%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM160^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 08:41:47 AM UTC 2026
% Result : Theorem 2.43s 1.34s
% Output : Refutation 2.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : COM160^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 04:15:30 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : COM160^1 : TPTP v9.2.1. Released v7.0.0.
% 0.07/0.32 % Domain : Computing Theory
% 0.07/0.32 % Problem : Abstract completeness 317
% 0.07/0.32 % Version : [Bla16] axioms : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [BPT14] Blanchette et al. (2014), Abstract Completeness
% 0.07/0.32 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.07/0.32 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bla16]
% 0.07/0.32 % Names : abstract_completeness__317.p [Bla16]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.07/0.32 % Syntax : Number of formulae : 365 ( 132 unt; 65 typ; 0 def)
% 0.07/0.32 % Number of atoms : 824 ( 205 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 13 ( 2 avg)
% 0.07/0.32 % Number of connectives : 5149 ( 60 ~; 6 |; 68 &;4631 @)
% 0.07/0.32 % ( 0 <=>; 384 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 28 ( 9 avg)
% 0.07/0.32 % Number of types : 4 ( 3 usr)
% 0.07/0.32 % Number of type conns : 327 ( 327 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 65 ( 62 usr; 8 con; 0-6 aty)
% 0.07/0.32 % Number of variables : 1224 ( 65 ^;1058 !; 36 ?;1224 :)
% 0.07/0.32 % ( 65 !>; 0 ?*; 0 @-; 0 @+)
% 0.07/0.32 % SPC : TH1_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.07/0.32 % 2016-07-13 14:54:49.610
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 %----Could-be-implicit typings (9)
% 0.07/0.32 thf(ty_t_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree,type,
% 0.07/0.32 abstra2103299360e_tree: $tType > $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_Product__Type_Oprod,type,
% 0.07/0.32 product_prod: $tType > $tType > $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_Stream_Ostream,type,
% 0.07/0.32 stream: $tType > $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_FSet_Ofset,type,
% 0.07/0.32 fset: $tType > $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_Set_Oset,type,
% 0.07/0.32 set: $tType > $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_Nat_Onat,type,
% 0.07/0.32 nat: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_tf_state,type,
% 0.07/0.32 state: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_itself,type,
% 0.07/0.32 itself: $tType > $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_tf_rule,type,
% 0.07/0.32 rule: $tType ).
% 0.07/0.32
% 0.07/0.32 %----Explicit typings (56)
% 0.07/0.32 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.07/0.32 finite_finite:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_HOL_Otype,type,
% 0.07/0.32 type:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Obot,type,
% 0.07/0.32 bot:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Oord,type,
% 0.07/0.32 ord:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Oorder,type,
% 0.07/0.32 order:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Olinorder,type,
% 0.07/0.32 linorder:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Opreorder,type,
% 0.07/0.32 preorder:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Countable_Ocountable,type,
% 0.07/0.32 countable:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.07/0.32 order_bot:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Owellorder,type,
% 0.07/0.32 wellorder:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem,type,
% 0.07/0.32 abstra1326562878System:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( set @ State ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_OminWait,type,
% 0.07/0.32 abstra1332369113inWait:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > State > nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_Oper,type,
% 0.07/0.32 abstra2096684367le_per:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( set @ State ) > Rule > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_Opos,type,
% 0.07/0.32 abstra2097340358le_pos:
% 0.07/0.32 !>[A: $tType] : ( ( stream @ A ) > A > nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OSaturated,type,
% 0.07/0.32 abstra1209608345urated:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( stream @ ( product_prod @ State @ Rule ) ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Oenabled,type,
% 0.07/0.32 abstra1874422341nabled:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > Rule > State > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Oepath,type,
% 0.07/0.32 abstra523868654_epath:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( stream @ ( product_prod @ State @ Rule ) ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Ofair,type,
% 0.07/0.32 abstra928354080m_fair:
% 0.07/0.32 !>[Rule: $tType] : ( ( stream @ Rule ) > ( stream @ Rule ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Ofenum,type,
% 0.07/0.32 abstra1774373515_fenum:
% 0.07/0.32 !>[Rule: $tType] : ( ( stream @ Rule ) > ( stream @ Rule ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OmkTree,type,
% 0.07/0.32 abstra1225283448mkTree:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > State > ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OpickEff,type,
% 0.07/0.32 abstra1276541928ickEff:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > Rule > State > ( fset @ State ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Osaturated,type,
% 0.07/0.32 abstra726722745urated:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > Rule > ( stream @ ( product_prod @ State @ Rule ) ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Otrim,type,
% 0.07/0.32 abstra1259602206m_trim:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > State > ( stream @ Rule ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Owf,type,
% 0.07/0.32 abstra1874736267tem_wf:
% 0.07/0.32 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Oipath,type,
% 0.07/0.32 abstra313004635_ipath:
% 0.07/0.32 !>[A: $tType] : ( ( abstra2103299360e_tree @ A ) > ( stream @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_ONode,type,
% 0.07/0.32 abstra388494275e_Node:
% 0.07/0.32 !>[A: $tType] : ( A > ( fset @ ( abstra2103299360e_tree @ A ) ) > ( abstra2103299360e_tree @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_Ocont,type,
% 0.07/0.32 abstra1749095923e_cont:
% 0.07/0.32 !>[A: $tType] : ( ( abstra2103299360e_tree @ A ) > ( fset @ ( abstra2103299360e_tree @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_Oroot,type,
% 0.07/0.32 abstra573067619e_root:
% 0.07/0.32 !>[A: $tType] : ( ( abstra2103299360e_tree @ A ) > A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Countable__Set_Ocountable,type,
% 0.07/0.32 countable_countable:
% 0.07/0.32 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_FSet_Ofimage,type,
% 0.07/0.32 fimage:
% 0.07/0.32 !>[A: $tType,B: $tType] : ( ( A > B ) > ( fset @ A ) > ( fset @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_FSet_Ofmember,type,
% 0.07/0.32 fmember:
% 0.07/0.32 !>[A: $tType] : ( A > ( fset @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.07/0.32 minus_minus:
% 0.07/0.32 !>[A: $tType] : ( A > A > A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_If,type,
% 0.07/0.32 if:
% 0.07/0.32 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.07/0.32 bot_bot:
% 0.07/0.32 !>[A: $tType] : A ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_OLeast,type,
% 0.07/0.32 ord_Least:
% 0.07/0.32 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.07/0.32 ord_less_eq:
% 0.07/0.32 !>[A: $tType] : ( A > A > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Product__Type_OPair,type,
% 0.07/0.32 product_Pair:
% 0.07/0.32 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 0.07/0.32 product_fst:
% 0.07/0.32 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 0.07/0.32 product_snd:
% 0.07/0.32 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Pure_Otype,type,
% 0.07/0.32 type2:
% 0.07/0.32 !>[A: $tType] : ( itself @ A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set_OCollect,type,
% 0.07/0.32 collect:
% 0.07/0.32 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set_Oinsert,type,
% 0.07/0.32 insert:
% 0.07/0.32 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Stream_Osdrop,type,
% 0.07/0.32 sdrop:
% 0.07/0.32 !>[A: $tType] : ( nat > ( stream @ A ) > ( stream @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Stream_Osdrop__while,type,
% 0.07/0.32 sdrop_while:
% 0.07/0.32 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > ( stream @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Stream_Ostream_Ocase__stream,type,
% 0.07/0.32 case_stream:
% 0.07/0.32 !>[A: $tType,B: $tType] : ( ( A > ( stream @ A ) > B ) > ( stream @ A ) > B ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Stream_Ostream_Oshd,type,
% 0.07/0.32 shd:
% 0.07/0.32 !>[A: $tType] : ( ( stream @ A ) > A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Stream_Ostream_Osset,type,
% 0.07/0.32 sset:
% 0.07/0.32 !>[A: $tType] : ( ( stream @ A ) > ( set @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Stream_Ostream_Ostl,type,
% 0.07/0.32 stl:
% 0.07/0.32 !>[A: $tType] : ( ( stream @ A ) > ( stream @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member,type,
% 0.07/0.32 member:
% 0.07/0.32 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_S,type,
% 0.07/0.32 s: set @ state ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_eff,type,
% 0.07/0.32 eff: rule > state > ( fset @ state ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_r,type,
% 0.07/0.32 r: rule ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_rules,type,
% 0.07/0.32 rules: stream @ rule ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_steps,type,
% 0.07/0.32 steps: stream @ ( product_prod @ state @ rule ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_stepsa____,type,
% 0.07/0.32 stepsa: stream @ ( product_prod @ state @ rule ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_thesis____,type,
% 0.07/0.32 thesis: $o ).
% 0.07/0.32
% 0.07/0.32 %----Relevant facts (256)
% 0.07/0.32 thf(fact_0_calculation_I1_J,axiom,
% 0.07/0.32 member @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ s ).
% 0.07/0.32
% 0.07/0.32 % calculation(1)
% 0.07/0.32 thf(fact_1_calculation_I3_J,axiom,
% 0.07/0.32 ( ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) )
% 0.07/0.32 != r ) ).
% 0.07/0.32
% 0.07/0.32 % calculation(3)
% 0.07/0.32 thf(fact_2_e,axiom,
% 0.07/0.32 ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ steps )
% 0.07/0.32 & ( member @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ steps ) ) @ s ) ) ).
% 0.07/0.32
% 0.07/0.32 % e
% 0.07/0.32 thf(fact_3_calculation_I2_J,axiom,
% 0.07/0.32 abstra1874422341nabled @ rule @ state @ eff @ r @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) ).
% 0.07/0.32
% 0.07/0.32 % calculation(2)
% 0.07/0.32 thf(fact_4_enabled__def,axiom,
% 0.07/0.32 ! [R: rule,S: state] :
% 0.07/0.32 ( ( abstra1874422341nabled @ rule @ state @ eff @ R @ S )
% 0.07/0.32 = ( ^ [P: ( fset @ state ) > $o] :
% 0.07/0.32 ? [X: fset @ state] : ( P @ X )
% 0.07/0.32 @ ( eff @ R @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % enabled_def
% 0.07/0.32 thf(fact_5_epath_Ocases,axiom,
% 0.07/0.32 ! [A2: stream @ ( product_prod @ state @ rule )] :
% 0.07/0.32 ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ A2 )
% 0.07/0.32 => ~ ( ( member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ A2 ) ) @ ( sset @ rule @ rules ) )
% 0.07/0.32 => ! [Sl: fset @ state] :
% 0.07/0.32 ( ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ A2 ) ) ) @ Sl )
% 0.07/0.32 => ( ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ A2 ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ A2 ) ) @ Sl )
% 0.07/0.32 => ~ ( abstra523868654_epath @ rule @ state @ eff @ rules @ ( stl @ ( product_prod @ state @ rule ) @ A2 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % epath.cases
% 0.07/0.32 thf(fact_6_epath_Ocoinduct,axiom,
% 0.07/0.32 ! [X2: ( stream @ ( product_prod @ state @ rule ) ) > $o,X3: stream @ ( product_prod @ state @ rule )] :
% 0.07/0.32 ( ( X2 @ X3 )
% 0.07/0.32 => ( ! [X4: stream @ ( product_prod @ state @ rule )] :
% 0.07/0.32 ( ( X2 @ X4 )
% 0.07/0.32 => ? [Steps: stream @ ( product_prod @ state @ rule ),Sl2: fset @ state] :
% 0.07/0.32 ( ( X4 = Steps )
% 0.07/0.32 & ( member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps ) ) @ ( sset @ rule @ rules ) )
% 0.07/0.32 & ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ Steps ) ) ) @ Sl2 )
% 0.07/0.32 & ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps ) ) @ Sl2 )
% 0.07/0.32 & ( ( X2 @ ( stl @ ( product_prod @ state @ rule ) @ Steps ) )
% 0.07/0.32 | ( abstra523868654_epath @ rule @ state @ eff @ rules @ ( stl @ ( product_prod @ state @ rule ) @ Steps ) ) ) ) )
% 0.07/0.32 => ( abstra523868654_epath @ rule @ state @ eff @ rules @ X3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % epath.coinduct
% 0.07/0.32 thf(fact_7_epath_Ointros,axiom,
% 0.07/0.32 ! [Steps2: stream @ ( product_prod @ state @ rule ),Sl3: fset @ state] :
% 0.07/0.32 ( ( member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps2 ) ) @ ( sset @ rule @ rules ) )
% 0.07/0.32 => ( ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ Steps2 ) ) ) @ Sl3 )
% 0.07/0.32 => ( ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps2 ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps2 ) ) @ Sl3 )
% 0.07/0.32 => ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ ( stl @ ( product_prod @ state @ rule ) @ Steps2 ) )
% 0.07/0.32 => ( abstra523868654_epath @ rule @ state @ eff @ rules @ Steps2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % epath.intros
% 0.07/0.32 thf(fact_8_epath_Osimps,axiom,
% 0.07/0.32 ! [A2: stream @ ( product_prod @ state @ rule )] :
% 0.07/0.32 ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ A2 )
% 0.07/0.32 = ( ? [Steps3: stream @ ( product_prod @ state @ rule ),Sl4: fset @ state] :
% 0.07/0.32 ( ( A2 = Steps3 )
% 0.07/0.32 & ( member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps3 ) ) @ ( sset @ rule @ rules ) )
% 0.07/0.32 & ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ Steps3 ) ) ) @ Sl4 )
% 0.07/0.32 & ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps3 ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps3 ) ) @ Sl4 )
% 0.07/0.32 & ( abstra523868654_epath @ rule @ state @ eff @ rules @ ( stl @ ( product_prod @ state @ rule ) @ Steps3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % epath.simps
% 0.07/0.32 thf(fact_9_stream_Oexpand,axiom,
% 0.07/0.32 ! [A: $tType,Stream: stream @ A,Stream2: stream @ A] :
% 0.07/0.32 ( ( ( ( shd @ A @ Stream )
% 0.07/0.32 = ( shd @ A @ Stream2 ) )
% 0.07/0.32 & ( ( stl @ A @ Stream )
% 0.07/0.32 = ( stl @ A @ Stream2 ) ) )
% 0.07/0.32 => ( Stream = Stream2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % stream.expand
% 0.07/0.32 thf(fact_10_stream_Ocoinduct,axiom,
% 0.07/0.32 ! [A: $tType,R2: ( stream @ A ) > ( stream @ A ) > $o,Stream: stream @ A,Stream2: stream @ A] :
% 0.07/0.32 ( ( R2 @ Stream @ Stream2 )
% 0.07/0.32 => ( ! [Stream3: stream @ A,Stream4: stream @ A] :
% 0.07/0.32 ( ( R2 @ Stream3 @ Stream4 )
% 0.07/0.32 => ( ( ( shd @ A @ Stream3 )
% 0.07/0.32 = ( shd @ A @ Stream4 ) )
% 0.07/0.32 & ( R2 @ ( stl @ A @ Stream3 ) @ ( stl @ A @ Stream4 ) ) ) )
% 0.07/0.32 => ( Stream = Stream2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % stream.coinduct
% 0.07/0.32 thf(fact_11_stream_Ocoinduct__strong,axiom,
% 0.07/0.32 ! [A: $tType,R2: ( stream @ A ) > ( stream @ A ) > $o,Stream: stream @ A,Stream2: stream @ A] :
% 0.07/0.32 ( ( R2 @ Stream @ Stream2 )
% 0.07/0.32 => ( ! [Stream3: stream @ A,Stream4: stream @ A] :
% 0.07/0.32 ( ( R2 @ Stream3 @ Stream4 )
% 0.07/0.32 => ( ( ( shd @ A @ Stream3 )
% 0.07/0.32 = ( shd @ A @ Stream4 ) )
% 0.07/0.32 & ( ( R2 @ ( stl @ A @ Stream3 ) @ ( stl @ A @ Stream4 ) )
% 0.07/0.32 | ( ( stl @ A @ Stream3 )
% 0.07/0.32 = ( stl @ A @ Stream4 ) ) ) ) )
% 0.07/0.32 => ( Stream = Stream2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % stream.coinduct_strong
% 0.07/0.32 thf(fact_12_RuleSystem__axioms,axiom,
% 0.07/0.32 abstra1326562878System @ rule @ state @ eff @ rules @ s ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_axioms
% 0.07/0.32 thf(fact_13_prod__eqI,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,P2: product_prod @ A @ B,Q: product_prod @ A @ B] :
% 0.07/0.32 ( ( ( product_fst @ A @ B @ P2 )
% 0.07/0.32 = ( product_fst @ A @ B @ Q ) )
% 0.07/0.32 => ( ( ( product_snd @ A @ B @ P2 )
% 0.07/0.32 = ( product_snd @ A @ B @ Q ) )
% 0.07/0.32 => ( P2 = Q ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_eqI
% 0.07/0.32 thf(fact_14_p,axiom,
% 0.07/0.32 abstra2096684367le_per @ rule @ state @ eff @ rules @ s @ r ).
% 0.07/0.32
% 0.07/0.32 % p
% 0.07/0.32 thf(fact_15_enabled__R,axiom,
% 0.07/0.32 ! [S: state] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ? [X4: rule] :
% 0.07/0.32 ( ( member @ rule @ X4 @ ( sset @ rule @ rules ) )
% 0.07/0.32 & ? [X1: fset @ state] : ( eff @ X4 @ S @ X1 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % enabled_R
% 0.07/0.32 thf(fact_16_calculation_I4_J,axiom,
% 0.07/0.32 member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ ( sset @ rule @ rules ) ).
% 0.07/0.32
% 0.07/0.32 % calculation(4)
% 0.07/0.32 thf(fact_17_eff__S,axiom,
% 0.07/0.32 ! [S: state,R: rule,Sl3: fset @ state,S2: state] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( member @ rule @ R @ ( sset @ rule @ rules ) )
% 0.07/0.32 => ( ( eff @ R @ S @ Sl3 )
% 0.07/0.32 => ( ( fmember @ state @ S2 @ Sl3 )
% 0.07/0.32 => ( member @ state @ S2 @ s ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eff_S
% 0.07/0.32 thf(fact_18_sset__fenum,axiom,
% 0.07/0.32 ( ( sset @ rule @ ( abstra1774373515_fenum @ rule @ rules ) )
% 0.07/0.32 = ( sset @ rule @ rules ) ) ).
% 0.07/0.32
% 0.07/0.32 % sset_fenum
% 0.07/0.32 thf(fact_19_pickEff,axiom,
% 0.07/0.32 ! [R: rule,S: state] :
% 0.07/0.32 ( ( abstra1874422341nabled @ rule @ state @ eff @ R @ S )
% 0.07/0.32 => ( eff @ R @ S @ ( abstra1276541928ickEff @ rule @ state @ eff @ R @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pickEff
% 0.07/0.32 thf(fact_20_RuleSystem_Oenabled__R,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ? [X4: Rule] :
% 0.07/0.32 ( ( member @ Rule @ X4 @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 & ? [X1: fset @ State] : ( Eff @ X4 @ S @ X1 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.enabled_R
% 0.07/0.32 thf(fact_21_RuleSystem__Defs_Oenabled__def,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType] :
% 0.07/0.32 ( ( abstra1874422341nabled @ Rule @ State )
% 0.07/0.32 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,R3: Rule,S4: State] :
% 0.07/0.32 ( ^ [P: ( fset @ State ) > $o] :
% 0.07/0.32 ? [X: fset @ State] : ( P @ X )
% 0.07/0.32 @ ( Eff2 @ R3 @ S4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.enabled_def
% 0.07/0.32 thf(fact_22_RuleSystem_Ointro,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,S3: set @ State,Rules: stream @ Rule,Eff: Rule > State > ( fset @ State ) > $o] :
% 0.07/0.32 ( ! [S5: State] :
% 0.07/0.32 ( ( member @ State @ S5 @ S3 )
% 0.07/0.32 => ! [R4: Rule] :
% 0.07/0.32 ( ( member @ Rule @ R4 @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 => ! [Sl: fset @ State] :
% 0.07/0.32 ( ( Eff @ R4 @ S5 @ Sl )
% 0.07/0.32 => ! [S6: State] :
% 0.07/0.32 ( ( fmember @ State @ S6 @ Sl )
% 0.07/0.32 => ( member @ State @ S6 @ S3 ) ) ) ) )
% 0.07/0.32 => ( ! [S5: State] :
% 0.07/0.32 ( ( member @ State @ S5 @ S3 )
% 0.07/0.32 => ? [X5: Rule] :
% 0.07/0.32 ( ( member @ Rule @ X5 @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 & ? [X12: fset @ State] : ( Eff @ X5 @ S5 @ X12 ) ) )
% 0.07/0.32 => ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.intro
% 0.07/0.32 thf(fact_23_RuleSystem_Oeff__S,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,R: Rule,Sl3: fset @ State,S2: State] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( member @ Rule @ R @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 => ( ( Eff @ R @ S @ Sl3 )
% 0.07/0.32 => ( ( fmember @ State @ S2 @ Sl3 )
% 0.07/0.32 => ( member @ State @ S2 @ S3 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.eff_S
% 0.07/0.32 thf(fact_24_RuleSystem__def,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State )
% 0.07/0.32 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rules2: stream @ Rule,S7: set @ State] :
% 0.07/0.32 ( ! [S4: State] :
% 0.07/0.32 ( ( member @ State @ S4 @ S7 )
% 0.07/0.32 => ! [R3: Rule] :
% 0.07/0.32 ( ( member @ Rule @ R3 @ ( sset @ Rule @ Rules2 ) )
% 0.07/0.32 => ! [Sl4: fset @ State] :
% 0.07/0.32 ( ( Eff2 @ R3 @ S4 @ Sl4 )
% 0.07/0.32 => ! [S8: State] :
% 0.07/0.32 ( ( fmember @ State @ S8 @ Sl4 )
% 0.07/0.32 => ( member @ State @ S8 @ S7 ) ) ) ) )
% 0.07/0.32 & ! [S4: State] :
% 0.07/0.32 ( ( member @ State @ S4 @ S7 )
% 0.07/0.32 => ? [X6: Rule] :
% 0.07/0.32 ( ( member @ Rule @ X6 @ ( sset @ Rule @ Rules2 ) )
% 0.07/0.32 & ( ^ [P: ( fset @ State ) > $o] :
% 0.07/0.32 ? [X: fset @ State] : ( P @ X )
% 0.07/0.32 @ ( Eff2 @ X6 @ S4 ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_def
% 0.07/0.32 thf(fact_25_stl__sset,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,A2: stream @ A] :
% 0.07/0.32 ( ( member @ A @ X3 @ ( sset @ A @ ( stl @ A @ A2 ) ) )
% 0.07/0.32 => ( member @ A @ X3 @ ( sset @ A @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % stl_sset
% 0.07/0.32 thf(fact_26_shd__sset,axiom,
% 0.07/0.32 ! [A: $tType,A2: stream @ A] : ( member @ A @ ( shd @ A @ A2 ) @ ( sset @ A @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % shd_sset
% 0.07/0.32 thf(fact_27_sset__induct,axiom,
% 0.07/0.32 ! [A: $tType,Y: A,S: stream @ A,P3: A > ( stream @ A ) > $o] :
% 0.07/0.32 ( ( member @ A @ Y @ ( sset @ A @ S ) )
% 0.07/0.32 => ( ! [S5: stream @ A] : ( P3 @ ( shd @ A @ S5 ) @ S5 )
% 0.07/0.32 => ( ! [S5: stream @ A,Y2: A] :
% 0.07/0.32 ( ( member @ A @ Y2 @ ( sset @ A @ ( stl @ A @ S5 ) ) )
% 0.07/0.32 => ( ( P3 @ Y2 @ ( stl @ A @ S5 ) )
% 0.07/0.32 => ( P3 @ Y2 @ S5 ) ) )
% 0.07/0.32 => ( P3 @ Y @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sset_induct
% 0.07/0.32 thf(fact_28_RuleSystem__Defs_Oepath_Ocoinduct,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,X2: ( stream @ ( product_prod @ State @ Rule ) ) > $o,X3: stream @ ( product_prod @ State @ Rule ),Rules: stream @ Rule,Eff: Rule > State > ( fset @ State ) > $o] :
% 0.07/0.32 ( ( X2 @ X3 )
% 0.07/0.32 => ( ! [X4: stream @ ( product_prod @ State @ Rule )] :
% 0.07/0.32 ( ( X2 @ X4 )
% 0.07/0.32 => ? [Steps: stream @ ( product_prod @ State @ Rule ),Sl2: fset @ State] :
% 0.07/0.32 ( ( X4 = Steps )
% 0.07/0.32 & ( member @ Rule @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps ) ) @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 & ( fmember @ State @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ ( stl @ ( product_prod @ State @ Rule ) @ Steps ) ) ) @ Sl2 )
% 0.07/0.32 & ( Eff @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps ) ) @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps ) ) @ Sl2 )
% 0.07/0.32 & ( ( X2 @ ( stl @ ( product_prod @ State @ Rule ) @ Steps ) )
% 0.07/0.32 | ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ ( stl @ ( product_prod @ State @ Rule ) @ Steps ) ) ) ) )
% 0.07/0.32 => ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ X3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.epath.coinduct
% 0.07/0.32 thf(fact_29_RuleSystem__Defs_Oepath_Ointros,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Steps2: stream @ ( product_prod @ State @ Rule ),Rules: stream @ Rule,Sl3: fset @ State,Eff: Rule > State > ( fset @ State ) > $o] :
% 0.07/0.32 ( ( member @ Rule @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps2 ) ) @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 => ( ( fmember @ State @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ ( stl @ ( product_prod @ State @ Rule ) @ Steps2 ) ) ) @ Sl3 )
% 0.07/0.32 => ( ( Eff @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps2 ) ) @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps2 ) ) @ Sl3 )
% 0.07/0.32 => ( ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ ( stl @ ( product_prod @ State @ Rule ) @ Steps2 ) )
% 0.07/0.32 => ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ Steps2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.epath.intros
% 0.07/0.32 thf(fact_30_RuleSystem__Defs_Oepath_Osimps,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType] :
% 0.07/0.32 ( ( abstra523868654_epath @ Rule @ State )
% 0.07/0.32 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rules2: stream @ Rule,A3: stream @ ( product_prod @ State @ Rule )] :
% 0.07/0.32 ? [Steps3: stream @ ( product_prod @ State @ Rule ),Sl4: fset @ State] :
% 0.07/0.32 ( ( A3 = Steps3 )
% 0.07/0.32 & ( member @ Rule @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps3 ) ) @ ( sset @ Rule @ Rules2 ) )
% 0.07/0.32 & ( fmember @ State @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ ( stl @ ( product_prod @ State @ Rule ) @ Steps3 ) ) ) @ Sl4 )
% 0.07/0.32 & ( Eff2 @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps3 ) ) @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps3 ) ) @ Sl4 )
% 0.07/0.32 & ( abstra523868654_epath @ Rule @ State @ Eff2 @ Rules2 @ ( stl @ ( product_prod @ State @ Rule ) @ Steps3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.epath.simps
% 0.07/0.32 thf(fact_31_RuleSystem__Defs_Oepath_Ocases,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,A2: stream @ ( product_prod @ State @ Rule )] :
% 0.07/0.32 ( ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ A2 )
% 0.07/0.32 => ~ ( ( member @ Rule @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ A2 ) ) @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 => ! [Sl: fset @ State] :
% 0.07/0.32 ( ( fmember @ State @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ ( stl @ ( product_prod @ State @ Rule ) @ A2 ) ) ) @ Sl )
% 0.07/0.32 => ( ( Eff @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ A2 ) ) @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ A2 ) ) @ Sl )
% 0.07/0.32 => ~ ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ ( stl @ ( product_prod @ State @ Rule ) @ A2 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.epath.cases
% 0.07/0.32 thf(fact_32_prod__eq__iff,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( ^ [Y3: product_prod @ A @ B,Z: product_prod @ A @ B] : ( Y3 = Z ) )
% 0.07/0.32 = ( ^ [S4: product_prod @ A @ B,T: product_prod @ A @ B] :
% 0.07/0.32 ( ( ( product_fst @ A @ B @ S4 )
% 0.07/0.32 = ( product_fst @ A @ B @ T ) )
% 0.07/0.32 & ( ( product_snd @ A @ B @ S4 )
% 0.07/0.32 = ( product_snd @ A @ B @ T ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_eq_iff
% 0.07/0.32 thf(fact_33_prod_Oexpand,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 0.07/0.32 ( ( ( ( product_fst @ A @ B @ Prod )
% 0.07/0.32 = ( product_fst @ A @ B @ Prod2 ) )
% 0.07/0.32 & ( ( product_snd @ A @ B @ Prod )
% 0.07/0.32 = ( product_snd @ A @ B @ Prod2 ) ) )
% 0.07/0.32 => ( Prod = Prod2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod.expand
% 0.07/0.32 thf(fact_34_Saturated__def,axiom,
% 0.07/0.32 ! [Steps2: stream @ ( product_prod @ state @ rule )] :
% 0.07/0.32 ( ( abstra1209608345urated @ rule @ state @ eff @ rules @ Steps2 )
% 0.07/0.32 = ( ! [X6: rule] :
% 0.07/0.32 ( ( member @ rule @ X6 @ ( sset @ rule @ rules ) )
% 0.07/0.32 => ( abstra726722745urated @ rule @ state @ eff @ X6 @ Steps2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Saturated_def
% 0.07/0.32 thf(fact_35_local_Oalw,axiom,
% 0.07/0.32 ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ stepsa )
% 0.07/0.32 & ( member @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ s ) ) ).
