 thf(func_def_164, type, sK71: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X0)).
% 91.49/14.56 thf(func_def_165, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2)).
% 91.49/14.56 thf(func_def_166, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ 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)).
% 91.49/14.56 thf(func_def_167, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ 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)).
% 91.49/14.56 thf(func_def_168, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_169, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2)).
% 91.49/14.56 thf(func_def_170, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ 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)).
% 91.49/14.56 thf(func_def_171, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ 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)).
% 91.49/14.56 thf(func_def_172, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_173, type, sK80: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_174, type, sK81: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_175, type, sK82: !>[X0: $tType]:(option @ X0 > X0)).
% 91.49/14.56 thf(func_def_176, type, sK83: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_177, type, sK84: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_178, type, sK85: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X1 > X1)).
% 91.49/14.56 thf(func_def_179, type, sK86: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X1 > X1 > X0)).
% 91.49/14.56 thf(func_def_180, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > option @ product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ expr @ X1 @ X2 @ X0) > X2 > X1)).
% 91.49/14.56 thf(func_def_181, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > option @ product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ expr @ X1 @ X2 @ X0) > X2 > product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ product_prod @ (X2 > option @ val @ X1 @ X2 @ X0) @ expr @ X1 @ X2 @ X0)).
% 91.49/14.56 thf(func_def_182, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X1)).
% 91.49/14.56 thf(func_def_183, type, sK90: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_184, type, sK91: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_185, type, sK92: r > (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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).
% 91.49/14.56 thf(func_def_186, type, sK93: r > (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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).
% 91.49/14.56 thf(func_def_187, type, sK94: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > option @ X0) @ product_prod @ (X1 > option @ X0) @ X1 > X1 > option @ X0)).
% 91.49/14.56 thf(func_def_188, type, sK95: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > option @ X0) @ product_prod @ (X1 > option @ X0) @ X1 > X1 > option @ X0)).
% 91.49/14.56 thf(func_def_189, type, sK96: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > option @ X0) @ product_prod @ (X1 > option @ X0) @ X1 > X1)).
% 91.49/14.56 thf(func_def_190, type, sK97: r > (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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).
% 91.49/14.56 thf(func_def_191, type, sK98: r > (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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).
% 91.49/14.56 thf(func_def_192, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2)).
% 91.49/14.56 thf(func_def_193, type, sK100: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r).
% 91.49/14.56 thf(func_def_194, type, sK101: r > (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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).
% 91.49/14.56 thf(func_def_195, type, sK102: r > (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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).
% 91.49/14.56 thf(func_def_196, type, sK103: !>[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)).
% 91.49/14.56 thf(func_def_197, type, sK104: !>[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)).
% 91.49/14.56 thf(func_def_198, type, sK105: !>[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)).
% 91.49/14.56 thf(func_def_199, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_200, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_201, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2)).
% 91.49/14.56 thf(func_def_202, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ 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)).
% 91.49/14.56 thf(func_def_203, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ 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)).
% 91.49/14.56 thf(func_def_204, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_205, type, sK112: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X0 > set @ X1 > X1)).
% 91.49/14.56 thf(func_def_206, type, sK113: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X0 > set @ X1 > X0)).
% 91.49/14.56 thf(func_def_207, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_208, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_209, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_210, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_211, type, sK118: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > X0)).
% 91.49/14.56 thf(func_def_212, type, sK119: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r).
% 91.49/14.56 thf(func_def_213, type, sK120: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_214, type, sK121: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > l > option @ val @ r @ l @ v).
% 91.49/14.56 thf(func_def_215, type, sK122: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_216, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_217, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_218, type, sK125: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_219, type, sK126: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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 > r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_220, type, sK127: !>[X0: $tType, X1: $tType]:(((X1 > X0) > $o) > X0 > X1)).
% 91.49/14.56 thf(func_def_221, type, sK128: !>[X0: $tType, X1: $tType]:(((X1 > X0) > $o) > X0 > X0)).
% 91.49/14.56 thf(func_def_222, type, sK129: !>[X0: $tType, X1: $tType]:(((X1 > X0) > $o) > X0 > X1 > X0)).
% 91.49/14.56 thf(func_def_223, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_224, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_225, type, sK132: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 91.49/14.56 thf(func_def_226, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_227, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2 > (expr @ X2 @ X1 @ X0 > X0 > expr @ X2 @ X1 @ X0 > expr @ X2 @ X1 @ X0) > X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0)).