% 0.07/0.32
% 0.07/0.32 % local.alw
% 0.07/0.32 thf(fact_36_NE__R,axiom,
% 0.07/0.32 ( ( sset @ rule @ rules )
% 0.07/0.32 != ( bot_bot @ ( set @ rule ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % NE_R
% 0.07/0.32 thf(fact_37_fair__stl,axiom,
% 0.07/0.32 ! [Rs: stream @ rule] :
% 0.07/0.32 ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( abstra928354080m_fair @ rule @ rules @ ( stl @ rule @ Rs ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fair_stl
% 0.07/0.32 thf(fact_38_exE__realizer_H,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P3: A > B > $o,P2: product_prod @ B @ A] :
% 0.07/0.32 ( ( P3 @ ( product_snd @ B @ A @ P2 ) @ ( product_fst @ B @ A @ P2 ) )
% 0.07/0.32 => ~ ! [X4: B,Y2: A] :
% 0.07/0.32 ~ ( P3 @ Y2 @ X4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % exE_realizer'
% 0.07/0.32 thf(fact_39_countable__R,axiom,
% 0.07/0.32 countable_countable @ rule @ ( sset @ rule @ rules ) ).
% 0.07/0.32
% 0.07/0.32 % countable_R
% 0.07/0.32 thf(fact_40_trim__enabled,axiom,
% 0.07/0.32 ! [S: state,Rs: stream @ rule] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % trim_enabled
% 0.07/0.32 thf(fact_41_trim__in__R,axiom,
% 0.07/0.32 ! [S: state,Rs: stream @ rule] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( member @ rule @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ ( sset @ rule @ rules ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % trim_in_R
% 0.07/0.32 thf(fact_42_wf__ipath__epath,axiom,
% 0.07/0.32 ! [T2: abstra2103299360e_tree @ ( product_prod @ state @ rule ),Steps2: stream @ ( product_prod @ state @ rule )] :
% 0.07/0.32 ( ( abstra1874736267tem_wf @ rule @ state @ eff @ rules @ T2 )
% 0.07/0.32 => ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ T2 @ Steps2 )
% 0.07/0.32 => ( abstra523868654_epath @ rule @ state @ eff @ rules @ Steps2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % wf_ipath_epath
% 0.07/0.32 thf(fact_43_minWait__ex,axiom,
% 0.07/0.32 ! [S: state,Rs: stream @ rule] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ? [N: nat] : ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ N @ Rs ) ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % minWait_ex
% 0.07/0.32 thf(fact_44_trim__fair,axiom,
% 0.07/0.32 ! [S: state,Rs: stream @ rule] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( abstra928354080m_fair @ rule @ rules @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % trim_fair
% 0.07/0.32 thf(fact_45_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A: $tType,A2: A,P3: A > $o] :
% 0.07/0.32 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 0.07/0.32 = ( P3 @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_46_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A] :
% 0.07/0.32 ( ( collect @ A
% 0.07/0.32 @ ^ [X6: A] : ( member @ A @ X6 @ A4 ) )
% 0.07/0.32 = A4 ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_47_Collect__cong,axiom,
% 0.07/0.32 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 0.07/0.32 ( ! [X4: A] :
% 0.07/0.32 ( ( P3 @ X4 )
% 0.07/0.32 = ( Q2 @ X4 ) )
% 0.07/0.32 => ( ( collect @ A @ P3 )
% 0.07/0.32 = ( collect @ A @ Q2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_cong
% 0.07/0.32 thf(fact_48_ext,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.07/0.32 ( ! [X4: A] :
% 0.07/0.32 ( ( F @ X4 )
% 0.07/0.32 = ( G @ X4 ) )
% 0.07/0.32 => ( F = G ) ) ).
% 0.07/0.32
% 0.07/0.32 % ext
% 0.07/0.32 thf(fact_49_sdrop__fair,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,M: nat] :
% 0.07/0.32 ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( abstra928354080m_fair @ rule @ rules @ ( sdrop @ rule @ M @ Rs ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sdrop_fair
% 0.07/0.32 thf(fact_50_fair__fenum,axiom,
% 0.07/0.32 abstra928354080m_fair @ rule @ rules @ ( abstra1774373515_fenum @ rule @ rules ) ).
% 0.07/0.32
% 0.07/0.32 % fair_fenum
% 0.07/0.32 thf(fact_51_RuleSystem__Defs_Osdrop__fair,axiom,
% 0.07/0.32 ! [Rule: $tType,Rules: stream @ Rule,Rs: stream @ Rule,M: nat] :
% 0.07/0.32 ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( abstra928354080m_fair @ Rule @ Rules @ ( sdrop @ Rule @ M @ Rs ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.sdrop_fair
% 0.07/0.32 thf(fact_52_RuleSystem__Defs_Ofair__fenum,axiom,
% 0.07/0.32 ! [Rule: $tType,Rules: stream @ Rule] : ( abstra928354080m_fair @ Rule @ Rules @ ( abstra1774373515_fenum @ Rule @ Rules ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.fair_fenum
% 0.07/0.32 thf(fact_53_RuleSystem_Otrim__fair,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( abstra928354080m_fair @ Rule @ Rules @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.trim_fair
% 0.07/0.32 thf(fact_54_RuleSystem__Defs_Owf__ipath__epath,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,T2: abstra2103299360e_tree @ ( product_prod @ State @ Rule ),Steps2: stream @ ( product_prod @ State @ Rule )] :
% 0.07/0.32 ( ( abstra1874736267tem_wf @ Rule @ State @ Eff @ Rules @ T2 )
% 0.07/0.32 => ( ( abstra313004635_ipath @ ( product_prod @ State @ Rule ) @ T2 @ Steps2 )
% 0.07/0.32 => ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ Steps2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.wf_ipath_epath
% 0.07/0.32 thf(fact_55_RuleSystem__Defs_Ocountable__R,axiom,
% 0.07/0.32 ! [Rule: $tType,Rules: stream @ Rule] : ( countable_countable @ Rule @ ( sset @ Rule @ Rules ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.countable_R
% 0.07/0.32 thf(fact_56_sdrop__stl,axiom,
% 0.07/0.32 ! [A: $tType,N2: nat,S: stream @ A] :
% 0.07/0.32 ( ( sdrop @ A @ N2 @ ( stl @ A @ S ) )
% 0.07/0.32 = ( stl @ A @ ( sdrop @ A @ N2 @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sdrop_stl
% 0.07/0.32 thf(fact_57_RuleSystem__Defs_ONE__R,axiom,
% 0.07/0.32 ! [Rule: $tType,Rules: stream @ Rule] :
% 0.07/0.32 ( ( sset @ Rule @ Rules )
% 0.07/0.32 != ( bot_bot @ ( set @ Rule ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.NE_R
% 0.07/0.32 thf(fact_58_RuleSystem__Defs_Ofair__stl,axiom,
% 0.07/0.32 ! [Rule: $tType,Rules: stream @ Rule,Rs: stream @ Rule] :
% 0.07/0.32 ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( abstra928354080m_fair @ Rule @ Rules @ ( stl @ Rule @ Rs ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.fair_stl
% 0.07/0.32 thf(fact_59_RuleSystem_OminWait__ex,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ? [N: nat] : ( abstra1874422341nabled @ Rule @ State @ Eff @ ( shd @ Rule @ ( sdrop @ Rule @ N @ Rs ) ) @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.minWait_ex
% 0.07/0.32 thf(fact_60_RuleSystem_Otrim__in__R,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( member @ Rule @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ ( sset @ Rule @ Rules ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.trim_in_R
% 0.07/0.32 thf(fact_61_RuleSystem_Otrim__enabled,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( abstra1874422341nabled @ Rule @ State @ Eff @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.trim_enabled
% 0.07/0.32 thf(fact_62_RuleSystem__Defs_OSaturated__def,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType] :
% 0.07/0.32 ( ( abstra1209608345urated @ Rule @ State )
% 0.07/0.32 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rules2: stream @ Rule,Steps3: stream @ ( product_prod @ State @ Rule )] :
% 0.07/0.32 ! [X6: Rule] :
% 0.07/0.32 ( ( member @ Rule @ X6 @ ( sset @ Rule @ Rules2 ) )
% 0.07/0.32 => ( abstra726722745urated @ Rule @ State @ Eff2 @ X6 @ Steps3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.Saturated_def
% 0.07/0.32 thf(fact_63_RuleSystem__Defs_OpickEff,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,R: Rule,S: State] :
% 0.07/0.32 ( ( abstra1874422341nabled @ Rule @ State @ Eff @ R @ S )
% 0.07/0.32 => ( Eff @ R @ S @ ( abstra1276541928ickEff @ Rule @ State @ Eff @ R @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.pickEff
% 0.07/0.32 thf(fact_64_RuleSystem__Defs_Osset__fenum,axiom,
% 0.07/0.32 ! [Rule: $tType,Rules: stream @ Rule] :
% 0.07/0.32 ( ( sset @ Rule @ ( abstra1774373515_fenum @ Rule @ Rules ) )
% 0.07/0.32 = ( sset @ Rule @ Rules ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.sset_fenum
% 0.07/0.32 thf(fact_65_trim__alt,axiom,
% 0.07/0.32 ! [S: state,Rs: stream @ rule] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S )
% 0.07/0.32 = ( sdrop @ rule @ ( abstra1332369113inWait @ rule @ state @ eff @ Rs @ S ) @ Rs ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % trim_alt
% 0.07/0.32 thf(fact_66_pos,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,R: rule] :
% 0.07/0.32 ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( ( member @ rule @ R @ ( sset @ rule @ rules ) )
% 0.07/0.32 => ( ( shd @ rule @ ( sdrop @ rule @ ( abstra2097340358le_pos @ rule @ Rs @ R ) @ Rs ) )
% 0.07/0.32 = R ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pos
% 0.07/0.32 thf(fact_67_trim__def,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,S: state] :
% 0.07/0.32 ( ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S )
% 0.07/0.32 = ( sdrop_while @ rule
% 0.07/0.32 @ ^ [R3: rule] :
% 0.07/0.32 ~ ( abstra1874422341nabled @ rule @ state @ eff @ R3 @ S )
% 0.07/0.32 @ Rs ) ) ).
% 0.07/0.32
% 0.07/0.32 % trim_def
% 0.07/0.32 thf(fact_68_wf__mkTree,axiom,
% 0.07/0.32 ! [S: state,Rs: stream @ rule] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( abstra1874736267tem_wf @ rule @ state @ eff @ rules @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % wf_mkTree
% 0.07/0.32 thf(fact_69_countable__empty,axiom,
% 0.07/0.32 ! [A: $tType] : ( countable_countable @ A @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % countable_empty
% 0.07/0.32 thf(fact_70_RuleSystem_Opos,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,Rs: stream @ Rule,R: Rule] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( ( member @ Rule @ R @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 => ( ( shd @ Rule @ ( sdrop @ Rule @ ( abstra2097340358le_pos @ Rule @ Rs @ R ) @ Rs ) )
% 0.07/0.32 = R ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.pos
% 0.07/0.32 thf(fact_71_in__cont__mkTree,axiom,
% 0.07/0.32 ! [S: state,Rs: stream @ rule,T3: abstra2103299360e_tree @ ( product_prod @ state @ rule )] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( ( fmember @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ T3 @ ( abstra1749095923e_cont @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) ) )
% 0.07/0.32 => ? [Sl5: fset @ state,S6: state] :
% 0.07/0.32 ( ( member @ state @ S6 @ s )
% 0.07/0.32 & ( eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S @ Sl5 )
% 0.07/0.32 & ( fmember @ state @ S6 @ Sl5 )
% 0.07/0.32 & ( T3
% 0.07/0.32 = ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S6 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % in_cont_mkTree
% 0.07/0.32 thf(fact_72_RuleSystem_Otrim__alt,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S )
% 0.07/0.32 = ( sdrop @ Rule @ ( abstra1332369113inWait @ Rule @ State @ Eff @ Rs @ S ) @ Rs ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.trim_alt
% 0.07/0.32 thf(fact_73_countableI__type,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( countable @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A4: set @ A] : ( countable_countable @ A @ A4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % countableI_type
% 0.07/0.32 thf(fact_74_ipath__mkTree__sdrop,axiom,
% 0.07/0.32 ! [S: state,Rs: stream @ rule,Steps2: stream @ ( product_prod @ state @ rule ),M: nat] :
% 0.07/0.32 ( ( member @ state @ S @ s )
% 0.07/0.32 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) @ Steps2 )
% 0.07/0.32 => ? [N: nat,S6: state] :
% 0.07/0.32 ( ( member @ state @ S6 @ s )
% 0.07/0.32 & ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( sdrop @ rule @ N @ Rs ) @ S6 ) @ ( sdrop @ ( product_prod @ state @ rule ) @ M @ Steps2 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ipath_mkTree_sdrop
% 0.07/0.32 thf(fact_75_sdrop__while_Osimps,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( sdrop_while @ A )
% 0.07/0.32 = ( ^ [P4: A > $o,S4: stream @ A] : ( if @ ( stream @ A ) @ ( P4 @ ( shd @ A @ S4 ) ) @ ( sdrop_while @ A @ P4 @ ( stl @ A @ S4 ) ) @ S4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sdrop_while.simps
% 0.07/0.32 thf(fact_76_RuleSystem_Oin__cont__mkTree,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule,T3: abstra2103299360e_tree @ ( product_prod @ State @ Rule )] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( ( fmember @ ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) @ T3 @ ( abstra1749095923e_cont @ ( product_prod @ State @ Rule ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ Rs @ S ) ) )
% 0.07/0.32 => ? [Sl5: fset @ State,S6: State] :
% 0.07/0.32 ( ( member @ State @ S6 @ S3 )
% 0.07/0.32 & ( Eff @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ S @ Sl5 )
% 0.07/0.32 & ( fmember @ State @ S6 @ Sl5 )
% 0.07/0.32 & ( T3
% 0.07/0.32 = ( abstra1225283448mkTree @ Rule @ State @ Eff @ ( stl @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ S6 ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.in_cont_mkTree
% 0.07/0.32 thf(fact_77_RuleSystem__Defs_Otrim__def,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType] :
% 0.07/0.32 ( ( abstra1259602206m_trim @ Rule @ State )
% 0.07/0.32 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rs2: stream @ Rule,S4: State] :
% 0.07/0.32 ( sdrop_while @ Rule
% 0.07/0.32 @ ^ [R3: Rule] :
% 0.07/0.32 ~ ( abstra1874422341nabled @ Rule @ State @ Eff2 @ R3 @ S4 )
% 0.07/0.32 @ Rs2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.trim_def
% 0.07/0.32 thf(fact_78_countable__Collect,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,Phi: A > $o] :
% 0.07/0.32 ( ( countable_countable @ A @ A4 )
% 0.07/0.32 => ( countable_countable @ A
% 0.07/0.32 @ ( collect @ A
% 0.07/0.32 @ ^ [A3: A] :
% 0.07/0.32 ( ( member @ A @ A3 @ A4 )
% 0.07/0.32 & ( Phi @ A3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % countable_Collect
% 0.07/0.32 thf(fact_79_RuleSystem_Owf__mkTree,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( abstra1874736267tem_wf @ Rule @ State @ Eff @ Rules @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ Rs @ S ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.wf_mkTree
% 0.07/0.32 thf(fact_80_RuleSystem_Oipath__mkTree__sdrop,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule,Steps2: stream @ ( product_prod @ State @ Rule ),M: nat] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( member @ State @ S @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( ( abstra313004635_ipath @ ( product_prod @ State @ Rule ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ Rs @ S ) @ Steps2 )
% 0.07/0.32 => ? [N: nat,S6: State] :
% 0.07/0.32 ( ( member @ State @ S6 @ S3 )
% 0.07/0.32 & ( abstra313004635_ipath @ ( product_prod @ State @ Rule ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ ( sdrop @ Rule @ N @ Rs ) @ S6 ) @ ( sdrop @ ( product_prod @ State @ Rule ) @ M @ Steps2 ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.ipath_mkTree_sdrop
% 0.07/0.32 thf(fact_81_minWait__le__pos,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,R: rule,S: state] :
% 0.07/0.32 ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 0.07/0.32 => ( ( member @ rule @ R @ ( sset @ rule @ rules ) )
% 0.07/0.32 => ( ( abstra1874422341nabled @ rule @ state @ eff @ R @ S )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( abstra1332369113inWait @ rule @ state @ eff @ Rs @ S ) @ ( abstra2097340358le_pos @ rule @ Rs @ R ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % minWait_le_pos
% 0.07/0.32 thf(fact_82_minWait__def,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,S: state] :
% 0.07/0.32 ( ( abstra1332369113inWait @ rule @ state @ eff @ Rs @ S )
% 0.07/0.32 = ( ord_Least @ nat
% 0.07/0.32 @ ^ [N3: nat] : ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ N3 @ Rs ) ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % minWait_def
% 0.07/0.32 thf(fact_83_mkTree_Osimps_I2_J,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,S: state] :
% 0.07/0.32 ( ( abstra1749095923e_cont @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) )
% 0.07/0.32 = ( fimage @ state @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) @ ( abstra1276541928ickEff @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % mkTree.simps(2)
% 0.07/0.32 thf(fact_84_minWait__least,axiom,
% 0.07/0.32 ! [N2: nat,Rs: stream @ rule,S: state] :
% 0.07/0.32 ( ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ N2 @ Rs ) ) @ S )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( abstra1332369113inWait @ rule @ state @ eff @ Rs @ S ) @ N2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % minWait_least
% 0.07/0.32 thf(fact_85_pos__def,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( abstra2097340358le_pos @ A )
% 0.07/0.32 = ( ^ [Rs2: stream @ A,R3: A] :
% 0.07/0.32 ( ord_Least @ nat
% 0.07/0.32 @ ^ [N3: nat] :
% 0.07/0.32 ( ( shd @ A @ ( sdrop @ A @ N3 @ Rs2 ) )
% 0.07/0.32 = R3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pos_def
% 0.07/0.32 thf(fact_86_pos__least,axiom,
% 0.07/0.32 ! [A: $tType,N2: nat,Rs: stream @ A,R: A] :
% 0.07/0.32 ( ( ( shd @ A @ ( sdrop @ A @ N2 @ Rs ) )
% 0.07/0.32 = R )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( abstra2097340358le_pos @ A @ Rs @ R ) @ N2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % pos_least
% 0.07/0.32 thf(fact_87_RuleSystem_Opos__least,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,A: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,N2: nat,Rs: stream @ A,R: A] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( ( shd @ A @ ( sdrop @ A @ N2 @ Rs ) )
% 0.07/0.32 = R )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( abstra2097340358le_pos @ A @ Rs @ R ) @ N2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.pos_least
% 0.07/0.32 thf(fact_88_RuleSystem_Opos__def,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType,A: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,Rs: stream @ A,R: A] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( abstra2097340358le_pos @ A @ Rs @ R )
% 0.07/0.32 = ( ord_Least @ nat
% 0.07/0.32 @ ^ [N3: nat] :
% 0.07/0.32 ( ( shd @ A @ ( sdrop @ A @ N3 @ Rs ) )
% 0.07/0.32 = R ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.pos_def
% 0.07/0.32 thf(fact_89_RuleSystem_OminWait__least,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,N2: nat,Rs: stream @ Rule,S: State] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( abstra1874422341nabled @ Rule @ State @ Eff @ ( shd @ Rule @ ( sdrop @ Rule @ N2 @ Rs ) ) @ S )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( abstra1332369113inWait @ Rule @ State @ Eff @ Rs @ S ) @ N2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.minWait_least
% 0.07/0.32 thf(fact_90_RuleSystem__Defs_OmkTree_Osimps_I2_J,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rs: stream @ Rule,S: State] :
% 0.07/0.32 ( ( abstra1749095923e_cont @ ( product_prod @ State @ Rule ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ Rs @ S ) )
% 0.07/0.32 = ( fimage @ State @ ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ ( stl @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) ) @ ( abstra1276541928ickEff @ Rule @ State @ Eff @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.mkTree.simps(2)
% 0.07/0.32 thf(fact_91_RuleSystem_OminWait__def,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,Rs: stream @ Rule,S: State] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( abstra1332369113inWait @ Rule @ State @ Eff @ Rs @ S )
% 0.07/0.32 = ( ord_Least @ nat
% 0.07/0.32 @ ^ [N3: nat] : ( abstra1874422341nabled @ Rule @ State @ Eff @ ( shd @ Rule @ ( sdrop @ Rule @ N3 @ Rs ) ) @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.minWait_def
% 0.07/0.32 thf(fact_92_RuleSystem_OminWait__le__pos,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,Rs: stream @ Rule,R: Rule,S: State] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 0.07/0.32 => ( ( member @ Rule @ R @ ( sset @ Rule @ Rules ) )
% 0.07/0.32 => ( ( abstra1874422341nabled @ Rule @ State @ Eff @ R @ S )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( abstra1332369113inWait @ Rule @ State @ Eff @ Rs @ S ) @ ( abstra2097340358le_pos @ Rule @ Rs @ R ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.minWait_le_pos
% 0.07/0.32 thf(fact_93_fimage__eqI,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,B2: A,F: B > A,X3: B,A4: fset @ B] :
% 0.07/0.32 ( ( B2
% 0.07/0.32 = ( F @ X3 ) )
% 0.07/0.32 => ( ( fmember @ B @ X3 @ A4 )
% 0.07/0.32 => ( fmember @ A @ B2 @ ( fimage @ B @ A @ F @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimage_eqI
% 0.07/0.32 thf(fact_94_fimage__ident,axiom,
% 0.07/0.32 ! [A: $tType,Y4: fset @ A] :
% 0.07/0.32 ( ( fimage @ A @ A
% 0.07/0.32 @ ^ [X6: A] : X6
% 0.07/0.32 @ Y4 )
% 0.07/0.32 = Y4 ) ).
% 0.07/0.32
% 0.07/0.32 % fimage_ident
% 0.07/0.32 thf(fact_95_fset_Omap__ident,axiom,
% 0.07/0.32 ! [A: $tType,T2: fset @ A] :
% 0.07/0.32 ( ( fimage @ A @ A
% 0.07/0.32 @ ^ [X6: A] : X6
% 0.07/0.32 @ T2 )
% 0.07/0.32 = T2 ) ).
% 0.07/0.32
% 0.07/0.32 % fset.map_ident
% 0.07/0.32 thf(fact_96_per__def,axiom,
% 0.07/0.32 ! [R: rule] :
% 0.07/0.32 ( ( abstra2096684367le_per @ rule @ state @ eff @ rules @ s @ R )
% 0.07/0.32 = ( ! [S4: state,R1: rule,Sl6: fset @ state,S8: state] :
% 0.07/0.32 ( ( ( member @ state @ S4 @ s )
% 0.07/0.32 & ( abstra1874422341nabled @ rule @ state @ eff @ R @ S4 )
% 0.07/0.32 & ( member @ rule @ R1 @ ( minus_minus @ ( set @ rule ) @ ( sset @ rule @ rules ) @ ( insert @ rule @ R @ ( bot_bot @ ( set @ rule ) ) ) ) )
% 0.07/0.32 & ( eff @ R1 @ S4 @ Sl6 )
% 0.07/0.32 & ( fmember @ state @ S8 @ Sl6 ) )
% 0.07/0.32 => ( abstra1874422341nabled @ rule @ state @ eff @ R @ S8 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % per_def
% 0.07/0.32 thf(fact_97_Least__le,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o,K: A] :
% 0.07/0.32 ( ( P3 @ K )
% 0.07/0.32 => ( ord_less_eq @ A @ ( ord_Least @ A @ P3 ) @ K ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Least_le
% 0.07/0.32 thf(fact_98_mkTree_Octr,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,S: state] :
% 0.07/0.32 ( ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S )
% 0.07/0.32 = ( abstra388494275e_Node @ ( product_prod @ state @ rule ) @ ( product_Pair @ state @ rule @ S @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) @ ( fimage @ state @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) @ ( abstra1276541928ickEff @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % mkTree.ctr
% 0.07/0.32 thf(fact_99_order__refl,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_refl
% 0.07/0.32 thf(fact_100_old_Oprod_Oinject,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 0.07/0.32 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.07/0.32 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.07/0.32 = ( ( A2 = A5 )
% 0.07/0.32 & ( B2 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % old.prod.inject
% 0.07/0.32 thf(fact_101_prod_Oinject,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,X13: A,X22: B,Y1: A,Y22: B] :
% 0.07/0.32 ( ( ( product_Pair @ A @ B @ X13 @ X22 )
% 0.07/0.32 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.07/0.32 = ( ( X13 = Y1 )
% 0.07/0.32 & ( X22 = Y22 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod.inject
% 0.07/0.32 thf(fact_102_bot__apply,axiom,
% 0.07/0.32 ! [C: $tType,D: $tType] :
% 0.07/0.32 ( ( bot @ C @ ( type2 @ C ) )
% 0.07/0.32 => ( ( bot_bot @ ( D > C ) )
% 0.07/0.32 = ( ^ [X6: D] : ( bot_bot @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot_apply
% 0.07/0.32 thf(fact_103_fsubsetI,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 0.07/0.32 ( ! [X4: A] :
% 0.07/0.32 ( ( fmember @ A @ X4 @ A4 )
% 0.07/0.32 => ( fmember @ A @ X4 @ B4 ) )
% 0.07/0.32 => ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % fsubsetI
% 0.07/0.32 thf(fact_104_tree_Oinject,axiom,
% 0.07/0.32 ! [A: $tType,X13: A,X22: fset @ ( abstra2103299360e_tree @ A ),Y1: A,Y22: fset @ ( abstra2103299360e_tree @ A )] :
% 0.07/0.32 ( ( ( abstra388494275e_Node @ A @ X13 @ X22 )
% 0.07/0.32 = ( abstra388494275e_Node @ A @ Y1 @ Y22 ) )
% 0.07/0.32 = ( ( X13 = Y1 )
% 0.07/0.32 & ( X22 = Y22 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % tree.inject
% 0.07/0.32 thf(fact_105_countable__insert,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,A2: A] :
% 0.07/0.32 ( ( countable_countable @ A @ A4 )
% 0.07/0.32 => ( countable_countable @ A @ ( insert @ A @ A2 @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % countable_insert
% 0.07/0.32 thf(fact_106_countable__insert__eq,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,A4: set @ A] :
% 0.07/0.32 ( ( countable_countable @ A @ ( insert @ A @ X3 @ A4 ) )
% 0.07/0.32 = ( countable_countable @ A @ A4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % countable_insert_eq
% 0.07/0.32 thf(fact_107_countable__Diff,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( countable_countable @ A @ A4 )
% 0.07/0.32 => ( countable_countable @ A @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % countable_Diff
% 0.07/0.32 thf(fact_108_prod_Ocollapse,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.07/0.32 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 0.07/0.32 = Prod ) ).
% 0.07/0.32
% 0.07/0.32 % prod.collapse
% 0.07/0.32 thf(fact_109_countable__Diff__eq,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,X3: A] :
% 0.07/0.32 ( ( countable_countable @ A @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.07/0.32 = ( countable_countable @ A @ A4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % countable_Diff_eq
% 0.07/0.32 thf(fact_110_fset__mp,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A,X3: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( fmember @ A @ X3 @ A4 )
% 0.07/0.32 => ( fmember @ A @ X3 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fset_mp
% 0.07/0.32 thf(fact_111_fin__mono,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A,X3: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( fmember @ A @ X3 @ A4 )
% 0.07/0.32 => ( fmember @ A @ X3 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fin_mono
% 0.07/0.32 thf(fact_112_fsubsetD,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A,C2: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( fmember @ A @ C2 @ A4 )
% 0.07/0.32 => ( fmember @ A @ C2 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fsubsetD
% 0.07/0.32 thf(fact_113_fset__rev__mp,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,A4: fset @ A,B4: fset @ A] :
% 0.07/0.32 ( ( fmember @ A @ X3 @ A4 )
% 0.07/0.32 => ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( fmember @ A @ X3 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fset_rev_mp
% 0.07/0.32 thf(fact_114_subset__fimage__iff,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,B4: fset @ A,F: B > A,A4: fset @ B] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ B4 @ ( fimage @ B @ A @ F @ A4 ) )
% 0.07/0.32 = ( ? [AA: fset @ B] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ B ) @ AA @ A4 )
% 0.07/0.32 & ( B4
% 0.07/0.32 = ( fimage @ B @ A @ F @ AA ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_fimage_iff
% 0.07/0.32 thf(fact_115_fimage__mono,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,A4: fset @ A,B4: fset @ A,F: A > B] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ord_less_eq @ ( fset @ B ) @ ( fimage @ A @ B @ F @ A4 ) @ ( fimage @ A @ B @ F @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimage_mono
% 0.07/0.32 thf(fact_116_tree_Oexhaust,axiom,
% 0.07/0.32 ! [A: $tType,Y: abstra2103299360e_tree @ A] :
% 0.07/0.32 ~ ! [X1: A,X23: fset @ ( abstra2103299360e_tree @ A )] :
% 0.07/0.32 ( Y
% 0.07/0.32 != ( abstra388494275e_Node @ A @ X1 @ X23 ) ) ).
% 0.07/0.32
% 0.07/0.32 % tree.exhaust
% 0.07/0.32 thf(fact_117_old_Oprod_Oinducts,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.07/0.32 ( ! [A6: A,B5: B] : ( P3 @ ( product_Pair @ A @ B @ A6 @ B5 ) )
% 0.07/0.32 => ( P3 @ Prod ) ) ).
% 0.07/0.32
% 0.07/0.32 % old.prod.inducts
% 0.07/0.32 thf(fact_118_old_Oprod_Oexhaust,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.07/0.32 ~ ! [A6: A,B5: B] :
% 0.07/0.32 ( Y
% 0.07/0.32 != ( product_Pair @ A @ B @ A6 @ B5 ) ) ).
% 0.07/0.32
% 0.07/0.32 % old.prod.exhaust
% 0.07/0.32 thf(fact_119_prod__induct7,axiom,
% 0.07/0.32 ! [G2: $tType,F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 0.07/0.32 ( ! [A6: A,B5: B,C3: C,D2: D,E2: E,F3: F2,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G2 ) @ E2 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) )
% 0.07/0.32 => ( P3 @ X3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_induct7
% 0.07/0.32 thf(fact_120_prod__induct6,axiom,
% 0.07/0.32 ! [F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.07/0.32 ( ! [A6: A,B5: B,C3: C,D2: D,E2: E,F3: F2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) )
% 0.07/0.32 => ( P3 @ X3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_induct6
% 0.07/0.32 thf(fact_121_prod__induct5,axiom,
% 0.07/0.32 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.07/0.32 ( ! [A6: A,B5: B,C3: C,D2: D,E2: E] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.07/0.32 => ( P3 @ X3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_induct5
% 0.07/0.32 thf(fact_122_prod__induct4,axiom,
% 0.07/0.32 ! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.07/0.32 ( ! [A6: A,B5: B,C3: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 0.07/0.32 => ( P3 @ X3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_induct4
% 0.07/0.32 thf(fact_123_prod__induct3,axiom,
% 0.07/0.32 ! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.07/0.32 ( ! [A6: A,B5: B,C3: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B5 @ C3 ) ) )
% 0.07/0.32 => ( P3 @ X3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_induct3
% 0.07/0.32 thf(fact_124_prod__cases7,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 0.07/0.32 ~ ! [A6: A,B5: B,C3: C,D2: D,E2: E,F3: F2,G3: G2] :
% 0.07/0.32 ( Y
% 0.07/0.32 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G2 ) @ E2 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_cases7
% 0.07/0.32 thf(fact_125_prod__cases6,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.07/0.32 ~ ! [A6: A,B5: B,C3: C,D2: D,E2: E,F3: F2] :
% 0.07/0.32 ( Y
% 0.07/0.32 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_cases6
% 0.07/0.32 thf(fact_126_prod__cases5,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.07/0.32 ~ ! [A6: A,B5: B,C3: C,D2: D,E2: E] :
% 0.07/0.32 ( Y
% 0.07/0.32 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_cases5
% 0.07/0.32 thf(fact_127_prod__cases4,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.07/0.32 ~ ! [A6: A,B5: B,C3: C,D2: D] :
% 0.07/0.32 ( Y
% 0.07/0.32 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_cases4
% 0.07/0.32 thf(fact_128_prod__cases3,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.07/0.32 ~ ! [A6: A,B5: B,C3: C] :
% 0.07/0.32 ( Y
% 0.07/0.32 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B5 @ C3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_cases3
% 0.07/0.32 thf(fact_129_Pair__inject,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 0.07/0.32 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.07/0.32 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.07/0.32 => ~ ( ( A2 = A5 )
% 0.07/0.32 => ( B2 != B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Pair_inject
% 0.07/0.32 thf(fact_130_prod__cases,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.07/0.32 ( ! [A6: A,B5: B] : ( P3 @ ( product_Pair @ A @ B @ A6 @ B5 ) )
% 0.07/0.32 => ( P3 @ P2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod_cases
% 0.07/0.32 thf(fact_131_surj__pair,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.07/0.32 ? [X4: A,Y2: B] :
% 0.07/0.32 ( P2
% 0.07/0.32 = ( product_Pair @ A @ B @ X4 @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % surj_pair
% 0.07/0.32 thf(fact_132_fst__conv,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,X13: A,X22: B] :
% 0.07/0.32 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X13 @ X22 ) )
% 0.07/0.32 = X13 ) ).
% 0.07/0.32
% 0.07/0.32 % fst_conv
% 0.07/0.32 thf(fact_133_fst__eqD,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,X3: A,Y: B,A2: A] :
% 0.07/0.32 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.07/0.32 = A2 )
% 0.07/0.32 => ( X3 = A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % fst_eqD
% 0.07/0.32 thf(fact_134_snd__conv,axiom,
% 0.07/0.32 ! [Aa: $tType,A: $tType,X13: Aa,X22: A] :
% 0.07/0.32 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X13 @ X22 ) )
% 0.07/0.32 = X22 ) ).
% 0.07/0.32
% 0.07/0.32 % snd_conv
% 0.07/0.32 thf(fact_135_snd__eqD,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,X3: B,Y: A,A2: A] :
% 0.07/0.32 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) )
% 0.07/0.32 = A2 )
% 0.07/0.32 => ( Y = A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % snd_eqD
% 0.07/0.32 thf(fact_136_uncountable__minus__countable,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ~ ( countable_countable @ A @ A4 )
% 0.07/0.32 => ( ( countable_countable @ A @ B4 )
% 0.07/0.32 => ~ ( countable_countable @ A @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % uncountable_minus_countable
% 0.07/0.32 thf(fact_137_countable__subset,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( countable_countable @ A @ B4 )
% 0.07/0.32 => ( countable_countable @ A @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % countable_subset
% 0.07/0.32 thf(fact_138_fimage__fsubsetI,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,A4: fset @ A,F: A > B,B4: fset @ B] :
% 0.07/0.32 ( ! [X4: A] :
% 0.07/0.32 ( ( fmember @ A @ X4 @ A4 )
% 0.07/0.32 => ( fmember @ B @ ( F @ X4 ) @ B4 ) )
% 0.07/0.32 => ( ord_less_eq @ ( fset @ B ) @ ( fimage @ A @ B @ F @ A4 ) @ B4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimage_fsubsetI
% 0.07/0.32 thf(fact_139_tree_Osel_I2_J,axiom,
% 0.07/0.32 ! [A: $tType,X13: A,X22: fset @ ( abstra2103299360e_tree @ A )] :
% 0.07/0.32 ( ( abstra1749095923e_cont @ A @ ( abstra388494275e_Node @ A @ X13 @ X22 ) )
% 0.07/0.32 = X22 ) ).
% 0.07/0.32
% 0.07/0.32 % tree.sel(2)
% 0.07/0.32 thf(fact_140_surjective__pairing,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,T2: product_prod @ A @ B] :
% 0.07/0.32 ( T2
% 0.07/0.32 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T2 ) @ ( product_snd @ A @ B @ T2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % surjective_pairing
% 0.07/0.32 thf(fact_141_prod_Oexhaust__sel,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.07/0.32 ( Prod
% 0.07/0.32 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % prod.exhaust_sel
% 0.07/0.32 thf(fact_142_conjI__realizer,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P3: A > $o,P2: A,Q2: B > $o,Q: B] :
% 0.07/0.32 ( ( P3 @ P2 )
% 0.07/0.32 => ( ( Q2 @ Q )
% 0.07/0.32 => ( ( P3 @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q ) ) )
% 0.07/0.32 & ( Q2 @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conjI_realizer
% 0.07/0.32 thf(fact_143_exI__realizer,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,P3: A > B > $o,Y: A,X3: B] :
% 0.07/0.32 ( ( P3 @ Y @ X3 )
% 0.07/0.32 => ( P3 @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % exI_realizer
% 0.07/0.32 thf(fact_144_le__funD,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 => ! [F: A > B,G: A > B,X3: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.07/0.32 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_funD
% 0.07/0.32 thf(fact_145_le__funE,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 => ! [F: A > B,G: A > B,X3: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.07/0.32 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_funE
% 0.07/0.32 thf(fact_146_le__funI,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 => ! [F: A > B,G: A > B] :
% 0.07/0.32 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.07/0.32 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_funI
% 0.07/0.32 thf(fact_147_le__fun__def,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 => ( ( ord_less_eq @ ( A > B ) )
% 0.07/0.32 = ( ^ [F4: A > B,G4: A > B] :
% 0.07/0.32 ! [X6: A] : ( ord_less_eq @ B @ ( F4 @ X6 ) @ ( G4 @ X6 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_fun_def
% 0.07/0.32 thf(fact_148_order__subst1,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( order @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.07/0.32 => ( ! [X4: B,Y2: B] :
% 0.07/0.32 ( ( ord_less_eq @ B @ X4 @ Y2 )
% 0.07/0.32 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_149_order__subst2,axiom,
% 0.07/0.32 ! [A: $tType,C: $tType] :
% 0.07/0.32 ( ( ( order @ C @ ( type2 @ C ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X4: A,Y2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X4 @ Y2 )
% 0.07/0.32 => ( ord_less_eq @ C @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.07/0.32 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_150_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( ord @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.07/0.32 => ( ! [X4: B,Y2: B] :
% 0.07/0.32 ( ( ord_less_eq @ B @ X4 @ Y2 )
% 0.07/0.32 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_151_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( ord @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X4: A,Y2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X4 @ Y2 )
% 0.07/0.32 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.07/0.32 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_152_eq__iff,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.07/0.32 = ( ^ [X6: A,Y5: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X6 @ Y5 )
% 0.07/0.32 & ( ord_less_eq @ A @ Y5 @ X6 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_153_antisym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X3: A,Y: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.07/0.32 => ( ( ord_less_eq @ A @ Y @ X3 )
% 0.07/0.32 => ( X3 = Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_154_linear,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X3: A,Y: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.07/0.32 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % linear
% 0.07/0.32 thf(fact_155_eq__refl,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X3: A,Y: A] :
% 0.07/0.32 ( ( X3 = Y )
% 0.07/0.32 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_156_le__cases,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X3: A,Y: A] :
% 0.07/0.32 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 0.07/0.32 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_cases
% 0.07/0.32 thf(fact_157_order_Otrans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_158_le__cases3,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X3: A,Y: A,Z2: A] :
% 0.07/0.32 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.07/0.32 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.07/0.32 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.07/0.32 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 0.07/0.32 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.07/0.32 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_cases3
% 0.07/0.32 thf(fact_159_antisym__conv,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [Y: A,X3: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ Y @ X3 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ X3 @ Y )
% 0.07/0.32 = ( X3 = Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_160_ord__eq__le__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ord @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C2: A] :
% 0.07/0.32 ( ( A2 = B2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_trans
% 0.07/0.32 thf(fact_161_ord__le__eq__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ord @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( B2 = C2 )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_trans
% 0.07/0.32 thf(fact_162_order__class_Oorder_Oantisym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.07/0.32 => ( A2 = B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.antisym
% 0.07/0.32 thf(fact_163_order__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X3: A,Y: A,Z2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.07/0.32 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.07/0.32 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_trans
% 0.07/0.32 thf(fact_164_dual__order_Orefl,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.refl
% 0.07/0.32 thf(fact_165_linorder__wlog,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > A > $o,A2: A,B2: A] :
% 0.07/0.32 ( ! [A6: A,B5: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A6 @ B5 )
% 0.07/0.32 => ( P3 @ A6 @ B5 ) )
% 0.07/0.32 => ( ! [A6: A,B5: A] :
% 0.07/0.32 ( ( P3 @ B5 @ A6 )
% 0.07/0.32 => ( P3 @ A6 @ B5 ) )
% 0.07/0.32 => ( P3 @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % linorder_wlog
% 0.07/0.32 thf(fact_166_dual__order_Otrans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A,C2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.07/0.32 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.trans
% 0.07/0.32 thf(fact_167_dual__order_Oantisym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( A2 = B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.antisym
% 0.07/0.32 thf(fact_168_bot__fun__def,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( bot @ B @ ( type2 @ B ) )
% 0.07/0.32 => ( ( bot_bot @ ( A > B ) )
% 0.07/0.32 = ( ^ [X6: A] : ( bot_bot @ B ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot_fun_def