% 91.49/14.56 thf(func_def_228, type, sK135: !>[X0: $tType]:((X0 > $o) > X0)).
% 91.49/14.56 thf(func_def_229, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0) > X2)).
% 91.49/14.56 thf(func_def_231, type, ph138: !>[X0: $tType]:(X0)).
% 91.49/14.56 thf(func_def_232, type, sK139: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ 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).
% 91.49/14.56 thf(func_def_233, type, sK140: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_234, type, sK141: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > r).
% 91.49/14.56 thf(func_def_235, type, sK142: (l > option @ val @ r @ l @ v) > cntxt @ 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) > (l > option @ val @ 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) > expr @ r @ l @ v > r).
% 91.49/14.56 thf(func_def_236, type, sK143: (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).
% 91.49/14.56 thf(func_def_237, type, sK144: (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).
% 91.49/14.56 thf(func_def_238, type, sK145: (r > option @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v) > expr @ r @ l @ v).
% 91.49/14.56 thf(func_def_239, type, sK146: (l > option @ val @ r @ l @ v) > val @ r @ l @ v > r > (l > option @ val @ 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) > cntxt @ r @ l @ v > l).
% 91.49/14.56 thf(f3364,plain,(
% 91.49/14.56 $false),
% 91.49/14.56 inference(subsumption_resolution,[status(thm)],[f1229,f1915])).
% 91.49/14.56 thf(f1915,plain,(
% 91.49/14.56 ( ! [X0 : product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v] : (((s_1 @ r3) != (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ X0))) )),
% 91.49/14.56 inference(trivial_inequality_removal,[status(thm)],[f1901])).
% 91.49/14.56 thf(f1901,plain,(
% 91.49/14.56 ( ! [X0 : product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v] : (((s_1 @ r3) != (some @ product_prod @ (l > option @ val @ r @ l @ v) @ product_prod @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ X0)) | ($true != $true)) )),
% 91.49/14.56 inference(superposition,[status(thm)],[f1669,f1516])).
% 91.49/14.56 thf(f1516,plain,(
% 91.49/14.56 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0,X4 : X2,X5 : product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0] : (((X3 @ X4) != (some @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0 @ X5)) | ((member @ X2 @ X4 @ (rID_G @ X2 @ X1 @ X0 @ X3)) = $true)) )),
% 91.49/14.56 inference(cnf_transformation,[status(thm)],[f782])).
% 91.49/14.56 thf(f782,plain,(
% 91.49/14.56 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0,X4 : X2,X5 : product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0] : (((member @ X2 @ X4 @ (rID_G @ X2 @ X1 @ X0 @ X3)) = $true) | ((X3 @ X4) != (some @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0 @ X5)))),
% 91.49/14.56 inference(ennf_transformation,[status(thm)],[f448])).
% 91.49/14.56 thf(f448,plain,(
% 91.49/14.56 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0,X4 : X2,X5 : product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0] : (((X3 @ X4) = (some @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0 @ X5)) => ((member @ X2 @ X4 @ (rID_G @ X2 @ X1 @ X0 @ X3)) = $true))),
% 91.49/14.56 inference(fool_elimination,[status(thm)],[f447])).
% 91.49/14.56 thf(f447,plain,(
% 91.49/14.56 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > option @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0,X4 : X2,X5 : product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0] : (((X3 @ X4) = (some @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ product_prod @ (X1 > option @ val @ X2 @ X1 @ X0) @ expr @ X2 @ X1 @ X0 @ X5)) => (member @ X2 @ X4 @ (rID_G @ X2 @ X1 @ X0 @ X3)))),
% 91.49/14.56 inference(rectify,[status(thm)],[f23])).
% 91.49/14.56 thf(f23,axiom,(
% 91.49/14.56 ! [X29 : $tType,X0 : $tType,X1 : $tType,X7 : X1 > option @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X29) @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X29) @ expr @ X1 @ X0 @ X29,X6 : X1,X30 : product_prod @ (X0 > option @ val @ X1 @ X0 @ X29) @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X29) @ expr @ X1 @ X0 @ X29] : (((X7 @ X6) = (some @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X29) @ product_prod @ (X0 > option @ val @ X1 @ X0 @ X29) @ expr @ X1 @ X0 @ X29 @ X30)) => (member @ X1 @ X6 @ (rID_G @ X1 @ X0 @ X29 @ X7)))),
% 91.49/14.56 file('/export/starexec/sandbox/tmp/tmp.ZhcMuhrmrf/DTF2THF_12937.p',fact_22_RID_092_060_094sub_062GI_I1_J)).