% 0.07/0.32 thf(fact_169_eqfelem__imp__iff,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,Y: A,A4: fset @ A] :
% 0.07/0.32 ( ( X3 = Y )
% 0.07/0.32 => ( ( fmember @ A @ X3 @ A4 )
% 0.07/0.32 = ( fmember @ A @ Y @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eqfelem_imp_iff
% 0.07/0.32 thf(fact_170_if__split__fmem2,axiom,
% 0.07/0.32 ! [A: $tType,A2: A,Q2: $o,X3: fset @ A,Y: fset @ A] :
% 0.07/0.32 ( ( fmember @ A @ A2 @ ( if @ ( fset @ A ) @ Q2 @ X3 @ Y ) )
% 0.07/0.32 = ( ( Q2
% 0.07/0.32 => ( fmember @ A @ A2 @ X3 ) )
% 0.07/0.32 & ( ~ Q2
% 0.07/0.32 => ( fmember @ A @ A2 @ Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % if_split_fmem2
% 0.07/0.32 thf(fact_171_if__split__fmem1,axiom,
% 0.07/0.32 ! [A: $tType,Q2: $o,X3: A,Y: A,B2: fset @ A] :
% 0.07/0.32 ( ( fmember @ A @ ( if @ A @ Q2 @ X3 @ Y ) @ B2 )
% 0.07/0.32 = ( ( Q2
% 0.07/0.32 => ( fmember @ A @ X3 @ B2 ) )
% 0.07/0.32 & ( ~ Q2
% 0.07/0.32 => ( fmember @ A @ Y @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % if_split_fmem1
% 0.07/0.32 thf(fact_172_eqfset__imp__iff,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A,X3: A] :
% 0.07/0.32 ( ( A4 = B4 )
% 0.07/0.32 => ( ( fmember @ A @ X3 @ A4 )
% 0.07/0.32 = ( fmember @ A @ X3 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eqfset_imp_iff
% 0.07/0.32 thf(fact_173_eq__fmem__trans,axiom,
% 0.07/0.32 ! [A: $tType,A2: A,B2: A,A4: fset @ A] :
% 0.07/0.32 ( ( A2 = B2 )
% 0.07/0.32 => ( ( fmember @ A @ B2 @ A4 )
% 0.07/0.32 => ( fmember @ A @ A2 @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_fmem_trans
% 0.07/0.32 thf(fact_174_fset__choice,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,A4: fset @ A,P3: A > B > $o] :
% 0.07/0.32 ( ! [X4: A] :
% 0.07/0.32 ( ( fmember @ A @ X4 @ A4 )
% 0.07/0.32 => ? [X12: B] : ( P3 @ X4 @ X12 ) )
% 0.07/0.32 => ? [F3: A > B] :
% 0.07/0.32 ! [X5: A] :
% 0.07/0.32 ( ( fmember @ A @ X5 @ A4 )
% 0.07/0.32 => ( P3 @ X5 @ ( F3 @ X5 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fset_choice
% 0.07/0.32 thf(fact_175_fequalityCE,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A,C2: A] :
% 0.07/0.32 ( ( A4 = B4 )
% 0.07/0.32 => ( ( ( fmember @ A @ C2 @ A4 )
% 0.07/0.32 => ~ ( fmember @ A @ C2 @ B4 ) )
% 0.07/0.32 => ~ ( ~ ( fmember @ A @ C2 @ A4 )
% 0.07/0.32 => ( fmember @ A @ C2 @ B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fequalityCE
% 0.07/0.32 thf(fact_176_fset__eqI,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 0.07/0.32 ( ! [X4: A] :
% 0.07/0.32 ( ( fmember @ A @ X4 @ A4 )
% 0.07/0.32 = ( fmember @ A @ X4 @ B4 ) )
% 0.07/0.32 => ( A4 = B4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % fset_eqI
% 0.07/0.32 thf(fact_177_RuleSystem_Oper__def,axiom,
% 0.07/0.32 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,R: Rule] :
% 0.07/0.32 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 0.07/0.32 => ( ( abstra2096684367le_per @ Rule @ State @ Eff @ Rules @ S3 @ R )
% 0.07/0.32 = ( ! [S4: State,R1: Rule,Sl6: fset @ State,S8: State] :
% 0.07/0.32 ( ( ( member @ State @ S4 @ S3 )
% 0.07/0.32 & ( abstra1874422341nabled @ Rule @ State @ Eff @ R @ S4 )
% 0.07/0.32 & ( member @ Rule @ R1 @ ( minus_minus @ ( set @ Rule ) @ ( sset @ Rule @ Rules ) @ ( insert @ Rule @ R @ ( bot_bot @ ( set @ Rule ) ) ) ) )
% 0.07/0.32 & ( Eff @ R1 @ S4 @ Sl6 )
% 0.07/0.32 & ( fmember @ State @ S8 @ Sl6 ) )
% 0.07/0.32 => ( abstra1874422341nabled @ Rule @ State @ Eff @ R @ S8 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem.per_def
% 0.07/0.32 thf(fact_178_LeastI2,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o,A2: A,Q2: A > $o] :
% 0.07/0.32 ( ( P3 @ A2 )
% 0.07/0.32 => ( ! [X4: A] :
% 0.07/0.32 ( ( P3 @ X4 )
% 0.07/0.32 => ( Q2 @ X4 ) )
% 0.07/0.32 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % LeastI2
% 0.07/0.32 thf(fact_179_LeastI__ex,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o] :
% 0.07/0.32 ( ? [X12: A] : ( P3 @ X12 )
% 0.07/0.32 => ( P3 @ ( ord_Least @ A @ P3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % LeastI_ex
% 0.07/0.32 thf(fact_180_LeastI2__ex,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o,Q2: A > $o] :
% 0.07/0.32 ( ? [X12: A] : ( P3 @ X12 )
% 0.07/0.32 => ( ! [X4: A] :
% 0.07/0.32 ( ( P3 @ X4 )
% 0.07/0.32 => ( Q2 @ X4 ) )
% 0.07/0.32 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % LeastI2_ex
% 0.07/0.32 thf(fact_181_RuleSystem__Defs_OmkTree_Ocode,axiom,
% 0.07/0.32 ! [State: $tType,Rule: $tType] :
% 0.07/0.32 ( ( abstra1225283448mkTree @ Rule @ State )
% 0.07/0.32 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rs2: stream @ Rule,S4: State] : ( abstra388494275e_Node @ ( product_prod @ State @ Rule ) @ ( product_Pair @ State @ Rule @ S4 @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff2 @ Rs2 @ S4 ) ) ) @ ( fimage @ State @ ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff2 @ ( stl @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff2 @ Rs2 @ S4 ) ) ) @ ( abstra1276541928ickEff @ Rule @ State @ Eff2 @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff2 @ Rs2 @ S4 ) ) @ S4 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RuleSystem_Defs.mkTree.code
% 0.07/0.32 thf(fact_182_fimage__fimage,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,C: $tType,F: B > A,G: C > B,A4: fset @ C] :
% 0.07/0.32 ( ( fimage @ B @ A @ F @ ( fimage @ C @ B @ G @ A4 ) )
% 0.07/0.32 = ( fimage @ C @ A
% 0.07/0.32 @ ^ [X6: C] : ( F @ ( G @ X6 ) )
% 0.07/0.32 @ A4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimage_fimage
% 0.07/0.32 thf(fact_183_LeastI,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o,K: A] :
% 0.07/0.32 ( ( P3 @ K )
% 0.07/0.32 => ( P3 @ ( ord_Least @ A @ P3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % LeastI
% 0.07/0.32 thf(fact_184_bot_Oextremum,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum
% 0.07/0.32 thf(fact_185_bot_Oextremum__unique,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.07/0.32 = ( A2
% 0.07/0.32 = ( bot_bot @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum_unique
% 0.07/0.32 thf(fact_186_bot_Oextremum__uniqueI,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.07/0.32 => ( A2
% 0.07/0.32 = ( bot_bot @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum_uniqueI
% 0.07/0.32 thf(fact_187_LeastI2__order,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o,X3: A,Q2: A > $o] :
% 0.07/0.32 ( ( P3 @ X3 )
% 0.07/0.32 => ( ! [Y2: A] :
% 0.07/0.32 ( ( P3 @ Y2 )
% 0.07/0.32 => ( ord_less_eq @ A @ X3 @ Y2 ) )
% 0.07/0.32 => ( ! [X4: A] :
% 0.07/0.32 ( ( P3 @ X4 )
% 0.07/0.32 => ( ! [Y6: A] :
% 0.07/0.32 ( ( P3 @ Y6 )
% 0.07/0.32 => ( ord_less_eq @ A @ X4 @ Y6 ) )
% 0.07/0.32 => ( Q2 @ X4 ) ) )
% 0.07/0.32 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % LeastI2_order
% 0.07/0.32 thf(fact_188_Least__equality,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o,X3: A] :
% 0.07/0.32 ( ( P3 @ X3 )
% 0.07/0.32 => ( ! [Y2: A] :
% 0.07/0.32 ( ( P3 @ Y2 )
% 0.07/0.32 => ( ord_less_eq @ A @ X3 @ Y2 ) )
% 0.07/0.32 => ( ( ord_Least @ A @ P3 )
% 0.07/0.32 = X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Least_equality
% 0.07/0.32 thf(fact_189_LeastI2__wellorder,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o,A2: A,Q2: A > $o] :
% 0.07/0.32 ( ( P3 @ A2 )
% 0.07/0.32 => ( ! [A6: A] :
% 0.07/0.32 ( ( P3 @ A6 )
% 0.07/0.32 => ( ! [B6: A] :
% 0.07/0.32 ( ( P3 @ B6 )
% 0.07/0.32 => ( ord_less_eq @ A @ A6 @ B6 ) )
% 0.07/0.32 => ( Q2 @ A6 ) ) )
% 0.07/0.32 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % LeastI2_wellorder
% 0.07/0.32 thf(fact_190_LeastI2__wellorder__ex,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P3: A > $o,Q2: A > $o] :
% 0.07/0.32 ( ? [X12: A] : ( P3 @ X12 )
% 0.07/0.32 => ( ! [A6: A] :
% 0.07/0.32 ( ( P3 @ A6 )
% 0.07/0.32 => ( ! [B6: A] :
% 0.07/0.32 ( ( P3 @ B6 )
% 0.07/0.32 => ( ord_less_eq @ A @ A6 @ B6 ) )
% 0.07/0.32 => ( Q2 @ A6 ) ) )
% 0.07/0.32 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % LeastI2_wellorder_ex
% 0.07/0.32 thf(fact_191_rev__fimage__eqI,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,X3: A,A4: fset @ A,B2: B,F: A > B] :
% 0.07/0.32 ( ( fmember @ A @ X3 @ A4 )
% 0.07/0.32 => ( ( B2
% 0.07/0.32 = ( F @ X3 ) )
% 0.07/0.32 => ( fmember @ B @ B2 @ ( fimage @ A @ B @ F @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % rev_fimage_eqI
% 0.07/0.32 thf(fact_192_fimage__cong,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,M2: fset @ A,N4: fset @ A,F: A > B,G: A > B] :
% 0.07/0.32 ( ( M2 = N4 )
% 0.07/0.32 => ( ! [X4: A] :
% 0.07/0.32 ( ( fmember @ A @ X4 @ N4 )
% 0.07/0.32 => ( ( F @ X4 )
% 0.07/0.32 = ( G @ X4 ) ) )
% 0.07/0.32 => ( ( fimage @ A @ B @ F @ M2 )
% 0.07/0.32 = ( fimage @ A @ B @ G @ N4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimage_cong
% 0.07/0.32 thf(fact_193_fimageI,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,X3: A,A4: fset @ A,F: A > B] :
% 0.07/0.32 ( ( fmember @ A @ X3 @ A4 )
% 0.07/0.32 => ( fmember @ B @ ( F @ X3 ) @ ( fimage @ A @ B @ F @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimageI
% 0.07/0.32 thf(fact_194_fimageE,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,B2: A,F: B > A,A4: fset @ B] :
% 0.07/0.32 ( ( fmember @ A @ B2 @ ( fimage @ B @ A @ F @ A4 ) )
% 0.07/0.32 => ~ ! [X4: B] :
% 0.07/0.32 ( ( B2
% 0.07/0.32 = ( F @ X4 ) )
% 0.07/0.32 => ~ ( fmember @ B @ X4 @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimageE
% 0.07/0.32 thf(fact_195_mkTree__unfold,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,S: state] :
% 0.07/0.32 ( ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S )
% 0.07/0.32 = ( case_stream @ rule @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) )
% 0.07/0.32 @ ^ [R3: rule,S8: stream @ rule] : ( abstra388494275e_Node @ ( product_prod @ state @ rule ) @ ( product_Pair @ state @ rule @ S @ R3 ) @ ( fimage @ state @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ S8 ) @ ( abstra1276541928ickEff @ rule @ state @ eff @ R3 @ S ) ) )
% 0.07/0.32 @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % mkTree_unfold
% 0.07/0.32 thf(fact_196_insert__Diff__single,axiom,
% 0.07/0.32 ! [A: $tType,A2: A,A4: set @ A] :
% 0.07/0.32 ( ( insert @ A @ A2 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.07/0.32 = ( insert @ A @ A2 @ A4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % insert_Diff_single
% 0.07/0.32 thf(fact_197_singleton__conv2,axiom,
% 0.07/0.32 ! [A: $tType,A2: A] :
% 0.07/0.32 ( ( collect @ A
% 0.07/0.32 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.07/0.32 @ A2 ) )
% 0.07/0.32 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % singleton_conv2
% 0.07/0.32 thf(fact_198_singleton__conv,axiom,
% 0.07/0.32 ! [A: $tType,A2: A] :
% 0.07/0.32 ( ( collect @ A
% 0.07/0.32 @ ^ [X6: A] : ( X6 = A2 ) )
% 0.07/0.32 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % singleton_conv
% 0.07/0.32 thf(fact_199_mkTree_Osimps_I1_J,axiom,
% 0.07/0.32 ! [Rs: stream @ rule,S: state] :
% 0.07/0.32 ( ( abstra573067619e_root @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) )
% 0.07/0.32 = ( product_Pair @ state @ rule @ S @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % mkTree.simps(1)
% 0.07/0.32 thf(fact_200_empty__Collect__eq,axiom,
% 0.07/0.32 ! [A: $tType,P3: A > $o] :
% 0.07/0.32 ( ( ( bot_bot @ ( set @ A ) )
% 0.07/0.32 = ( collect @ A @ P3 ) )
% 0.07/0.32 = ( ! [X6: A] :
% 0.07/0.32 ~ ( P3 @ X6 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % empty_Collect_eq
% 0.07/0.32 thf(fact_201_Collect__empty__eq,axiom,
% 0.07/0.32 ! [A: $tType,P3: A > $o] :
% 0.07/0.32 ( ( ( collect @ A @ P3 )
% 0.07/0.32 = ( bot_bot @ ( set @ A ) ) )
% 0.07/0.32 = ( ! [X6: A] :
% 0.07/0.32 ~ ( P3 @ X6 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_empty_eq
% 0.07/0.32 thf(fact_202_all__not__in__conv,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A] :
% 0.07/0.32 ( ( ! [X6: A] :
% 0.07/0.32 ~ ( member @ A @ X6 @ A4 ) )
% 0.07/0.32 = ( A4
% 0.07/0.32 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % all_not_in_conv
% 0.07/0.32 thf(fact_203_empty__iff,axiom,
% 0.07/0.32 ! [A: $tType,C2: A] :
% 0.07/0.32 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % empty_iff
% 0.07/0.32 thf(fact_204_subset__antisym,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A4 )
% 0.07/0.32 => ( A4 = B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_antisym
% 0.07/0.32 thf(fact_205_subsetI,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ! [X4: A] :
% 0.07/0.32 ( ( member @ A @ X4 @ A4 )
% 0.07/0.32 => ( member @ A @ X4 @ B4 ) )
% 0.07/0.32 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % subsetI
% 0.07/0.32 thf(fact_206_insert__absorb2,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,A4: set @ A] :
% 0.07/0.32 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A4 ) )
% 0.07/0.32 = ( insert @ A @ X3 @ A4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % insert_absorb2
% 0.07/0.32 thf(fact_207_insert__iff,axiom,
% 0.07/0.32 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 0.07/0.32 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 0.07/0.32 = ( ( A2 = B2 )
% 0.07/0.32 | ( member @ A @ A2 @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % insert_iff
% 0.07/0.32 thf(fact_208_insertCI,axiom,
% 0.07/0.32 ! [A: $tType,A2: A,B4: set @ A,B2: A] :
% 0.07/0.32 ( ( ~ ( member @ A @ A2 @ B4 )
% 0.07/0.32 => ( A2 = B2 ) )
% 0.07/0.32 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % insertCI
% 0.07/0.32 thf(fact_209_Diff__idemp,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) @ B4 )
% 0.07/0.32 = ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % Diff_idemp
% 0.07/0.32 thf(fact_210_Diff__iff,axiom,
% 0.07/0.32 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) )
% 0.07/0.32 = ( ( member @ A @ C2 @ A4 )
% 0.07/0.32 & ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Diff_iff
% 0.07/0.32 thf(fact_211_DiffI,axiom,
% 0.07/0.32 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( member @ A @ C2 @ A4 )
% 0.07/0.32 => ( ~ ( member @ A @ C2 @ B4 )
% 0.07/0.32 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % DiffI
% 0.07/0.32 thf(fact_212_fempty__iff,axiom,
% 0.07/0.32 ! [A: $tType,C2: A] :
% 0.07/0.32 ~ ( fmember @ A @ C2 @ ( bot_bot @ ( fset @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fempty_iff
% 0.07/0.32 thf(fact_213_all__not__fin__conv,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A] :
% 0.07/0.32 ( ( ! [X6: A] :
% 0.07/0.32 ~ ( fmember @ A @ X6 @ A4 ) )
% 0.07/0.32 = ( A4
% 0.07/0.32 = ( bot_bot @ ( fset @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % all_not_fin_conv
% 0.07/0.32 thf(fact_214_fempty__fsubsetI,axiom,
% 0.07/0.32 ! [A: $tType,X3: fset @ A] : ( ord_less_eq @ ( fset @ A ) @ ( bot_bot @ ( fset @ A ) ) @ X3 ) ).
% 0.07/0.32
% 0.07/0.32 % fempty_fsubsetI
% 0.07/0.32 thf(fact_215_fsubset__fempty,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ ( bot_bot @ ( fset @ A ) ) )
% 0.07/0.32 = ( A4
% 0.07/0.32 = ( bot_bot @ ( fset @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fsubset_fempty
% 0.07/0.32 thf(fact_216_fsubset__antisym,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( ord_less_eq @ ( fset @ A ) @ B4 @ A4 )
% 0.07/0.32 => ( A4 = B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fsubset_antisym
% 0.07/0.32 thf(fact_217_fimage__fempty,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,F: B > A] :
% 0.07/0.32 ( ( fimage @ B @ A @ F @ ( bot_bot @ ( fset @ B ) ) )
% 0.07/0.32 = ( bot_bot @ ( fset @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimage_fempty
% 0.07/0.32 thf(fact_218_fempty__is__fimage,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,F: B > A,A4: fset @ B] :
% 0.07/0.32 ( ( ( bot_bot @ ( fset @ A ) )
% 0.07/0.32 = ( fimage @ B @ A @ F @ A4 ) )
% 0.07/0.32 = ( A4
% 0.07/0.32 = ( bot_bot @ ( fset @ B ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fempty_is_fimage
% 0.07/0.32 thf(fact_219_fimage__is__fempty,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,F: B > A,A4: fset @ B] :
% 0.07/0.32 ( ( ( fimage @ B @ A @ F @ A4 )
% 0.07/0.32 = ( bot_bot @ ( fset @ A ) ) )
% 0.07/0.32 = ( A4
% 0.07/0.32 = ( bot_bot @ ( fset @ B ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fimage_is_fempty
% 0.07/0.32 thf(fact_220_empty__subsetI,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.07/0.32
% 0.07/0.32 % empty_subsetI
% 0.07/0.32 thf(fact_221_subset__empty,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.07/0.32 = ( A4
% 0.07/0.32 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_empty
% 0.07/0.32 thf(fact_222_singletonI,axiom,
% 0.07/0.32 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % singletonI
% 0.07/0.32 thf(fact_223_insert__subset,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B4 )
% 0.07/0.32 = ( ( member @ A @ X3 @ B4 )
% 0.07/0.32 & ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % insert_subset
% 0.07/0.32 thf(fact_224_Diff__cancel,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A] :
% 0.07/0.32 ( ( minus_minus @ ( set @ A ) @ A4 @ A4 )
% 0.07/0.32 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Diff_cancel
% 0.07/0.32 thf(fact_225_empty__Diff,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A] :
% 0.07/0.32 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 )
% 0.07/0.32 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % empty_Diff
% 0.07/0.32 thf(fact_226_Diff__empty,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A] :
% 0.07/0.32 ( ( minus_minus @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.07/0.32 = A4 ) ).
% 0.07/0.32
% 0.07/0.32 % Diff_empty
% 0.07/0.32 thf(fact_227_insert__Diff1,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,B4: set @ A,A4: set @ A] :
% 0.07/0.32 ( ( member @ A @ X3 @ B4 )
% 0.07/0.32 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B4 )
% 0.07/0.32 = ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % insert_Diff1
% 0.07/0.32 thf(fact_228_Diff__insert0,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ~ ( member @ A @ X3 @ A4 )
% 0.07/0.32 => ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ B4 ) )
% 0.07/0.32 = ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Diff_insert0
% 0.07/0.32 thf(fact_229_singleton__insert__inj__eq,axiom,
% 0.07/0.32 ! [A: $tType,B2: A,A2: A,A4: set @ A] :
% 0.07/0.32 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.07/0.32 = ( insert @ A @ A2 @ A4 ) )
% 0.07/0.32 = ( ( A2 = B2 )
% 0.07/0.32 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % singleton_insert_inj_eq
% 0.07/0.32 thf(fact_230_singleton__insert__inj__eq_H,axiom,
% 0.07/0.32 ! [A: $tType,A2: A,A4: set @ A,B2: A] :
% 0.07/0.32 ( ( ( insert @ A @ A2 @ A4 )
% 0.07/0.32 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.07/0.32 = ( ( A2 = B2 )
% 0.07/0.32 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % singleton_insert_inj_eq'
% 0.07/0.32 thf(fact_231_Diff__eq__empty__iff,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( ( minus_minus @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 = ( bot_bot @ ( set @ A ) ) )
% 0.07/0.32 = ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % Diff_eq_empty_iff
% 0.07/0.32 thf(fact_232_tree_Ocollapse,axiom,
% 0.07/0.32 ! [A: $tType,Tree: abstra2103299360e_tree @ A] :
% 0.07/0.32 ( ( abstra388494275e_Node @ A @ ( abstra573067619e_root @ A @ Tree ) @ ( abstra1749095923e_cont @ A @ Tree ) )
% 0.07/0.32 = Tree ) ).
% 0.07/0.32
% 0.07/0.32 % tree.collapse
% 0.07/0.32 thf(fact_233_Collect__mono__iff,axiom,
% 0.07/0.32 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q2 ) )
% 0.07/0.32 = ( ! [X6: A] :
% 0.07/0.32 ( ( P3 @ X6 )
% 0.07/0.32 => ( Q2 @ X6 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mono_iff
% 0.07/0.32 thf(fact_234_fset__eq__fsubset,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ^ [Y3: fset @ A,Z: fset @ A] : ( Y3 = Z ) )
% 0.07/0.32 = ( ^ [A7: fset @ A,B7: fset @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ A7 @ B7 )
% 0.07/0.32 & ( ord_less_eq @ ( fset @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fset_eq_fsubset
% 0.07/0.32 thf(fact_235_contra__subsetD,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ~ ( member @ A @ C2 @ B4 )
% 0.07/0.32 => ~ ( member @ A @ C2 @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % contra_subsetD
% 0.07/0.32 thf(fact_236_fsubset__trans,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A,C4: fset @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( ord_less_eq @ ( fset @ A ) @ B4 @ C4 )
% 0.07/0.32 => ( ord_less_eq @ ( fset @ A ) @ A4 @ C4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fsubset_trans
% 0.07/0.32 thf(fact_237_set__eq__subset,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ^ [Y3: set @ A,Z: set @ A] : ( Y3 = Z ) )
% 0.07/0.32 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.07/0.32 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % set_eq_subset
% 0.07/0.32 thf(fact_238_fsubset__refl,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A] : ( ord_less_eq @ ( fset @ A ) @ A4 @ A4 ) ).
% 0.07/0.32
% 0.07/0.32 % fsubset_refl
% 0.07/0.32 thf(fact_239_subset__trans,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.07/0.32 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_trans
% 0.07/0.32 thf(fact_240_Collect__mono,axiom,
% 0.07/0.32 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 0.07/0.32 ( ! [X4: A] :
% 0.07/0.32 ( ( P3 @ X4 )
% 0.07/0.32 => ( Q2 @ X4 ) )
% 0.07/0.32 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mono
% 0.07/0.32 thf(fact_241_fequalityD2,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 0.07/0.32 ( ( A4 = B4 )
% 0.07/0.32 => ( ord_less_eq @ ( fset @ A ) @ B4 @ A4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % fequalityD2
% 0.07/0.32 thf(fact_242_fequalityD1,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 0.07/0.32 ( ( A4 = B4 )
% 0.07/0.32 => ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % fequalityD1
% 0.07/0.32 thf(fact_243_subset__refl,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.07/0.32
% 0.07/0.32 % subset_refl
% 0.07/0.32 thf(fact_244_rev__subsetD,axiom,
% 0.07/0.32 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( member @ A @ C2 @ A4 )
% 0.07/0.32 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % rev_subsetD
% 0.07/0.32 thf(fact_245_fequalityE,axiom,
% 0.07/0.32 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 0.07/0.32 ( ( A4 = B4 )
% 0.07/0.32 => ~ ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 0.07/0.32 => ~ ( ord_less_eq @ ( fset @ A ) @ B4 @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % fequalityE
% 0.07/0.32 thf(fact_246_subset__iff,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) )
% 0.07/0.32 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.07/0.32 ! [T: A] :
% 0.07/0.32 ( ( member @ A @ T @ A7 )
% 0.07/0.32 => ( member @ A @ T @ B7 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_iff
% 0.07/0.32 thf(fact_247_set__rev__mp,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( member @ A @ X3 @ A4 )
% 0.07/0.32 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( member @ A @ X3 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % set_rev_mp
% 0.07/0.32 thf(fact_248_equalityD2,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( A4 = B4 )
% 0.07/0.32 => ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityD2
% 0.07/0.32 thf(fact_249_equalityD1,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( A4 = B4 )
% 0.07/0.32 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityD1
% 0.07/0.32 thf(fact_250_subset__eq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) )
% 0.07/0.32 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.07/0.32 ! [X6: A] :
% 0.07/0.32 ( ( member @ A @ X6 @ A7 )
% 0.07/0.32 => ( member @ A @ X6 @ B7 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_eq
% 0.07/0.32 thf(fact_251_equalityE,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.07/0.32 ( ( A4 = B4 )
% 0.07/0.32 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityE
% 0.07/0.32 thf(fact_252_subsetCE,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( member @ A @ C2 @ A4 )
% 0.07/0.32 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subsetCE
% 0.07/0.32 thf(fact_253_subsetD,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( member @ A @ C2 @ A4 )
% 0.07/0.32 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subsetD
% 0.07/0.32 thf(fact_254_in__mono,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A,X3: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( member @ A @ X3 @ A4 )
% 0.07/0.32 => ( member @ A @ X3 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % in_mono
% 0.07/0.32 thf(fact_255_set__mp,axiom,
% 0.07/0.32 ! [A: $tType,A4: set @ A,B4: set @ A,X3: A] :
% 0.07/0.32 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.07/0.32 => ( ( member @ A @ X3 @ A4 )
% 0.07/0.32 => ( member @ A @ X3 @ B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % set_mp
% 0.07/0.32
% 0.07/0.32 %----Type constructors (39)
% 0.07/0.32 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.07/0.32 & ( finite_finite @ A9 @ ( type2 @ A9 ) ) )
% 0.07/0.32 => ( finite_finite @ ( product_prod @ A8 @ A9 ) @ ( type2 @ ( product_prod @ A8 @ A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_FSet_Ofset___Finite__Set_Ofinite_1,axiom,
% 0.07/0.32 ! [A8: $tType] :
% 0.07/0.32 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.07/0.32 => ( finite_finite @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Finite__Set_Ofinite_2,axiom,
% 0.07/0.32 finite_finite @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Set_Oset___Finite__Set_Ofinite_3,axiom,
% 0.07/0.32 ! [A8: $tType] :
% 0.07/0.32 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.07/0.32 => ( finite_finite @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Finite__Set_Ofinite_4,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.07/0.32 & ( finite_finite @ A9 @ ( type2 @ A9 ) ) )
% 0.07/0.32 => ( finite_finite @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( order_bot @ A9 @ ( type2 @ A9 ) )
% 0.07/0.32 => ( order_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Countable_Ocountable,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.07/0.32 & ( countable @ A9 @ ( type2 @ A9 ) ) )
% 0.07/0.32 => ( countable @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.07/0.32 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.07/0.32 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Orderings_Oord,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.07/0.32 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Orderings_Obot,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 0.07/0.32 => ( bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.07/0.32 wellorder @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Oorder__bot_5,axiom,
% 0.07/0.32 order_bot @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Countable_Ocountable_6,axiom,
% 0.07/0.32 countable @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Opreorder_7,axiom,
% 0.07/0.32 preorder @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.07/0.32 linorder @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Oorder_8,axiom,
% 0.07/0.32 order @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Oord_9,axiom,
% 0.07/0.32 ord @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Obot_10,axiom,
% 0.07/0.32 bot @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Set_Oset___Orderings_Oorder__bot_11,axiom,
% 0.07/0.32 ! [A8: $tType] : ( order_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Set_Oset___Countable_Ocountable_12,axiom,
% 0.07/0.32 ! [A8: $tType] :
% 0.07/0.32 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.07/0.32 => ( countable @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Set_Oset___Orderings_Opreorder_13,axiom,
% 0.07/0.32 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Set_Oset___Orderings_Oorder_14,axiom,
% 0.07/0.32 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Set_Oset___Orderings_Oord_15,axiom,
% 0.07/0.32 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Set_Oset___Orderings_Obot_16,axiom,
% 0.07/0.32 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Oorder__bot_17,axiom,
% 0.07/0.32 order_bot @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Countable_Ocountable_18,axiom,
% 0.07/0.32 countable @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Opreorder_19,axiom,
% 0.07/0.32 preorder @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Olinorder_20,axiom,
% 0.07/0.32 linorder @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Oorder_21,axiom,
% 0.07/0.32 order @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Oord_22,axiom,
% 0.07/0.32 ord @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Obot_23,axiom,
% 0.07/0.32 bot @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_FSet_Ofset___Orderings_Oorder__bot_24,axiom,
% 0.07/0.32 ! [A8: $tType] : ( order_bot @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_FSet_Ofset___Countable_Ocountable_25,axiom,
% 0.07/0.32 ! [A8: $tType] :
% 0.07/0.32 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.07/0.32 => ( countable @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_FSet_Ofset___Orderings_Opreorder_26,axiom,
% 0.07/0.32 ! [A8: $tType] : ( preorder @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_FSet_Ofset___Orderings_Oorder_27,axiom,
% 0.07/0.32 ! [A8: $tType] : ( order @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_FSet_Ofset___Orderings_Oord_28,axiom,
% 0.07/0.32 ! [A8: $tType] : ( ord @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_FSet_Ofset___Orderings_Obot_29,axiom,
% 0.07/0.32 ! [A8: $tType] : ( bot @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Product__Type_Oprod___Countable_Ocountable_30,axiom,
% 0.07/0.32 ! [A8: $tType,A9: $tType] :
% 0.07/0.32 ( ( ( countable @ A8 @ ( type2 @ A8 ) )
% 0.07/0.32 & ( countable @ A9 @ ( type2 @ A9 ) ) )
% 0.07/0.32 => ( countable @ ( product_prod @ A8 @ A9 ) @ ( type2 @ ( product_prod @ A8 @ A9 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %----Helper facts (3)
% 0.07/0.32 thf(help_If_3_1_T,axiom,
% 0.07/0.32 ! [P3: $o] :
% 0.07/0.32 ( ( P3 = $true )
% 0.07/0.32 | ( P3 = $false ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_2_1_T,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,Y: A] :
% 0.07/0.32 ( ( if @ A @ $false @ X3 @ Y )
% 0.07/0.32 = Y ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_1_1_T,axiom,
% 0.07/0.32 ! [A: $tType,X3: A,Y: A] :
% 0.07/0.32 ( ( if @ A @ $true @ X3 @ Y )
% 0.07/0.32 = X3 ) ).
% 0.07/0.32
% 0.07/0.32 %----Conjectures (2)
% 0.07/0.32 thf(conj_0,hypothesis,
% 0.07/0.32 ! [Sl7: fset @ state] :
% 0.07/0.32 ( ( ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ Sl7 )
% 0.07/0.32 & ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ stepsa ) ) ) @ Sl7 ) )
% 0.07/0.32 => thesis ) ).
% 0.07/0.32
% 0.07/0.32 thf(conj_1,conjecture,
% 0.07/0.32 thesis ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 2.36/1.22 ---- Embedded in THF ---
% 2.36/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.36/1.23 %%% Generated on Tue Feb 24 04:15:31 EST 2026
% 2.36/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 2.36/1.23 %%% Logic specification used:
% 2.36/1.23 %%% thf(spec, logic, $$dhol).
% 2.36/1.23
% 2.36/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VC7EeYKUxt/DTF2DTF19284.p
% 2.36/1.23 thf(ty_t_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree, type, abstra2103299360e_tree: ($tType > $tType)).
% 2.36/1.23 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.36/1.23 thf(ty_t_Stream_Ostream, type, stream: ($tType > $tType)).
% 2.36/1.23 thf(ty_t_FSet_Ofset, type, fset: ($tType > $tType)).
% 2.36/1.23 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.36/1.23 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.36/1.23 thf(ty_tf_state, type, state: $tType).
% 2.36/1.23 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.36/1.23 thf(ty_tf_rule, type, rule: $tType).
% 2.36/1.23 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_Countable_Ocountable, type, countable: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem, type, abstra1326562878System: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > ((stream @ Rule) > ((set @ State) > $o)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_OminWait, type, abstra1332369113inWait: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > ((stream @ Rule) > (State > nat)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_Oper, type, abstra2096684367le_per: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > ((stream @ Rule) > ((set @ State) > (Rule > $o))))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_Opos, type, abstra2097340358le_pos: (!> [A:$tType]: (((stream @ A) > (A > nat))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OSaturated, type, abstra1209608345urated: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > ((stream @ Rule) > ((stream @ ((product_prod @ State) @ Rule)) > $o)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Oenabled, type, abstra1874422341nabled: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > (Rule > (State > $o)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Oepath, type, abstra523868654_epath: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > ((stream @ Rule) > ((stream @ ((product_prod @ State) @ Rule)) > $o)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Ofair, type, abstra928354080m_fair: (!> [Rule:$tType]: (((stream @ Rule) > ((stream @ Rule) > $o))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Ofenum, type, abstra1774373515_fenum: (!> [Rule:$tType]: (((stream @ Rule) > (stream @ Rule))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OmkTree, type, abstra1225283448mkTree: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > ((stream @ Rule) > (State > (abstra2103299360e_tree @ ((product_prod @ State) @ Rule)))))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OpickEff, type, abstra1276541928ickEff: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > (Rule > (State > (fset @ State))))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Osaturated, type, abstra726722745urated: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > (Rule > ((stream @ ((product_prod @ State) @ Rule)) > $o)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Otrim, type, abstra1259602206m_trim: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > ((stream @ Rule) > (State > (stream @ Rule))))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Owf, type, abstra1874736267tem_wf: (!> [Rule:$tType,State:$tType]: (((Rule > (State > ((fset @ State) > $o))) > ((stream @ Rule) > ((abstra2103299360e_tree @ ((product_prod @ State) @ Rule)) > $o)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Oipath, type, abstra313004635_ipath: (!> [A:$tType]: (((abstra2103299360e_tree @ A) > ((stream @ A) > $o))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_ONode, type, abstra388494275e_Node: (!> [A:$tType]: ((A > ((fset @ (abstra2103299360e_tree @ A)) > (abstra2103299360e_tree @ A)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_Ocont, type, abstra1749095923e_cont: (!> [A:$tType]: (((abstra2103299360e_tree @ A) > (fset @ (abstra2103299360e_tree @ A)))))).
% 2.36/1.23 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_Oroot, type, abstra573067619e_root: (!> [A:$tType]: (((abstra2103299360e_tree @ A) > A)))).
% 2.36/1.23 thf(sy_c_Countable__Set_Ocountable, type, countable_countable: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.36/1.23 thf(sy_c_FSet_Ofimage, type, fimage: (!> [A:$tType,B:$tType]: (((A > B) > ((fset @ A) > (fset @ B)))))).
% 2.36/1.23 thf(sy_c_FSet_Ofmember, type, fmember: (!> [A:$tType]: ((A > ((fset @ A) > $o))))).
% 2.36/1.23 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.36/1.23 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.36/1.23 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.36/1.23 thf(sy_c_Orderings_Oord__class_OLeast, type, ord_Least: (!> [A:$tType]: (((A > $o) > A)))).
% 2.36/1.23 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.36/1.23 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.36/1.23 thf(sy_c_Product__Type_Oprod_Ofst, type, product_fst: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > A)))).
% 2.36/1.23 thf(sy_c_Product__Type_Oprod_Osnd, type, product_snd: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > B)))).
% 2.36/1.23 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.36/1.23 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.36/1.23 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.36/1.23 thf(sy_c_Stream_Osdrop, type, sdrop: (!> [A:$tType]: ((nat > ((stream @ A) > (stream @ A)))))).
% 2.36/1.23 thf(sy_c_Stream_Osdrop__while, type, sdrop_while: (!> [A:$tType]: (((A > $o) > ((stream @ A) > (stream @ A)))))).
% 2.36/1.23 thf(sy_c_Stream_Ostream_Ocase__stream, type, case_stream: (!> [A:$tType,B:$tType]: (((A > ((stream @ A) > B)) > ((stream @ A) > B))))).
% 2.36/1.23 thf(sy_c_Stream_Ostream_Oshd, type, shd: (!> [A:$tType]: (((stream @ A) > A)))).
% 2.36/1.23 thf(sy_c_Stream_Ostream_Osset, type, sset: (!> [A:$tType]: (((stream @ A) > (set @ A))))).
% 2.36/1.23 thf(sy_c_Stream_Ostream_Ostl, type, stl: (!> [A:$tType]: (((stream @ A) > (stream @ A))))).
% 2.36/1.23 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.36/1.23 thf(sy_v_S, type, s: (set @ state)).
% 2.36/1.23 thf(sy_v_eff, type, eff: (rule > (state > ((fset @ state) > $o)))).
% 2.36/1.23 thf(sy_v_r, type, r: rule).
% 2.36/1.23 thf(sy_v_rules, type, rules: (stream @ rule)).
% 2.36/1.23 thf(sy_v_steps, type, steps: (stream @ ((product_prod @ state) @ rule))).
% 2.36/1.23 thf(sy_v_stepsa____, type, stepsa: (stream @ ((product_prod @ state) @ rule))).
% 2.36/1.23 thf(sy_v_thesis____, type, thesis: $o).
% 2.36/1.23 thf(fact_0_calculation_I1_J, axiom, (((member @ state) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ stepsa))) @ s)).
% 2.36/1.23 thf(fact_1_calculation_I3_J, axiom, ((((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ stepsa)) != r)).
% 2.36/1.23 thf(fact_2_e, axiom, ((((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ steps) & (((member @ state) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ steps))) @ s))).
% 2.36/1.23 thf(fact_3_calculation_I2_J, axiom, (((((abstra1874422341nabled @ rule) @ state) @ eff) @ r) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ stepsa)))).
% 2.36/1.23 thf(fact_4_enabled__def, axiom, (! [R:rule,S:state]: (((((((abstra1874422341nabled @ rule) @ state) @ eff) @ R) @ S) = ((^ [P:((fset @ state) > $o)]: ((? [X:(fset @ state)]: ((P @ X))))) @ ((eff @ R) @ S)))))).
% 2.36/1.23 thf(fact_5_epath_Ocases, axiom, (! [A2:(stream @ ((product_prod @ state) @ rule))]: (((((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ A2) => (~ (((((member @ rule) @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ A2))) @ ((sset @ rule) @ rules)) => (! [Sl:(fset @ state)]: (((((fmember @ state) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ ((stl @ ((product_prod @ state) @ rule)) @ A2)))) @ Sl) => ((((eff @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ A2))) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ A2))) @ Sl) => (~ ((((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ ((stl @ ((product_prod @ state) @ rule)) @ A2))))))))))))))).
% 2.36/1.23 thf(fact_6_epath_Ocoinduct, axiom, (! [X2:((stream @ ((product_prod @ state) @ rule)) > $o),X3:(stream @ ((product_prod @ state) @ rule))]: (((X2 @ X3) => ((! [X4:(stream @ ((product_prod @ state) @ rule))]: (((X2 @ X4) => (? [Steps:(stream @ ((product_prod @ state) @ rule)),Sl2:(fset @ state)]: (((X4 = Steps) & ((((member @ rule) @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps))) @ ((sset @ rule) @ rules)) & ((((fmember @ state) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ ((stl @ ((product_prod @ state) @ rule)) @ Steps)))) @ Sl2) & ((((eff @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps))) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps))) @ Sl2) & ((X2 @ ((stl @ ((product_prod @ state) @ rule)) @ Steps)) | (((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ ((stl @ ((product_prod @ state) @ rule)) @ Steps)))))))))))) => (((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ X3)))))).
% 2.36/1.23 thf(fact_7_epath_Ointros, axiom, (! [Steps2:(stream @ ((product_prod @ state) @ rule)),Sl3:(fset @ state)]: (((((member @ rule) @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps2))) @ ((sset @ rule) @ rules)) => ((((fmember @ state) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ ((stl @ ((product_prod @ state) @ rule)) @ Steps2)))) @ Sl3) => ((((eff @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps2))) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps2))) @ Sl3) => ((((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ ((stl @ ((product_prod @ state) @ rule)) @ Steps2)) => (((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ Steps2)))))))).
% 2.36/1.23 thf(fact_8_epath_Osimps, axiom, (! [A2:(stream @ ((product_prod @ state) @ rule))]: (((((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ A2) = (? [Steps3:(stream @ ((product_prod @ state) @ rule)),Sl4:(fset @ state)]: (((A2 = Steps3) & ((((member @ rule) @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps3))) @ ((sset @ rule) @ rules)) & ((((fmember @ state) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ ((stl @ ((product_prod @ state) @ rule)) @ Steps3)))) @ Sl4) & ((((eff @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps3))) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ Steps3))) @ Sl4) & (((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ ((stl @ ((product_prod @ state) @ rule)) @ Steps3)))))))))))).
% 2.36/1.23 thf(fact_9_stream_Oexpand, axiom, (! [A:$tType,Stream:(stream @ A),Stream2:(stream @ A)]: ((((((shd @ A) @ Stream) = ((shd @ A) @ Stream2)) & (((stl @ A) @ Stream) = ((stl @ A) @ Stream2))) => (Stream = Stream2))))).
% 2.36/1.23 thf(fact_10_stream_Ocoinduct, axiom, (! [A:$tType,R2:((stream @ A) > ((stream @ A) > $o)),Stream:(stream @ A),Stream2:(stream @ A)]: ((((R2 @ Stream) @ Stream2) => ((! [Stream3:(stream @ A),Stream4:(stream @ A)]: ((((R2 @ Stream3) @ Stream4) => ((((shd @ A) @ Stream3) = ((shd @ A) @ Stream4)) & ((R2 @ ((stl @ A) @ Stream3)) @ ((stl @ A) @ Stream4)))))) => (Stream = Stream2)))))).
% 2.36/1.23 thf(fact_11_stream_Ocoinduct__strong, axiom, (! [A:$tType,R2:((stream @ A) > ((stream @ A) > $o)),Stream:(stream @ A),Stream2:(stream @ A)]: ((((R2 @ Stream) @ Stream2) => ((! [Stream3:(stream @ A),Stream4:(stream @ A)]: ((((R2 @ Stream3) @ Stream4) => ((((shd @ A) @ Stream3) = ((shd @ A) @ Stream4)) & (((R2 @ ((stl @ A) @ Stream3)) @ ((stl @ A) @ Stream4)) | (((stl @ A) @ Stream3) = ((stl @ A) @ Stream4))))))) => (Stream = Stream2)))))).
% 2.36/1.23 thf(fact_12_RuleSystem__axioms, axiom, (((((abstra1326562878System @ rule) @ state) @ eff) @ rules) @ s)).
% 2.36/1.23 thf(fact_13_prod__eqI, axiom, (! [B:$tType,A:$tType,P2:((product_prod @ A) @ B),Q:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ P2) = (((product_fst @ A) @ B) @ Q)) => (((((product_snd @ A) @ B) @ P2) = (((product_snd @ A) @ B) @ Q)) => (P2 = Q)))))).
% 2.36/1.23 thf(fact_14_p, axiom, ((((((abstra2096684367le_per @ rule) @ state) @ eff) @ rules) @ s) @ r)).
% 2.36/1.23 thf(fact_15_enabled__R, axiom, (! [S:state]: (((((member @ state) @ S) @ s) => (? [X4:rule]: (((((member @ rule) @ X4) @ ((sset @ rule) @ rules)) & (? [X1:(fset @ state)]: ((((eff @ X4) @ S) @ X1)))))))))).
% 2.36/1.23 thf(fact_16_calculation_I4_J, axiom, (((member @ rule) @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ stepsa))) @ ((sset @ rule) @ rules))).
% 2.36/1.23 thf(fact_17_eff__S, axiom, (! [S:state,R:rule,Sl3:(fset @ state),S2:state]: (((((member @ state) @ S) @ s) => ((((member @ rule) @ R) @ ((sset @ rule) @ rules)) => ((((eff @ R) @ S) @ Sl3) => ((((fmember @ state) @ S2) @ Sl3) => (((member @ state) @ S2) @ s)))))))).
% 2.36/1.23 thf(fact_18_sset__fenum, axiom, (((sset @ rule) @ ((abstra1774373515_fenum @ rule) @ rules)) = ((sset @ rule) @ rules))).
% 2.36/1.23 thf(fact_19_pickEff, axiom, (! [R:rule,S:state]: (((((((abstra1874422341nabled @ rule) @ state) @ eff) @ R) @ S) => (((eff @ R) @ S) @ (((((abstra1276541928ickEff @ rule) @ state) @ eff) @ R) @ S)))))).
% 2.36/1.23 thf(fact_20_RuleSystem_Oenabled__R, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => (? [X4:Rule]: (((((member @ Rule) @ X4) @ ((sset @ Rule) @ Rules)) & (? [X1:(fset @ State)]: ((((Eff @ X4) @ S) @ X1))))))))))).
% 2.36/1.23 thf(fact_21_RuleSystem__Defs_Oenabled__def, axiom, (! [State:$tType,Rule:$tType]: ((((abstra1874422341nabled @ Rule) @ State) = (^ [Eff2:(Rule > (State > ((fset @ State) > $o))),R3:Rule,S4:State]: (((^ [P:((fset @ State) > $o)]: ((? [X:(fset @ State)]: ((P @ X))))) @ ((Eff2 @ R3) @ S4)))))))).
% 2.36/1.23 thf(fact_22_RuleSystem_Ointro, axiom, (! [Rule:$tType,State:$tType,S3:(set @ State),Rules:(stream @ Rule),Eff:(Rule > (State > ((fset @ State) > $o)))]: (((! [S5:State]: (((((member @ State) @ S5) @ S3) => (! [R4:Rule]: (((((member @ Rule) @ R4) @ ((sset @ Rule) @ Rules)) => (! [Sl:(fset @ State)]: (((((Eff @ R4) @ S5) @ Sl) => (! [S6:State]: (((((fmember @ State) @ S6) @ Sl) => (((member @ State) @ S6) @ S3))))))))))))) => ((! [S5:State]: (((((member @ State) @ S5) @ S3) => (? [X5:Rule]: (((((member @ Rule) @ X5) @ ((sset @ Rule) @ Rules)) & (? [X12:(fset @ State)]: ((((Eff @ X5) @ S5) @ X12))))))))) => (((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3)))))).
% 2.36/1.23 thf(fact_23_RuleSystem_Oeff__S, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,R:Rule,Sl3:(fset @ State),S2:State]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((member @ Rule) @ R) @ ((sset @ Rule) @ Rules)) => ((((Eff @ R) @ S) @ Sl3) => ((((fmember @ State) @ S2) @ Sl3) => (((member @ State) @ S2) @ S3))))))))).
% 2.36/1.23 thf(fact_24_RuleSystem__def, axiom, (! [State:$tType,Rule:$tType]: ((((abstra1326562878System @ Rule) @ State) = (^ [Eff2:(Rule > (State > ((fset @ State) > $o))),Rules2:(stream @ Rule),S7:(set @ State)]: (((! [S4:State]: (((((member @ State) @ S4) @ S7) => (! [R3:Rule]: (((((member @ Rule) @ R3) @ ((sset @ Rule) @ Rules2)) => (! [Sl4:(fset @ State)]: (((((Eff2 @ R3) @ S4) @ Sl4) => (! [S8:State]: (((((fmember @ State) @ S8) @ Sl4) => (((member @ State) @ S8) @ S7))))))))))))) & (! [S4:State]: (((((member @ State) @ S4) @ S7) => (? [X6:Rule]: (((((member @ Rule) @ X6) @ ((sset @ Rule) @ Rules2)) & ((^ [P:((fset @ State) > $o)]: ((? [X:(fset @ State)]: ((P @ X))))) @ ((Eff2 @ X6) @ S4))))))))))))))).