% 91.49/14.56 thf(f1669,plain,(
% 91.49/14.56 ($true != (member @ r @ r3 @ (rID_G @ r @ l @ v @ s_1)))),
% 91.49/14.56 inference(definition_unfolding,[status(thm)],[f1534,f1351])).
% 91.49/14.56 thf(f1351,plain,(
% 91.49/14.56 (right_forkee = r3)),
% 91.49/14.56 inference(cnf_transformation,[status(thm)],[f767])).
% 91.49/14.56 thf(f767,plain,(
% 91.49/14.56 (right_forkee = r3)),
% 91.49/14.56 inference(flattening,[status(thm)],[f269])).
% 91.49/14.56 thf(f269,negated_conjecture,(
% 91.49/14.56 ~(right_forkee != r3)),
% 91.49/14.56 inference(negated_conjecture,[status(cth)],[f268])).
% 91.49/14.56 thf(f268,conjecture,(
% 91.49/14.56 (right_forkee != r3)),
% 91.49/14.56 file('/export/starexec/sandbox/tmp/tmp.ZhcMuhrmrf/DTF2THF_12937.p',conj_0)).
% 91.49/14.56 thf(f1534,plain,(
% 91.49/14.56 ((member @ r @ right_forkee @ (rID_G @ r @ l @ v @ s_1)) != $true)),
% 91.49/14.56 inference(cnf_transformation,[status(thm)],[f726])).
% 91.49/14.56 thf(f726,plain,(
% 91.49/14.56 ((member @ r @ right_forkee @ (rID_G @ r @ l @ v @ s_1)) != $true)),
% 91.49/14.56 inference(flattening,[status(thm)],[f480])).
% 91.49/14.56 thf(f480,plain,(
% 91.49/14.56 ~((member @ r @ right_forkee @ (rID_G @ r @ l @ v @ s_1)) = $true)),
% 91.49/14.56 inference(fool_elimination,[status(thm)],[f479])).
% 91.49/14.56 thf(f479,plain,(
% 91.49/14.56 ~(member @ r @ right_forkee @ (rID_G @ r @ l @ v @ s_1))),
% 91.49/14.56 inference(rectify,[status(thm)],[f1])).
% 91.49/14.56 thf(f1,axiom,(
% 91.49/14.56 ~(member @ r @ right_forkee @ (rID_G @ r @ l @ v @ s_1))),
% 91.49/14.56 file('/export/starexec/sandbox/tmp/tmp.ZhcMuhrmrf/DTF2THF_12937.p',fact_0_local_Ofork_I3_J)).
% 91.49/14.56 thf(f1229,plain,(
% 91.49/14.56 ((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 @ sigma2 @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau2 @ (plug @ r @ l @ v @ e2 @ (rfork @ r @ l @ v @ e4))))))),
% 91.49/14.56 inference(cnf_transformation,[status(thm)],[f7])).
% 91.49/14.56 thf(f7,axiom,(
% 91.49/14.56 ((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 @ sigma2 @ (product_Pair @ (l > option @ val @ r @ l @ v) @ expr @ r @ l @ v @ tau2 @ (plug @ r @ l @ v @ e2 @ (rfork @ r @ l @ v @ e4))))))),
% 91.49/14.56 file('/export/starexec/sandbox/tmp/tmp.ZhcMuhrmrf/DTF2THF_12937.p',fact_6_local_Ofork_I2_J)).
% 91.49/14.56 % SZS output end Proof for DTF2THF_12937
% 91.49/14.56 % (13653)------------------------------
% 91.49/14.56 % (13653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.49/14.56 % (13653)Termination reason: Refutation
% 91.49/14.56
% 91.49/14.56 % (13653)Memory used [KB]: 14711
% 91.49/14.56 % (13653)Time elapsed: 0.687 s
% 91.49/14.56 % (13653)Instructions burned: 2484 (million)
% 91.49/14.56 % (13653)------------------------------
% 91.49/14.56 % (13653)------------------------------
% 91.49/14.56 % (13154)Success in time 12.709 s
%------------------------------------------------------------------------------