% 2.36/1.23 thf(fact_25_stl__sset, axiom, (! [A:$tType,X3:A,A2:(stream @ A)]: (((((member @ A) @ X3) @ ((sset @ A) @ ((stl @ A) @ A2))) => (((member @ A) @ X3) @ ((sset @ A) @ A2)))))).
% 2.36/1.23 thf(fact_26_shd__sset, axiom, (! [A:$tType,A2:(stream @ A)]: ((((member @ A) @ ((shd @ A) @ A2)) @ ((sset @ A) @ A2))))).
% 2.36/1.23 thf(fact_27_sset__induct, axiom, (! [A:$tType,Y:A,S:(stream @ A),P3:(A > ((stream @ A) > $o))]: (((((member @ A) @ Y) @ ((sset @ A) @ S)) => ((! [S5:(stream @ A)]: (((P3 @ ((shd @ A) @ S5)) @ S5))) => ((! [S5:(stream @ A),Y2:A]: (((((member @ A) @ Y2) @ ((sset @ A) @ ((stl @ A) @ S5))) => (((P3 @ Y2) @ ((stl @ A) @ S5)) => ((P3 @ Y2) @ S5))))) => ((P3 @ Y) @ S))))))).
% 2.36/1.23 thf(fact_28_RuleSystem__Defs_Oepath_Ocoinduct, axiom, (! [Rule:$tType,State:$tType,X2:((stream @ ((product_prod @ State) @ Rule)) > $o),X3:(stream @ ((product_prod @ State) @ Rule)),Rules:(stream @ Rule),Eff:(Rule > (State > ((fset @ State) > $o)))]: (((X2 @ X3) => ((! [X4:(stream @ ((product_prod @ State) @ Rule))]: (((X2 @ X4) => (? [Steps:(stream @ ((product_prod @ State) @ Rule)),Sl2:(fset @ State)]: (((X4 = Steps) & ((((member @ Rule) @ (((product_snd @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps))) @ ((sset @ Rule) @ Rules)) & ((((fmember @ State) @ (((product_fst @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ ((stl @ ((product_prod @ State) @ Rule)) @ Steps)))) @ Sl2) & ((((Eff @ (((product_snd @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps))) @ (((product_fst @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps))) @ Sl2) & ((X2 @ ((stl @ ((product_prod @ State) @ Rule)) @ Steps)) | (((((abstra523868654_epath @ Rule) @ State) @ Eff) @ Rules) @ ((stl @ ((product_prod @ State) @ Rule)) @ Steps)))))))))))) => (((((abstra523868654_epath @ Rule) @ State) @ Eff) @ Rules) @ X3)))))).
% 2.36/1.23 thf(fact_29_RuleSystem__Defs_Oepath_Ointros, axiom, (! [Rule:$tType,State:$tType,Steps2:(stream @ ((product_prod @ State) @ Rule)),Rules:(stream @ Rule),Sl3:(fset @ State),Eff:(Rule > (State > ((fset @ State) > $o)))]: (((((member @ Rule) @ (((product_snd @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps2))) @ ((sset @ Rule) @ Rules)) => ((((fmember @ State) @ (((product_fst @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ ((stl @ ((product_prod @ State) @ Rule)) @ Steps2)))) @ Sl3) => ((((Eff @ (((product_snd @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps2))) @ (((product_fst @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps2))) @ Sl3) => ((((((abstra523868654_epath @ Rule) @ State) @ Eff) @ Rules) @ ((stl @ ((product_prod @ State) @ Rule)) @ Steps2)) => (((((abstra523868654_epath @ Rule) @ State) @ Eff) @ Rules) @ Steps2)))))))).
% 2.36/1.23 thf(fact_30_RuleSystem__Defs_Oepath_Osimps, axiom, (! [State:$tType,Rule:$tType]: ((((abstra523868654_epath @ Rule) @ State) = (^ [Eff2:(Rule > (State > ((fset @ State) > $o))),Rules2:(stream @ Rule),A3:(stream @ ((product_prod @ State) @ Rule))]: ((? [Steps3:(stream @ ((product_prod @ State) @ Rule)),Sl4:(fset @ State)]: (((A3 = Steps3) & ((((member @ Rule) @ (((product_snd @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps3))) @ ((sset @ Rule) @ Rules2)) & ((((fmember @ State) @ (((product_fst @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ ((stl @ ((product_prod @ State) @ Rule)) @ Steps3)))) @ Sl4) & ((((Eff2 @ (((product_snd @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps3))) @ (((product_fst @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ Steps3))) @ Sl4) & (((((abstra523868654_epath @ Rule) @ State) @ Eff2) @ Rules2) @ ((stl @ ((product_prod @ State) @ Rule)) @ Steps3)))))))))))))).
% 2.36/1.23 thf(fact_31_RuleSystem__Defs_Oepath_Ocases, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),A2:(stream @ ((product_prod @ State) @ Rule))]: (((((((abstra523868654_epath @ Rule) @ State) @ Eff) @ Rules) @ A2) => (~ (((((member @ Rule) @ (((product_snd @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ A2))) @ ((sset @ Rule) @ Rules)) => (! [Sl:(fset @ State)]: (((((fmember @ State) @ (((product_fst @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ ((stl @ ((product_prod @ State) @ Rule)) @ A2)))) @ Sl) => ((((Eff @ (((product_snd @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ A2))) @ (((product_fst @ State) @ Rule) @ ((shd @ ((product_prod @ State) @ Rule)) @ A2))) @ Sl) => (~ ((((((abstra523868654_epath @ Rule) @ State) @ Eff) @ Rules) @ ((stl @ ((product_prod @ State) @ Rule)) @ A2))))))))))))))).
% 2.36/1.23 thf(fact_32_prod__eq__iff, axiom, (! [B:$tType,A:$tType]: (((^ [Y3:((product_prod @ A) @ B),Z:((product_prod @ A) @ B)]: ((Y3 = Z))) = (^ [S4:((product_prod @ A) @ B),T:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ S4) = (((product_fst @ A) @ B) @ T)) & ((((product_snd @ A) @ B) @ S4) = (((product_snd @ A) @ B) @ T))))))))).
% 2.36/1.23 thf(fact_33_prod_Oexpand, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B),Prod2:((product_prod @ A) @ B)]: (((((((product_fst @ A) @ B) @ Prod) = (((product_fst @ A) @ B) @ Prod2)) & ((((product_snd @ A) @ B) @ Prod) = (((product_snd @ A) @ B) @ Prod2))) => (Prod = Prod2))))).
% 2.36/1.23 thf(fact_34_Saturated__def, axiom, (! [Steps2:(stream @ ((product_prod @ state) @ rule))]: (((((((abstra1209608345urated @ rule) @ state) @ eff) @ rules) @ Steps2) = (! [X6:rule]: (((((member @ rule) @ X6) @ ((sset @ rule) @ rules)) => (((((abstra726722745urated @ rule) @ state) @ eff) @ X6) @ Steps2)))))))).
% 2.36/1.23 thf(fact_35_local_Oalw, axiom, ((((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ stepsa) & (((member @ state) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ stepsa))) @ s))).
% 2.36/1.23 thf(fact_36_NE__R, axiom, (((sset @ rule) @ rules) != (bot_bot @ (set @ rule)))).
% 2.36/1.23 thf(fact_37_fair__stl, axiom, (! [Rs:(stream @ rule)]: (((((abstra928354080m_fair @ rule) @ rules) @ Rs) => (((abstra928354080m_fair @ rule) @ rules) @ ((stl @ rule) @ Rs)))))).
% 2.36/1.23 thf(fact_38_exE__realizer_H, axiom, (! [A:$tType,B:$tType,P3:(A > (B > $o)),P2:((product_prod @ B) @ A)]: ((((P3 @ (((product_snd @ B) @ A) @ P2)) @ (((product_fst @ B) @ A) @ P2)) => (~ ((! [X4:B,Y2:A]: ((~ (((P3 @ Y2) @ X4))))))))))).
% 2.36/1.23 thf(fact_39_countable__R, axiom, ((countable_countable @ rule) @ ((sset @ rule) @ rules))).
% 2.36/1.23 thf(fact_40_trim__enabled, axiom, (! [S:state,Rs:(stream @ rule)]: (((((member @ state) @ S) @ s) => ((((abstra928354080m_fair @ rule) @ rules) @ Rs) => (((((abstra1874422341nabled @ rule) @ state) @ eff) @ ((shd @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S))) @ S)))))).
% 2.36/1.23 thf(fact_41_trim__in__R, axiom, (! [S:state,Rs:(stream @ rule)]: (((((member @ state) @ S) @ s) => ((((abstra928354080m_fair @ rule) @ rules) @ Rs) => (((member @ rule) @ ((shd @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S))) @ ((sset @ rule) @ rules))))))).
% 2.36/1.23 thf(fact_42_wf__ipath__epath, axiom, (! [T2:(abstra2103299360e_tree @ ((product_prod @ state) @ rule)),Steps2:(stream @ ((product_prod @ state) @ rule))]: (((((((abstra1874736267tem_wf @ rule) @ state) @ eff) @ rules) @ T2) => ((((abstra313004635_ipath @ ((product_prod @ state) @ rule)) @ T2) @ Steps2) => (((((abstra523868654_epath @ rule) @ state) @ eff) @ rules) @ Steps2)))))).
% 2.36/1.23 thf(fact_43_minWait__ex, axiom, (! [S:state,Rs:(stream @ rule)]: (((((member @ state) @ S) @ s) => ((((abstra928354080m_fair @ rule) @ rules) @ Rs) => (? [N:nat]: ((((((abstra1874422341nabled @ rule) @ state) @ eff) @ ((shd @ rule) @ (((sdrop @ rule) @ N) @ Rs))) @ S)))))))).
% 2.36/1.23 thf(fact_44_trim__fair, axiom, (! [S:state,Rs:(stream @ rule)]: (((((member @ state) @ S) @ s) => ((((abstra928354080m_fair @ rule) @ rules) @ Rs) => (((abstra928354080m_fair @ rule) @ rules) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S))))))).
% 2.36/1.23 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P3:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P3)) = (P3 @ A2))))).
% 2.36/1.23 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X6:A]: ((((member @ A) @ X6) @ A4)))) = A4)))).
% 2.36/1.23 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o)]: (((! [X4:A]: (((P3 @ X4) = (Q2 @ X4)))) => (((collect @ A) @ P3) = ((collect @ A) @ Q2)))))).
% 2.36/1.23 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.36/1.23 thf(fact_49_sdrop__fair, axiom, (! [Rs:(stream @ rule),M:nat]: (((((abstra928354080m_fair @ rule) @ rules) @ Rs) => (((abstra928354080m_fair @ rule) @ rules) @ (((sdrop @ rule) @ M) @ Rs)))))).
% 2.36/1.23 thf(fact_50_fair__fenum, axiom, (((abstra928354080m_fair @ rule) @ rules) @ ((abstra1774373515_fenum @ rule) @ rules))).
% 2.36/1.23 thf(fact_51_RuleSystem__Defs_Osdrop__fair, axiom, (! [Rule:$tType,Rules:(stream @ Rule),Rs:(stream @ Rule),M:nat]: (((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => (((abstra928354080m_fair @ Rule) @ Rules) @ (((sdrop @ Rule) @ M) @ Rs)))))).
% 2.36/1.23 thf(fact_52_RuleSystem__Defs_Ofair__fenum, axiom, (! [Rule:$tType,Rules:(stream @ Rule)]: ((((abstra928354080m_fair @ Rule) @ Rules) @ ((abstra1774373515_fenum @ Rule) @ Rules))))).
% 2.36/1.23 thf(fact_53_RuleSystem_Otrim__fair, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,Rs:(stream @ Rule)]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => (((abstra928354080m_fair @ Rule) @ Rules) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff) @ Rs) @ S)))))))).
% 2.36/1.23 thf(fact_54_RuleSystem__Defs_Owf__ipath__epath, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),T2:(abstra2103299360e_tree @ ((product_prod @ State) @ Rule)),Steps2:(stream @ ((product_prod @ State) @ Rule))]: (((((((abstra1874736267tem_wf @ Rule) @ State) @ Eff) @ Rules) @ T2) => ((((abstra313004635_ipath @ ((product_prod @ State) @ Rule)) @ T2) @ Steps2) => (((((abstra523868654_epath @ Rule) @ State) @ Eff) @ Rules) @ Steps2)))))).
% 2.36/1.23 thf(fact_55_RuleSystem__Defs_Ocountable__R, axiom, (! [Rule:$tType,Rules:(stream @ Rule)]: (((countable_countable @ Rule) @ ((sset @ Rule) @ Rules))))).
% 2.36/1.23 thf(fact_56_sdrop__stl, axiom, (! [A:$tType,N2:nat,S:(stream @ A)]: (((((sdrop @ A) @ N2) @ ((stl @ A) @ S)) = ((stl @ A) @ (((sdrop @ A) @ N2) @ S)))))).
% 2.36/1.23 thf(fact_57_RuleSystem__Defs_ONE__R, axiom, (! [Rule:$tType,Rules:(stream @ Rule)]: ((((sset @ Rule) @ Rules) != (bot_bot @ (set @ Rule)))))).
% 2.36/1.23 thf(fact_58_RuleSystem__Defs_Ofair__stl, axiom, (! [Rule:$tType,Rules:(stream @ Rule),Rs:(stream @ Rule)]: (((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => (((abstra928354080m_fair @ Rule) @ Rules) @ ((stl @ Rule) @ Rs)))))).
% 2.36/1.23 thf(fact_59_RuleSystem_OminWait__ex, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,Rs:(stream @ Rule)]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => (? [N:nat]: ((((((abstra1874422341nabled @ Rule) @ State) @ Eff) @ ((shd @ Rule) @ (((sdrop @ Rule) @ N) @ Rs))) @ S))))))))).
% 2.36/1.23 thf(fact_60_RuleSystem_Otrim__in__R, axiom, (! [State:$tType,Rule:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,Rs:(stream @ Rule)]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => (((member @ Rule) @ ((shd @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff) @ Rs) @ S))) @ ((sset @ Rule) @ Rules)))))))).
% 2.36/1.23 thf(fact_61_RuleSystem_Otrim__enabled, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,Rs:(stream @ Rule)]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => (((((abstra1874422341nabled @ Rule) @ State) @ Eff) @ ((shd @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff) @ Rs) @ S))) @ S))))))).
% 2.36/1.23 thf(fact_62_RuleSystem__Defs_OSaturated__def, axiom, (! [State:$tType,Rule:$tType]: ((((abstra1209608345urated @ Rule) @ State) = (^ [Eff2:(Rule > (State > ((fset @ State) > $o))),Rules2:(stream @ Rule),Steps3:(stream @ ((product_prod @ State) @ Rule))]: ((! [X6:Rule]: (((((member @ Rule) @ X6) @ ((sset @ Rule) @ Rules2)) => (((((abstra726722745urated @ Rule) @ State) @ Eff2) @ X6) @ Steps3)))))))))).
% 2.36/1.23 thf(fact_63_RuleSystem__Defs_OpickEff, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),R:Rule,S:State]: (((((((abstra1874422341nabled @ Rule) @ State) @ Eff) @ R) @ S) => (((Eff @ R) @ S) @ (((((abstra1276541928ickEff @ Rule) @ State) @ Eff) @ R) @ S)))))).
% 2.36/1.23 thf(fact_64_RuleSystem__Defs_Osset__fenum, axiom, (! [Rule:$tType,Rules:(stream @ Rule)]: ((((sset @ Rule) @ ((abstra1774373515_fenum @ Rule) @ Rules)) = ((sset @ Rule) @ Rules))))).
% 2.36/1.23 thf(fact_65_trim__alt, axiom, (! [S:state,Rs:(stream @ rule)]: (((((member @ state) @ S) @ s) => ((((abstra928354080m_fair @ rule) @ rules) @ Rs) => ((((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S) = (((sdrop @ rule) @ (((((abstra1332369113inWait @ rule) @ state) @ eff) @ Rs) @ S)) @ Rs))))))).
% 2.36/1.23 thf(fact_66_pos, axiom, (! [Rs:(stream @ rule),R:rule]: (((((abstra928354080m_fair @ rule) @ rules) @ Rs) => ((((member @ rule) @ R) @ ((sset @ rule) @ rules)) => (((shd @ rule) @ (((sdrop @ rule) @ (((abstra2097340358le_pos @ rule) @ Rs) @ R)) @ Rs)) = R)))))).
% 2.36/1.23 thf(fact_67_trim__def, axiom, (! [Rs:(stream @ rule),S:state]: (((((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S) = (((sdrop_while @ rule) @ (^ [R3:rule]: ((~ ((((((abstra1874422341nabled @ rule) @ state) @ eff) @ R3) @ S)))))) @ Rs))))).
% 2.36/1.23 thf(fact_68_wf__mkTree, axiom, (! [S:state,Rs:(stream @ rule)]: (((((member @ state) @ S) @ s) => ((((abstra928354080m_fair @ rule) @ rules) @ Rs) => (((((abstra1874736267tem_wf @ rule) @ state) @ eff) @ rules) @ (((((abstra1225283448mkTree @ rule) @ state) @ eff) @ Rs) @ S))))))).
% 2.36/1.23 thf(fact_69_countable__empty, axiom, (! [A:$tType]: (((countable_countable @ A) @ (bot_bot @ (set @ A)))))).
% 2.36/1.23 thf(fact_70_RuleSystem_Opos, axiom, (! [State:$tType,Rule:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),Rs:(stream @ Rule),R:Rule]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => ((((member @ Rule) @ R) @ ((sset @ Rule) @ Rules)) => (((shd @ Rule) @ (((sdrop @ Rule) @ (((abstra2097340358le_pos @ Rule) @ Rs) @ R)) @ Rs)) = R))))))).
% 2.36/1.23 thf(fact_71_in__cont__mkTree, axiom, (! [S:state,Rs:(stream @ rule),T3:(abstra2103299360e_tree @ ((product_prod @ state) @ rule))]: (((((member @ state) @ S) @ s) => ((((abstra928354080m_fair @ rule) @ rules) @ Rs) => ((((fmember @ (abstra2103299360e_tree @ ((product_prod @ state) @ rule))) @ T3) @ ((abstra1749095923e_cont @ ((product_prod @ state) @ rule)) @ (((((abstra1225283448mkTree @ rule) @ state) @ eff) @ Rs) @ S))) => (? [Sl5:(fset @ state),S6:state]: (((((member @ state) @ S6) @ s) & ((((eff @ ((shd @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S))) @ S) @ Sl5) & ((((fmember @ state) @ S6) @ Sl5) & (T3 = (((((abstra1225283448mkTree @ rule) @ state) @ eff) @ ((stl @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S))) @ S6))))))))))))).
% 2.36/1.23 thf(fact_72_RuleSystem_Otrim__alt, axiom, (! [State:$tType,Rule:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,Rs:(stream @ Rule)]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => ((((((abstra1259602206m_trim @ Rule) @ State) @ Eff) @ Rs) @ S) = (((sdrop @ Rule) @ (((((abstra1332369113inWait @ Rule) @ State) @ Eff) @ Rs) @ S)) @ Rs)))))))).
% 2.36/1.23 thf(fact_73_countableI__type, axiom, (! [A:$tType]: ((((countable @ A) @ (type2 @ A)) => (! [A4:(set @ A)]: (((countable_countable @ A) @ A4))))))).
% 2.36/1.23 thf(fact_74_ipath__mkTree__sdrop, axiom, (! [S:state,Rs:(stream @ rule),Steps2:(stream @ ((product_prod @ state) @ rule)),M:nat]: (((((member @ state) @ S) @ s) => ((((abstra928354080m_fair @ rule) @ rules) @ Rs) => ((((abstra313004635_ipath @ ((product_prod @ state) @ rule)) @ (((((abstra1225283448mkTree @ rule) @ state) @ eff) @ Rs) @ S)) @ Steps2) => (? [N:nat,S6:state]: (((((member @ state) @ S6) @ s) & (((abstra313004635_ipath @ ((product_prod @ state) @ rule)) @ (((((abstra1225283448mkTree @ rule) @ state) @ eff) @ (((sdrop @ rule) @ N) @ Rs)) @ S6)) @ (((sdrop @ ((product_prod @ state) @ rule)) @ M) @ Steps2))))))))))).
% 2.36/1.23 thf(fact_75_sdrop__while_Osimps, axiom, (! [A:$tType]: (((sdrop_while @ A) = (^ [P4:(A > $o),S4:(stream @ A)]: (((((if @ (stream @ A)) @ (P4 @ ((shd @ A) @ S4))) @ (((sdrop_while @ A) @ P4) @ ((stl @ A) @ S4))) @ S4))))))).
% 2.36/1.23 thf(fact_76_RuleSystem_Oin__cont__mkTree, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,Rs:(stream @ Rule),T3:(abstra2103299360e_tree @ ((product_prod @ State) @ Rule))]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => ((((fmember @ (abstra2103299360e_tree @ ((product_prod @ State) @ Rule))) @ T3) @ ((abstra1749095923e_cont @ ((product_prod @ State) @ Rule)) @ (((((abstra1225283448mkTree @ Rule) @ State) @ Eff) @ Rs) @ S))) => (? [Sl5:(fset @ State),S6:State]: (((((member @ State) @ S6) @ S3) & ((((Eff @ ((shd @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff) @ Rs) @ S))) @ S) @ Sl5) & ((((fmember @ State) @ S6) @ Sl5) & (T3 = (((((abstra1225283448mkTree @ Rule) @ State) @ Eff) @ ((stl @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff) @ Rs) @ S))) @ S6)))))))))))))).
% 2.36/1.23 thf(fact_77_RuleSystem__Defs_Otrim__def, axiom, (! [State:$tType,Rule:$tType]: ((((abstra1259602206m_trim @ Rule) @ State) = (^ [Eff2:(Rule > (State > ((fset @ State) > $o))),Rs2:(stream @ Rule),S4:State]: ((((sdrop_while @ Rule) @ (^ [R3:Rule]: ((~ ((((((abstra1874422341nabled @ Rule) @ State) @ Eff2) @ R3) @ S4)))))) @ Rs2))))))).
% 2.36/1.23 thf(fact_78_countable__Collect, axiom, (! [A:$tType,A4:(set @ A),Phi:(A > $o)]: ((((countable_countable @ A) @ A4) => ((countable_countable @ A) @ ((collect @ A) @ (^ [A3:A]: (((((member @ A) @ A3) @ A4) & (Phi @ A3)))))))))).
% 2.36/1.23 thf(fact_79_RuleSystem_Owf__mkTree, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,Rs:(stream @ Rule)]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => (((((abstra1874736267tem_wf @ Rule) @ State) @ Eff) @ Rules) @ (((((abstra1225283448mkTree @ Rule) @ State) @ Eff) @ Rs) @ S)))))))).
% 2.36/1.23 thf(fact_80_RuleSystem_Oipath__mkTree__sdrop, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),S:State,Rs:(stream @ Rule),Steps2:(stream @ ((product_prod @ State) @ Rule)),M:nat]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((member @ State) @ S) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => ((((abstra313004635_ipath @ ((product_prod @ State) @ Rule)) @ (((((abstra1225283448mkTree @ Rule) @ State) @ Eff) @ Rs) @ S)) @ Steps2) => (? [N:nat,S6:State]: (((((member @ State) @ S6) @ S3) & (((abstra313004635_ipath @ ((product_prod @ State) @ Rule)) @ (((((abstra1225283448mkTree @ Rule) @ State) @ Eff) @ (((sdrop @ Rule) @ N) @ Rs)) @ S6)) @ (((sdrop @ ((product_prod @ State) @ Rule)) @ M) @ Steps2)))))))))))).
% 2.36/1.23 thf(fact_81_minWait__le__pos, axiom, (! [Rs:(stream @ rule),R:rule,S:state]: (((((abstra928354080m_fair @ rule) @ rules) @ Rs) => ((((member @ rule) @ R) @ ((sset @ rule) @ rules)) => ((((((abstra1874422341nabled @ rule) @ state) @ eff) @ R) @ S) => (((ord_less_eq @ nat) @ (((((abstra1332369113inWait @ rule) @ state) @ eff) @ Rs) @ S)) @ (((abstra2097340358le_pos @ rule) @ Rs) @ R)))))))).
% 2.36/1.23 thf(fact_82_minWait__def, axiom, (! [Rs:(stream @ rule),S:state]: (((((((abstra1332369113inWait @ rule) @ state) @ eff) @ Rs) @ S) = ((ord_Least @ nat) @ (^ [N3:nat]: ((((((abstra1874422341nabled @ rule) @ state) @ eff) @ ((shd @ rule) @ (((sdrop @ rule) @ N3) @ Rs))) @ S)))))))).
% 2.36/1.23 thf(fact_83_mkTree_Osimps_I2_J, axiom, (! [Rs:(stream @ rule),S:state]: ((((abstra1749095923e_cont @ ((product_prod @ state) @ rule)) @ (((((abstra1225283448mkTree @ rule) @ state) @ eff) @ Rs) @ S)) = ((((fimage @ state) @ (abstra2103299360e_tree @ ((product_prod @ state) @ rule))) @ ((((abstra1225283448mkTree @ rule) @ state) @ eff) @ ((stl @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S)))) @ (((((abstra1276541928ickEff @ rule) @ state) @ eff) @ ((shd @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S))) @ S)))))).
% 2.36/1.23 thf(fact_84_minWait__least, axiom, (! [N2:nat,Rs:(stream @ rule),S:state]: (((((((abstra1874422341nabled @ rule) @ state) @ eff) @ ((shd @ rule) @ (((sdrop @ rule) @ N2) @ Rs))) @ S) => (((ord_less_eq @ nat) @ (((((abstra1332369113inWait @ rule) @ state) @ eff) @ Rs) @ S)) @ N2))))).
% 2.36/1.23 thf(fact_85_pos__def, axiom, (! [A:$tType]: (((abstra2097340358le_pos @ A) = (^ [Rs2:(stream @ A),R3:A]: (((ord_Least @ nat) @ (^ [N3:nat]: ((((shd @ A) @ (((sdrop @ A) @ N3) @ Rs2)) = R3)))))))))).
% 2.36/1.23 thf(fact_86_pos__least, axiom, (! [A:$tType,N2:nat,Rs:(stream @ A),R:A]: (((((shd @ A) @ (((sdrop @ A) @ N2) @ Rs)) = R) => (((ord_less_eq @ nat) @ (((abstra2097340358le_pos @ A) @ Rs) @ R)) @ N2))))).
% 2.36/1.23 thf(fact_87_RuleSystem_Opos__least, axiom, (! [Rule:$tType,State:$tType,A:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),N2:nat,Rs:(stream @ A),R:A]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((shd @ A) @ (((sdrop @ A) @ N2) @ Rs)) = R) => (((ord_less_eq @ nat) @ (((abstra2097340358le_pos @ A) @ Rs) @ R)) @ N2)))))).
% 2.36/1.23 thf(fact_88_RuleSystem_Opos__def, axiom, (! [State:$tType,Rule:$tType,A:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),Rs:(stream @ A),R:A]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((abstra2097340358le_pos @ A) @ Rs) @ R) = ((ord_Least @ nat) @ (^ [N3:nat]: ((((shd @ A) @ (((sdrop @ A) @ N3) @ Rs)) = R))))))))).
% 2.36/1.23 thf(fact_89_RuleSystem_OminWait__least, axiom, (! [State:$tType,Rule:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),N2:nat,Rs:(stream @ Rule),S:State]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((((abstra1874422341nabled @ Rule) @ State) @ Eff) @ ((shd @ Rule) @ (((sdrop @ Rule) @ N2) @ Rs))) @ S) => (((ord_less_eq @ nat) @ (((((abstra1332369113inWait @ Rule) @ State) @ Eff) @ Rs) @ S)) @ N2)))))).
% 2.36/1.23 thf(fact_90_RuleSystem__Defs_OmkTree_Osimps_I2_J, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rs:(stream @ Rule),S:State]: ((((abstra1749095923e_cont @ ((product_prod @ State) @ Rule)) @ (((((abstra1225283448mkTree @ Rule) @ State) @ Eff) @ Rs) @ S)) = ((((fimage @ State) @ (abstra2103299360e_tree @ ((product_prod @ State) @ Rule))) @ ((((abstra1225283448mkTree @ Rule) @ State) @ Eff) @ ((stl @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff) @ Rs) @ S)))) @ (((((abstra1276541928ickEff @ Rule) @ State) @ Eff) @ ((shd @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff) @ Rs) @ S))) @ S)))))).
% 2.36/1.23 thf(fact_91_RuleSystem_OminWait__def, axiom, (! [State:$tType,Rule:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),Rs:(stream @ Rule),S:State]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((((abstra1332369113inWait @ Rule) @ State) @ Eff) @ Rs) @ S) = ((ord_Least @ nat) @ (^ [N3:nat]: ((((((abstra1874422341nabled @ Rule) @ State) @ Eff) @ ((shd @ Rule) @ (((sdrop @ Rule) @ N3) @ Rs))) @ S))))))))).
% 2.36/1.23 thf(fact_92_RuleSystem_OminWait__le__pos, axiom, (! [State:$tType,Rule:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),Rs:(stream @ Rule),R:Rule,S:State]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => ((((abstra928354080m_fair @ Rule) @ Rules) @ Rs) => ((((member @ Rule) @ R) @ ((sset @ Rule) @ Rules)) => ((((((abstra1874422341nabled @ Rule) @ State) @ Eff) @ R) @ S) => (((ord_less_eq @ nat) @ (((((abstra1332369113inWait @ Rule) @ State) @ Eff) @ Rs) @ S)) @ (((abstra2097340358le_pos @ Rule) @ Rs) @ R))))))))).
% 2.36/1.23 thf(fact_93_fimage__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X3:B,A4:(fset @ B)]: (((B2 = (F @ X3)) => ((((fmember @ B) @ X3) @ A4) => (((fmember @ A) @ B2) @ ((((fimage @ B) @ A) @ F) @ A4))))))).
% 2.36/1.23 thf(fact_94_fimage__ident, axiom, (! [A:$tType,Y4:(fset @ A)]: ((((((fimage @ A) @ A) @ (^ [X6:A]: (X6))) @ Y4) = Y4)))).
% 2.36/1.23 thf(fact_95_fset_Omap__ident, axiom, (! [A:$tType,T2:(fset @ A)]: ((((((fimage @ A) @ A) @ (^ [X6:A]: (X6))) @ T2) = T2)))).
% 2.36/1.23 thf(fact_96_per__def, axiom, (! [R:rule]: ((((((((abstra2096684367le_per @ rule) @ state) @ eff) @ rules) @ s) @ R) = (! [S4:state,R1:rule,Sl6:(fset @ state),S8:state]: ((((((member @ state) @ S4) @ s) & ((((((abstra1874422341nabled @ rule) @ state) @ eff) @ R) @ S4) & ((((member @ rule) @ R1) @ (((minus_minus @ (set @ rule)) @ ((sset @ rule) @ rules)) @ (((insert @ rule) @ R) @ (bot_bot @ (set @ rule))))) & ((((eff @ R1) @ S4) @ Sl6) & (((fmember @ state) @ S8) @ Sl6))))) => (((((abstra1874422341nabled @ rule) @ state) @ eff) @ R) @ S8)))))))).
% 2.36/1.23 thf(fact_97_Least__le, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P3:(A > $o),K:A]: (((P3 @ K) => (((ord_less_eq @ A) @ ((ord_Least @ A) @ P3)) @ K)))))))).
% 2.36/1.23 thf(fact_98_mkTree_Octr, axiom, (! [Rs:(stream @ rule),S:state]: (((((((abstra1225283448mkTree @ rule) @ state) @ eff) @ Rs) @ S) = (((abstra388494275e_Node @ ((product_prod @ state) @ rule)) @ ((((product_Pair @ state) @ rule) @ S) @ ((shd @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S)))) @ ((((fimage @ state) @ (abstra2103299360e_tree @ ((product_prod @ state) @ rule))) @ ((((abstra1225283448mkTree @ rule) @ state) @ eff) @ ((stl @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S)))) @ (((((abstra1276541928ickEff @ rule) @ state) @ eff) @ ((shd @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S))) @ S))))))).
% 2.36/1.23 thf(fact_99_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.36/1.23 thf(fact_100_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B3)) = ((A2 = A5) & (B2 = B3)))))).
% 2.36/1.23 thf(fact_101_prod_Oinject, axiom, (! [A:$tType,B:$tType,X13:A,X22:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X13) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X13 = Y1) & (X22 = Y22)))))).
% 2.36/1.23 thf(fact_102_bot__apply, axiom, (! [C:$tType,D:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D > C)) = (^ [X6:D]: ((bot_bot @ C)))))))).
% 2.36/1.23 thf(fact_103_fsubsetI, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A)]: (((! [X4:A]: (((((fmember @ A) @ X4) @ A4) => (((fmember @ A) @ X4) @ B4)))) => (((ord_less_eq @ (fset @ A)) @ A4) @ B4))))).
% 2.36/1.23 thf(fact_104_tree_Oinject, axiom, (! [A:$tType,X13:A,X22:(fset @ (abstra2103299360e_tree @ A)),Y1:A,Y22:(fset @ (abstra2103299360e_tree @ A))]: ((((((abstra388494275e_Node @ A) @ X13) @ X22) = (((abstra388494275e_Node @ A) @ Y1) @ Y22)) = ((X13 = Y1) & (X22 = Y22)))))).
% 2.36/1.23 thf(fact_105_countable__insert, axiom, (! [A:$tType,A4:(set @ A),A2:A]: ((((countable_countable @ A) @ A4) => ((countable_countable @ A) @ (((insert @ A) @ A2) @ A4)))))).
% 2.36/1.23 thf(fact_106_countable__insert__eq, axiom, (! [A:$tType,X3:A,A4:(set @ A)]: ((((countable_countable @ A) @ (((insert @ A) @ X3) @ A4)) = ((countable_countable @ A) @ A4))))).
% 2.36/1.23 thf(fact_107_countable__Diff, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: ((((countable_countable @ A) @ A4) => ((countable_countable @ A) @ (((minus_minus @ (set @ A)) @ A4) @ B4)))))).
% 2.36/1.23 thf(fact_108_prod_Ocollapse, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)) = Prod)))).
% 2.36/1.23 thf(fact_109_countable__Diff__eq, axiom, (! [A:$tType,A4:(set @ A),X3:A]: ((((countable_countable @ A) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) = ((countable_countable @ A) @ A4))))).
% 2.36/1.23 thf(fact_110_fset__mp, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A),X3:A]: (((((ord_less_eq @ (fset @ A)) @ A4) @ B4) => ((((fmember @ A) @ X3) @ A4) => (((fmember @ A) @ X3) @ B4)))))).
% 2.36/1.23 thf(fact_111_fin__mono, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A),X3:A]: (((((ord_less_eq @ (fset @ A)) @ A4) @ B4) => ((((fmember @ A) @ X3) @ A4) => (((fmember @ A) @ X3) @ B4)))))).
% 2.36/1.23 thf(fact_112_fsubsetD, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A),C2:A]: (((((ord_less_eq @ (fset @ A)) @ A4) @ B4) => ((((fmember @ A) @ C2) @ A4) => (((fmember @ A) @ C2) @ B4)))))).
% 2.36/1.23 thf(fact_113_fset__rev__mp, axiom, (! [A:$tType,X3:A,A4:(fset @ A),B4:(fset @ A)]: (((((fmember @ A) @ X3) @ A4) => ((((ord_less_eq @ (fset @ A)) @ A4) @ B4) => (((fmember @ A) @ X3) @ B4)))))).
% 2.36/1.23 thf(fact_114_subset__fimage__iff, axiom, (! [A:$tType,B:$tType,B4:(fset @ A),F:(B > A),A4:(fset @ B)]: (((((ord_less_eq @ (fset @ A)) @ B4) @ ((((fimage @ B) @ A) @ F) @ A4)) = (? [AA:(fset @ B)]: (((((ord_less_eq @ (fset @ B)) @ AA) @ A4) & (B4 = ((((fimage @ B) @ A) @ F) @ AA))))))))).
% 2.36/1.23 thf(fact_115_fimage__mono, axiom, (! [B:$tType,A:$tType,A4:(fset @ A),B4:(fset @ A),F:(A > B)]: (((((ord_less_eq @ (fset @ A)) @ A4) @ B4) => (((ord_less_eq @ (fset @ B)) @ ((((fimage @ A) @ B) @ F) @ A4)) @ ((((fimage @ A) @ B) @ F) @ B4)))))).
% 2.36/1.23 thf(fact_116_tree_Oexhaust, axiom, (! [A:$tType,Y:(abstra2103299360e_tree @ A)]: ((~ ((! [X1:A,X23:(fset @ (abstra2103299360e_tree @ A))]: ((Y != (((abstra388494275e_Node @ A) @ X1) @ X23))))))))).
% 2.36/1.23 thf(fact_117_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P3:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A6:A,B5:B]: ((P3 @ ((((product_Pair @ A) @ B) @ A6) @ B5)))) => (P3 @ Prod))))).
% 2.36/1.23 thf(fact_118_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A6:A,B5:B]: ((Y != ((((product_Pair @ A) @ B) @ A6) @ B5))))))))).
% 2.36/1.23 thf(fact_119_prod__induct7, axiom, (! [G2:$tType,F2:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))))))]: (((! [A6:A,B5:B,C3:C,D2:D,E2:E,F3:F2,G3:G2]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G2)) @ E2) @ ((((product_Pair @ F2) @ G2) @ F3) @ G3))))))))) => (P3 @ X3))))).
% 2.36/1.23 thf(fact_120_prod__induct6, axiom, (! [F2:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))))]: (((! [A6:A,B5:B,C3:C,D2:D,E2:E,F3:F2]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F2)) @ D2) @ ((((product_Pair @ E) @ F2) @ E2) @ F3)))))))) => (P3 @ X3))))).
% 2.36/1.23 thf(fact_121_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A6:A,B5:B,C3:C,D2:D,E2:E]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P3 @ X3))))).
% 2.36/1.23 thf(fact_122_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A6:A,B5:B,C3:C,D2:D]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C3) @ D2)))))) => (P3 @ X3))))).
% 2.36/1.23 thf(fact_123_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A6:A,B5:B,C3:C]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A6) @ ((((product_Pair @ B) @ C) @ B5) @ C3))))) => (P3 @ X3))))).
% 2.36/1.23 thf(fact_124_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F2:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))))))]: ((~ ((! [A6:A,B5:B,C3:C,D2:D,E2:E,F3:F2,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G2)) @ E2) @ ((((product_Pair @ F2) @ G2) @ F3) @ G3)))))))))))))).
% 2.36/1.23 thf(fact_125_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))))]: ((~ ((! [A6:A,B5:B,C3:C,D2:D,E2:E,F3:F2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F2)) @ D2) @ ((((product_Pair @ E) @ F2) @ E2) @ F3))))))))))))).
% 2.36/1.23 thf(fact_126_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A6:A,B5:B,C3:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.36/1.23 thf(fact_127_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A6:A,B5:B,C3:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C3) @ D2))))))))))).
% 2.36/1.23 thf(fact_128_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A6:A,B5:B,C3:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A6) @ ((((product_Pair @ B) @ C) @ B5) @ C3)))))))))).
% 2.36/1.23 thf(fact_129_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B3)) => (~ (((A2 = A5) => (B2 != B3)))))))).
% 2.36/1.23 thf(fact_130_prod__cases, axiom, (! [B:$tType,A:$tType,P3:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A6:A,B5:B]: ((P3 @ ((((product_Pair @ A) @ B) @ A6) @ B5)))) => (P3 @ P2))))).
% 2.36/1.23 thf(fact_131_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X4:A,Y2:B]: ((P2 = ((((product_Pair @ A) @ B) @ X4) @ Y2))))))).
% 2.36/1.23 thf(fact_132_fst__conv, axiom, (! [B:$tType,A:$tType,X13:A,X22:B]: (((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X13) @ X22)) = X13)))).
% 2.36/1.23 thf(fact_133_fst__eqD, axiom, (! [B:$tType,A:$tType,X3:A,Y:B,A2:A]: ((((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) = A2) => (X3 = A2))))).
% 2.36/1.23 thf(fact_134_snd__conv, axiom, (! [Aa:$tType,A:$tType,X13:Aa,X22:A]: (((((product_snd @ Aa) @ A) @ ((((product_Pair @ Aa) @ A) @ X13) @ X22)) = X22)))).
% 2.36/1.23 thf(fact_135_snd__eqD, axiom, (! [B:$tType,A:$tType,X3:B,Y:A,A2:A]: ((((((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X3) @ Y)) = A2) => (Y = A2))))).
% 2.36/1.23 thf(fact_136_uncountable__minus__countable, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((~ (((countable_countable @ A) @ A4))) => (((countable_countable @ A) @ B4) => (~ (((countable_countable @ A) @ (((minus_minus @ (set @ A)) @ A4) @ B4))))))))).
% 2.36/1.23 thf(fact_137_countable__subset, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => (((countable_countable @ A) @ B4) => ((countable_countable @ A) @ A4)))))).
% 2.36/1.23 thf(fact_138_fimage__fsubsetI, axiom, (! [A:$tType,B:$tType,A4:(fset @ A),F:(A > B),B4:(fset @ B)]: (((! [X4:A]: (((((fmember @ A) @ X4) @ A4) => (((fmember @ B) @ (F @ X4)) @ B4)))) => (((ord_less_eq @ (fset @ B)) @ ((((fimage @ A) @ B) @ F) @ A4)) @ B4))))).
% 2.36/1.23 thf(fact_139_tree_Osel_I2_J, axiom, (! [A:$tType,X13:A,X22:(fset @ (abstra2103299360e_tree @ A))]: ((((abstra1749095923e_cont @ A) @ (((abstra388494275e_Node @ A) @ X13) @ X22)) = X22)))).
% 2.36/1.23 thf(fact_140_surjective__pairing, axiom, (! [B:$tType,A:$tType,T2:((product_prod @ A) @ B)]: ((T2 = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ T2)) @ (((product_snd @ A) @ B) @ T2)))))).
% 2.36/1.23 thf(fact_141_prod_Oexhaust__sel, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))).
% 2.36/1.23 thf(fact_142_conjI__realizer, axiom, (! [A:$tType,B:$tType,P3:(A > $o),P2:A,Q2:(B > $o),Q:B]: (((P3 @ P2) => ((Q2 @ Q) => ((P3 @ (((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ P2) @ Q))) & (Q2 @ (((product_snd @ A) @ B) @ ((((product_Pair @ A) @ B) @ P2) @ Q))))))))).
% 2.36/1.23 thf(fact_143_exI__realizer, axiom, (! [B:$tType,A:$tType,P3:(A > (B > $o)),Y:A,X3:B]: ((((P3 @ Y) @ X3) => ((P3 @ (((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X3) @ Y))) @ (((product_fst @ B) @ A) @ ((((product_Pair @ B) @ A) @ X3) @ Y))))))).
% 2.36/1.23 thf(fact_144_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3))))))))).
% 2.36/1.23 thf(fact_145_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3))))))))).
% 2.36/1.23 thf(fact_146_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B)]: (((! [X4:A]: ((((ord_less_eq @ B) @ (F @ X4)) @ (G @ X4)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.36/1.23 thf(fact_147_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F4:(A > B),G4:(A > B)]: ((! [X6:A]: ((((ord_less_eq @ B) @ (F4 @ X6)) @ (G4 @ X6))))))))))).
% 2.36/1.23 thf(fact_148_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X4:B,Y2:B]: (((((ord_less_eq @ B) @ X4) @ Y2) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.36/1.23 thf(fact_149_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C) @ (F @ B2)) @ C2) => ((! [X4:A,Y2:A]: (((((ord_less_eq @ A) @ X4) @ Y2) => (((ord_less_eq @ C) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C2)))))))))).
% 2.36/1.23 thf(fact_150_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X4:B,Y2:B]: (((((ord_less_eq @ B) @ X4) @ Y2) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.36/1.23 thf(fact_151_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C2) => ((! [X4:A,Y2:A]: (((((ord_less_eq @ A) @ X4) @ Y2) => (((ord_less_eq @ B) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C2)))))))))).
% 2.36/1.23 thf(fact_152_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [X6:A,Y5:A]: (((((ord_less_eq @ A) @ X6) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X6))))))))).
% 2.36/1.23 thf(fact_153_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ X3) => (X3 = Y))))))))).
% 2.36/1.23 thf(fact_154_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) | (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 2.36/1.23 thf(fact_155_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((X3 = Y) => (((ord_less_eq @ A) @ X3) @ Y)))))))).
% 2.36/1.23 thf(fact_156_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y))) => (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 2.36/1.23 thf(fact_157_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.36/1.23 thf(fact_158_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X3)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y))))))))))))))))).
% 2.36/1.23 thf(fact_159_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X3:A]: (((((ord_less_eq @ A) @ Y) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y) = (X3 = Y))))))))).
% 2.36/1.23 thf(fact_160_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.36/1.23 thf(fact_161_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.36/1.23 thf(fact_162_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.36/1.23 thf(fact_163_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 2.36/1.23 thf(fact_164_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.36/1.23 thf(fact_165_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P3:(A > (A > $o)),A2:A,B2:A]: (((! [A6:A,B5:A]: (((((ord_less_eq @ A) @ A6) @ B5) => ((P3 @ A6) @ B5)))) => ((! [A6:A,B5:A]: ((((P3 @ B5) @ A6) => ((P3 @ A6) @ B5)))) => ((P3 @ A2) @ B2))))))))).
% 2.36/1.23 thf(fact_166_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.36/1.23 thf(fact_167_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.36/1.23 thf(fact_168_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X6:A]: ((bot_bot @ B)))))))).
% 2.36/1.23 thf(fact_169_eqfelem__imp__iff, axiom, (! [A:$tType,X3:A,Y:A,A4:(fset @ A)]: (((X3 = Y) => ((((fmember @ A) @ X3) @ A4) = (((fmember @ A) @ Y) @ A4)))))).
% 2.36/1.23 thf(fact_170_if__split__fmem2, axiom, (! [A:$tType,A2:A,Q2:$o,X3:(fset @ A),Y:(fset @ A)]: (((((fmember @ A) @ A2) @ ((((if @ (fset @ A)) @ Q2) @ X3) @ Y)) = ((Q2 => (((fmember @ A) @ A2) @ X3)) & ((~ (Q2)) => (((fmember @ A) @ A2) @ Y))))))).
% 2.36/1.23 thf(fact_171_if__split__fmem1, axiom, (! [A:$tType,Q2:$o,X3:A,Y:A,B2:(fset @ A)]: (((((fmember @ A) @ ((((if @ A) @ Q2) @ X3) @ Y)) @ B2) = ((Q2 => (((fmember @ A) @ X3) @ B2)) & ((~ (Q2)) => (((fmember @ A) @ Y) @ B2))))))).
% 2.36/1.23 thf(fact_172_eqfset__imp__iff, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A),X3:A]: (((A4 = B4) => ((((fmember @ A) @ X3) @ A4) = (((fmember @ A) @ X3) @ B4)))))).
% 2.36/1.23 thf(fact_173_eq__fmem__trans, axiom, (! [A:$tType,A2:A,B2:A,A4:(fset @ A)]: (((A2 = B2) => ((((fmember @ A) @ B2) @ A4) => (((fmember @ A) @ A2) @ A4)))))).
% 2.36/1.23 thf(fact_174_fset__choice, axiom, (! [B:$tType,A:$tType,A4:(fset @ A),P3:(A > (B > $o))]: (((! [X4:A]: (((((fmember @ A) @ X4) @ A4) => (? [X12:B]: (((P3 @ X4) @ X12)))))) => (? [F3:(A > B)]: ((! [X5:A]: (((((fmember @ A) @ X5) @ A4) => ((P3 @ X5) @ (F3 @ X5))))))))))).
% 2.36/1.23 thf(fact_175_fequalityCE, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A),C2:A]: (((A4 = B4) => (((((fmember @ A) @ C2) @ A4) => (~ ((((fmember @ A) @ C2) @ B4)))) => (~ (((~ ((((fmember @ A) @ C2) @ A4))) => (((fmember @ A) @ C2) @ B4))))))))).
% 2.36/1.23 thf(fact_176_fset__eqI, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A)]: (((! [X4:A]: (((((fmember @ A) @ X4) @ A4) = (((fmember @ A) @ X4) @ B4)))) => (A4 = B4))))).
% 2.36/1.23 thf(fact_177_RuleSystem_Oper__def, axiom, (! [Rule:$tType,State:$tType,Eff:(Rule > (State > ((fset @ State) > $o))),Rules:(stream @ Rule),S3:(set @ State),R:Rule]: (((((((abstra1326562878System @ Rule) @ State) @ Eff) @ Rules) @ S3) => (((((((abstra2096684367le_per @ Rule) @ State) @ Eff) @ Rules) @ S3) @ R) = (! [S4:State,R1:Rule,Sl6:(fset @ State),S8:State]: ((((((member @ State) @ S4) @ S3) & ((((((abstra1874422341nabled @ Rule) @ State) @ Eff) @ R) @ S4) & ((((member @ Rule) @ R1) @ (((minus_minus @ (set @ Rule)) @ ((sset @ Rule) @ Rules)) @ (((insert @ Rule) @ R) @ (bot_bot @ (set @ Rule))))) & ((((Eff @ R1) @ S4) @ Sl6) & (((fmember @ State) @ S8) @ Sl6))))) => (((((abstra1874422341nabled @ Rule) @ State) @ Eff) @ R) @ S8))))))))).
% 2.36/1.23 thf(fact_178_LeastI2, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P3:(A > $o),A2:A,Q2:(A > $o)]: (((P3 @ A2) => ((! [X4:A]: (((P3 @ X4) => (Q2 @ X4)))) => (Q2 @ ((ord_Least @ A) @ P3)))))))))).
% 2.36/1.23 thf(fact_179_LeastI__ex, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P3:(A > $o)]: (((? [X12:A]: ((P3 @ X12))) => (P3 @ ((ord_Least @ A) @ P3))))))))).
% 2.36/1.23 thf(fact_180_LeastI2__ex, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P3:(A > $o),Q2:(A > $o)]: (((? [X12:A]: ((P3 @ X12))) => ((! [X4:A]: (((P3 @ X4) => (Q2 @ X4)))) => (Q2 @ ((ord_Least @ A) @ P3)))))))))).
% 2.36/1.23 thf(fact_181_RuleSystem__Defs_OmkTree_Ocode, axiom, (! [State:$tType,Rule:$tType]: ((((abstra1225283448mkTree @ Rule) @ State) = (^ [Eff2:(Rule > (State > ((fset @ State) > $o))),Rs2:(stream @ Rule),S4:State]: ((((abstra388494275e_Node @ ((product_prod @ State) @ Rule)) @ ((((product_Pair @ State) @ Rule) @ S4) @ ((shd @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff2) @ Rs2) @ S4)))) @ ((((fimage @ State) @ (abstra2103299360e_tree @ ((product_prod @ State) @ Rule))) @ ((((abstra1225283448mkTree @ Rule) @ State) @ Eff2) @ ((stl @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff2) @ Rs2) @ S4)))) @ (((((abstra1276541928ickEff @ Rule) @ State) @ Eff2) @ ((shd @ Rule) @ (((((abstra1259602206m_trim @ Rule) @ State) @ Eff2) @ Rs2) @ S4))) @ S4))))))))).
% 2.36/1.23 thf(fact_182_fimage__fimage, axiom, (! [A:$tType,B:$tType,C:$tType,F:(B > A),G:(C > B),A4:(fset @ C)]: ((((((fimage @ B) @ A) @ F) @ ((((fimage @ C) @ B) @ G) @ A4)) = ((((fimage @ C) @ A) @ (^ [X6:C]: ((F @ (G @ X6))))) @ A4))))).
% 2.36/1.23 thf(fact_183_LeastI, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P3:(A > $o),K:A]: (((P3 @ K) => (P3 @ ((ord_Least @ A) @ P3))))))))).
% 2.36/1.23 thf(fact_184_bot_Oextremum, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A2))))))).
% 2.36/1.23 thf(fact_185_bot_Oextremum__unique, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) = (A2 = (bot_bot @ A))))))))).
% 2.36/1.23 thf(fact_186_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) => (A2 = (bot_bot @ A))))))))).
% 2.36/1.23 thf(fact_187_LeastI2__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [P3:(A > $o),X3:A,Q2:(A > $o)]: (((P3 @ X3) => ((! [Y2:A]: (((P3 @ Y2) => (((ord_less_eq @ A) @ X3) @ Y2)))) => ((! [X4:A]: (((P3 @ X4) => ((! [Y6:A]: (((P3 @ Y6) => (((ord_less_eq @ A) @ X4) @ Y6)))) => (Q2 @ X4))))) => (Q2 @ ((ord_Least @ A) @ P3))))))))))).
% 2.36/1.23 thf(fact_188_Least__equality, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [P3:(A > $o),X3:A]: (((P3 @ X3) => ((! [Y2:A]: (((P3 @ Y2) => (((ord_less_eq @ A) @ X3) @ Y2)))) => (((ord_Least @ A) @ P3) = X3))))))))).
% 2.36/1.23 thf(fact_189_LeastI2__wellorder, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P3:(A > $o),A2:A,Q2:(A > $o)]: (((P3 @ A2) => ((! [A6:A]: (((P3 @ A6) => ((! [B6:A]: (((P3 @ B6) => (((ord_less_eq @ A) @ A6) @ B6)))) => (Q2 @ A6))))) => (Q2 @ ((ord_Least @ A) @ P3)))))))))).
% 2.36/1.23 thf(fact_190_LeastI2__wellorder__ex, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P3:(A > $o),Q2:(A > $o)]: (((? [X12:A]: ((P3 @ X12))) => ((! [A6:A]: (((P3 @ A6) => ((! [B6:A]: (((P3 @ B6) => (((ord_less_eq @ A) @ A6) @ B6)))) => (Q2 @ A6))))) => (Q2 @ ((ord_Least @ A) @ P3)))))))))).
% 2.36/1.23 thf(fact_191_rev__fimage__eqI, axiom, (! [B:$tType,A:$tType,X3:A,A4:(fset @ A),B2:B,F:(A > B)]: (((((fmember @ A) @ X3) @ A4) => ((B2 = (F @ X3)) => (((fmember @ B) @ B2) @ ((((fimage @ A) @ B) @ F) @ A4))))))).
% 2.36/1.23 thf(fact_192_fimage__cong, axiom, (! [B:$tType,A:$tType,M2:(fset @ A),N4:(fset @ A),F:(A > B),G:(A > B)]: (((M2 = N4) => ((! [X4:A]: (((((fmember @ A) @ X4) @ N4) => ((F @ X4) = (G @ X4))))) => (((((fimage @ A) @ B) @ F) @ M2) = ((((fimage @ A) @ B) @ G) @ N4))))))).
% 2.36/1.23 thf(fact_193_fimageI, axiom, (! [B:$tType,A:$tType,X3:A,A4:(fset @ A),F:(A > B)]: (((((fmember @ A) @ X3) @ A4) => (((fmember @ B) @ (F @ X3)) @ ((((fimage @ A) @ B) @ F) @ A4)))))).
% 2.36/1.23 thf(fact_194_fimageE, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),A4:(fset @ B)]: (((((fmember @ A) @ B2) @ ((((fimage @ B) @ A) @ F) @ A4)) => (~ ((! [X4:B]: (((B2 = (F @ X4)) => (~ ((((fmember @ B) @ X4) @ A4)))))))))))).
% 2.36/1.23 thf(fact_195_mkTree__unfold, axiom, (! [Rs:(stream @ rule),S:state]: (((((((abstra1225283448mkTree @ rule) @ state) @ eff) @ Rs) @ S) = ((((case_stream @ rule) @ (abstra2103299360e_tree @ ((product_prod @ state) @ rule))) @ (^ [R3:rule,S8:(stream @ rule)]: ((((abstra388494275e_Node @ ((product_prod @ state) @ rule)) @ ((((product_Pair @ state) @ rule) @ S) @ R3)) @ ((((fimage @ state) @ (abstra2103299360e_tree @ ((product_prod @ state) @ rule))) @ ((((abstra1225283448mkTree @ rule) @ state) @ eff) @ S8)) @ (((((abstra1276541928ickEff @ rule) @ state) @ eff) @ R3) @ S)))))) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S)))))).
% 2.36/1.23 thf(fact_196_insert__Diff__single, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: (((((insert @ A) @ A2) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))) = (((insert @ A) @ A2) @ A4))))).
% 2.36/1.23 thf(fact_197_singleton__conv2, axiom, (! [A:$tType,A2:A]: ((((collect @ A) @ ((^ [Y3:A,Z:A]: ((Y3 = Z))) @ A2)) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.36/1.23 thf(fact_198_singleton__conv, axiom, (! [A:$tType,A2:A]: ((((collect @ A) @ (^ [X6:A]: ((X6 = A2)))) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.36/1.23 thf(fact_199_mkTree_Osimps_I1_J, axiom, (! [Rs:(stream @ rule),S:state]: ((((abstra573067619e_root @ ((product_prod @ state) @ rule)) @ (((((abstra1225283448mkTree @ rule) @ state) @ eff) @ Rs) @ S)) = ((((product_Pair @ state) @ rule) @ S) @ ((shd @ rule) @ (((((abstra1259602206m_trim @ rule) @ state) @ eff) @ Rs) @ S))))))).
% 2.36/1.23 thf(fact_200_empty__Collect__eq, axiom, (! [A:$tType,P3:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P3)) = (! [X6:A]: ((~ ((P3 @ X6))))))))).
% 2.36/1.23 thf(fact_201_Collect__empty__eq, axiom, (! [A:$tType,P3:(A > $o)]: (((((collect @ A) @ P3) = (bot_bot @ (set @ A))) = (! [X6:A]: ((~ ((P3 @ X6))))))))).
% 2.36/1.23 thf(fact_202_all__not__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X6:A]: ((~ ((((member @ A) @ X6) @ A4))))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.36/1.23 thf(fact_203_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.36/1.23 thf(fact_204_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ A4) => (A4 = B4)))))).
% 2.36/1.23 thf(fact_205_subsetI, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A4) => (((member @ A) @ X4) @ B4)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B4))))).
% 2.36/1.23 thf(fact_206_insert__absorb2, axiom, (! [A:$tType,X3:A,A4:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ X3) @ A4)) = (((insert @ A) @ X3) @ A4))))).
% 2.36/1.23 thf(fact_207_insert__iff, axiom, (! [A:$tType,A2:A,B2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A4)) = ((A2 = B2) | (((member @ A) @ A2) @ A4)))))).
% 2.36/1.23 thf(fact_208_insertCI, axiom, (! [A:$tType,A2:A,B4:(set @ A),B2:A]: ((((~ ((((member @ A) @ A2) @ B4))) => (A2 = B2)) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B4)))))).
% 2.36/1.23 thf(fact_209_Diff__idemp, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B4)) @ B4) = (((minus_minus @ (set @ A)) @ A4) @ B4))))).
% 2.36/1.23 thf(fact_210_Diff__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B4)) = ((((member @ A) @ C2) @ A4) & (~ ((((member @ A) @ C2) @ B4)))))))).
% 2.36/1.23 thf(fact_211_DiffI, axiom, (! [A:$tType,C2:A,A4:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A4) => ((~ ((((member @ A) @ C2) @ B4))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B4))))))).
% 2.36/1.23 thf(fact_212_fempty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((fmember @ A) @ C2) @ (bot_bot @ (fset @ A)))))))).
% 2.36/1.23 thf(fact_213_all__not__fin__conv, axiom, (! [A:$tType,A4:(fset @ A)]: (((! [X6:A]: ((~ ((((fmember @ A) @ X6) @ A4))))) = (A4 = (bot_bot @ (fset @ A))))))).
% 2.36/1.23 thf(fact_214_fempty__fsubsetI, axiom, (! [A:$tType,X3:(fset @ A)]: ((((ord_less_eq @ (fset @ A)) @ (bot_bot @ (fset @ A))) @ X3)))).
% 2.36/1.23 thf(fact_215_fsubset__fempty, axiom, (! [A:$tType,A4:(fset @ A)]: (((((ord_less_eq @ (fset @ A)) @ A4) @ (bot_bot @ (fset @ A))) = (A4 = (bot_bot @ (fset @ A))))))).
% 2.36/1.23 thf(fact_216_fsubset__antisym, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A)]: (((((ord_less_eq @ (fset @ A)) @ A4) @ B4) => ((((ord_less_eq @ (fset @ A)) @ B4) @ A4) => (A4 = B4)))))).
% 2.36/1.23 thf(fact_217_fimage__fempty, axiom, (! [B:$tType,A:$tType,F:(B > A)]: ((((((fimage @ B) @ A) @ F) @ (bot_bot @ (fset @ B))) = (bot_bot @ (fset @ A)))))).
% 2.36/1.23 thf(fact_218_fempty__is__fimage, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(fset @ B)]: ((((bot_bot @ (fset @ A)) = ((((fimage @ B) @ A) @ F) @ A4)) = (A4 = (bot_bot @ (fset @ B))))))).
% 2.36/1.23 thf(fact_219_fimage__is__fempty, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(fset @ B)]: (((((((fimage @ B) @ A) @ F) @ A4) = (bot_bot @ (fset @ A))) = (A4 = (bot_bot @ (fset @ B))))))).
% 2.36/1.23 thf(fact_220_empty__subsetI, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4)))).
% 2.36/1.23 thf(fact_221_subset__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.36/1.23 thf(fact_222_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.36/1.23 thf(fact_223_insert__subset, axiom, (! [A:$tType,X3:A,A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ A4)) @ B4) = ((((member @ A) @ X3) @ B4) & (((ord_less_eq @ (set @ A)) @ A4) @ B4)))))).
% 2.36/1.23 thf(fact_224_Diff__cancel, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ A4) = (bot_bot @ (set @ A)))))).
% 2.36/1.23 thf(fact_225_empty__Diff, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4) = (bot_bot @ (set @ A)))))).
% 2.36/1.23 thf(fact_226_Diff__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = A4)))).
% 2.36/1.23 thf(fact_227_insert__Diff1, axiom, (! [A:$tType,X3:A,B4:(set @ A),A4:(set @ A)]: (((((member @ A) @ X3) @ B4) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A4)) @ B4) = (((minus_minus @ (set @ A)) @ A4) @ B4)))))).
% 2.36/1.23 thf(fact_228_Diff__insert0, axiom, (! [A:$tType,X3:A,A4:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ X3) @ A4))) => ((((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X3) @ B4)) = (((minus_minus @ (set @ A)) @ A4) @ B4)))))).
% 2.36/1.23 thf(fact_229_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A2:A,A4:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A2) @ A4)) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.36/1.23 thf(fact_230_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A2:A,A4:(set @ A),B2:A]: ((((((insert @ A) @ A2) @ A4) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.36/1.23 thf(fact_231_Diff__eq__empty__iff, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: ((((((minus_minus @ (set @ A)) @ A4) @ B4) = (bot_bot @ (set @ A))) = (((ord_less_eq @ (set @ A)) @ A4) @ B4))))).
% 2.36/1.23 thf(fact_232_tree_Ocollapse, axiom, (! [A:$tType,Tree:(abstra2103299360e_tree @ A)]: (((((abstra388494275e_Node @ A) @ ((abstra573067619e_root @ A) @ Tree)) @ ((abstra1749095923e_cont @ A) @ Tree)) = Tree)))).
% 2.36/1.23 thf(fact_233_Collect__mono__iff, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q2)) = (! [X6:A]: (((P3 @ X6) => (Q2 @ X6)))))))).
% 2.36/1.23 thf(fact_234_fset__eq__fsubset, axiom, (! [A:$tType]: (((^ [Y3:(fset @ A),Z:(fset @ A)]: ((Y3 = Z))) = (^ [A7:(fset @ A),B7:(fset @ A)]: (((((ord_less_eq @ (fset @ A)) @ A7) @ B7) & (((ord_less_eq @ (fset @ A)) @ B7) @ A7)))))))).
% 2.36/1.23 thf(fact_235_contra__subsetD, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((~ ((((member @ A) @ C2) @ B4))) => (~ ((((member @ A) @ C2) @ A4)))))))).
% 2.36/1.23 thf(fact_236_fsubset__trans, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A),C4:(fset @ A)]: (((((ord_less_eq @ (fset @ A)) @ A4) @ B4) => ((((ord_less_eq @ (fset @ A)) @ B4) @ C4) => (((ord_less_eq @ (fset @ A)) @ A4) @ C4)))))).
% 2.36/1.23 thf(fact_237_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z:(set @ A)]: ((Y3 = Z))) = (^ [A7:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B7) & (((ord_less_eq @ (set @ A)) @ B7) @ A7)))))))).
% 2.36/1.23 thf(fact_238_fsubset__refl, axiom, (! [A:$tType,A4:(fset @ A)]: ((((ord_less_eq @ (fset @ A)) @ A4) @ A4)))).
% 2.36/1.23 thf(fact_239_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C4) => (((ord_less_eq @ (set @ A)) @ A4) @ C4)))))).
% 2.36/1.23 thf(fact_240_Collect__mono, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o)]: (((! [X4:A]: (((P3 @ X4) => (Q2 @ X4)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q2)))))).
% 2.36/1.23 thf(fact_241_fequalityD2, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A)]: (((A4 = B4) => (((ord_less_eq @ (fset @ A)) @ B4) @ A4))))).
% 2.36/1.23 thf(fact_242_fequalityD1, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A)]: (((A4 = B4) => (((ord_less_eq @ (fset @ A)) @ A4) @ B4))))).
% 2.36/1.23 thf(fact_243_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 2.36/1.23 thf(fact_244_rev__subsetD, axiom, (! [A:$tType,C2:A,A4:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B4) => (((member @ A) @ C2) @ B4)))))).
% 2.36/1.23 thf(fact_245_fequalityE, axiom, (! [A:$tType,A4:(fset @ A),B4:(fset @ A)]: (((A4 = B4) => (~ (((((ord_less_eq @ (fset @ A)) @ A4) @ B4) => (~ ((((ord_less_eq @ (fset @ A)) @ B4) @ A4)))))))))).
% 2.36/1.23 thf(fact_246_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A7) => (((member @ A) @ T) @ B7)))))))))).
% 2.36/1.23 thf(fact_247_set__rev__mp, axiom, (! [A:$tType,X3:A,A4:(set @ A),B4:(set @ A)]: (((((member @ A) @ X3) @ A4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B4) => (((member @ A) @ X3) @ B4)))))).
% 2.36/1.23 thf(fact_248_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((A4 = B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A4))))).
% 2.36/1.23 thf(fact_249_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((A4 = B4) => (((ord_less_eq @ (set @ A)) @ A4) @ B4))))).
% 2.36/1.23 thf(fact_250_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [X6:A]: (((((member @ A) @ X6) @ A7) => (((member @ A) @ X6) @ B7)))))))))).
% 2.36/1.23 thf(fact_251_equalityE, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((A4 = B4) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => (~ ((((ord_less_eq @ (set @ A)) @ B4) @ A4)))))))))).
% 2.36/1.23 thf(fact_252_subsetCE, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B4)))))).
% 2.36/1.23 thf(fact_253_subsetD, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B4)))))).
% 2.36/1.23 thf(fact_254_in__mono, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B4)))))).
% 2.36/1.23 thf(fact_255_set__mp, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B4)))))).
% 2.36/1.23 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite, axiom, (! [A8:$tType,A9:$tType]: (((((finite_finite @ A8) @ (type2 @ A8)) & ((finite_finite @ A9) @ (type2 @ A9))) => ((finite_finite @ ((product_prod @ A8) @ A9)) @ (type2 @ ((product_prod @ A8) @ A9))))))).
% 2.36/1.23 thf(tcon_FSet_Ofset___Finite__Set_Ofinite_1, axiom, (! [A8:$tType]: ((((finite_finite @ A8) @ (type2 @ A8)) => ((finite_finite @ (fset @ A8)) @ (type2 @ (fset @ A8))))))).
% 2.36/1.23 thf(tcon_HOL_Obool___Finite__Set_Ofinite_2, axiom, ((finite_finite @ $o) @ (type2 @ $o))).
% 2.36/1.23 thf(tcon_Set_Oset___Finite__Set_Ofinite_3, axiom, (! [A8:$tType]: ((((finite_finite @ A8) @ (type2 @ A8)) => ((finite_finite @ (set @ A8)) @ (type2 @ (set @ A8))))))).
% 2.36/1.23 thf(tcon_fun___Finite__Set_Ofinite_4, axiom, (! [A8:$tType,A9:$tType]: (((((finite_finite @ A8) @ (type2 @ A8)) & ((finite_finite @ A9) @ (type2 @ A9))) => ((finite_finite @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.36/1.23 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A8:$tType,A9:$tType]: ((((order_bot @ A9) @ (type2 @ A9)) => ((order_bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.36/1.23 thf(tcon_fun___Countable_Ocountable, axiom, (! [A8:$tType,A9:$tType]: (((((finite_finite @ A8) @ (type2 @ A8)) & ((countable @ A9) @ (type2 @ A9))) => ((countable @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.36/1.23 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.36/1.23 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A9) @ (type2 @ A9)) => ((order @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.36/1.23 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.36/1.23 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: ((((bot @ A9) @ (type2 @ A9)) => ((bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.36/1.23 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, ((wellorder @ nat) @ (type2 @ nat))).
% 2.36/1.23 thf(tcon_Nat_Onat___Orderings_Oorder__bot_5, axiom, ((order_bot @ nat) @ (type2 @ nat))).
% 2.36/1.23 thf(tcon_Nat_Onat___Countable_Ocountable_6, axiom, ((countable @ nat) @ (type2 @ nat))).
% 2.36/1.23 thf(tcon_Nat_Onat___Orderings_Opreorder_7, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.36/1.23 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.36/1.23 thf(tcon_Nat_Onat___Orderings_Oorder_8, axiom, ((order @ nat) @ (type2 @ nat))).
% 2.36/1.23 thf(tcon_Nat_Onat___Orderings_Oord_9, axiom, ((ord @ nat) @ (type2 @ nat))).
% 2.36/1.23 thf(tcon_Nat_Onat___Orderings_Obot_10, axiom, ((bot @ nat) @ (type2 @ nat))).
% 2.36/1.23 thf(tcon_Set_Oset___Orderings_Oorder__bot_11, axiom, (! [A8:$tType]: (((order_bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.36/1.23 thf(tcon_Set_Oset___Countable_Ocountable_12, axiom, (! [A8:$tType]: ((((finite_finite @ A8) @ (type2 @ A8)) => ((countable @ (set @ A8)) @ (type2 @ (set @ A8))))))).
% 2.36/1.23 thf(tcon_Set_Oset___Orderings_Opreorder_13, axiom, (! [A8:$tType]: (((preorder @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.36/1.23 thf(tcon_Set_Oset___Orderings_Oorder_14, axiom, (! [A8:$tType]: (((order @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.36/1.23 thf(tcon_Set_Oset___Orderings_Oord_15, axiom, (! [A8:$tType]: (((ord @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.36/1.23 thf(tcon_Set_Oset___Orderings_Obot_16, axiom, (! [A8:$tType]: (((bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.36/1.23 thf(tcon_HOL_Obool___Orderings_Oorder__bot_17, axiom, ((order_bot @ $o) @ (type2 @ $o))).
% 2.36/1.23 thf(tcon_HOL_Obool___Countable_Ocountable_18, axiom, ((countable @ $o) @ (type2 @ $o))).
% 2.36/1.23 thf(tcon_HOL_Obool___Orderings_Opreorder_19, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.36/1.23 thf(tcon_HOL_Obool___Orderings_Olinorder_20, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.36/1.23 thf(tcon_HOL_Obool___Orderings_Oorder_21, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.36/1.23 thf(tcon_HOL_Obool___Orderings_Oord_22, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.36/1.23 thf(tcon_HOL_Obool___Orderings_Obot_23, axiom, ((bot @ $o) @ (type2 @ $o))).
% 2.36/1.23 thf(tcon_FSet_Ofset___Orderings_Oorder__bot_24, axiom, (! [A8:$tType]: (((order_bot @ (fset @ A8)) @ (type2 @ (fset @ A8)))))).
% 2.36/1.23 thf(tcon_FSet_Ofset___Countable_Ocountable_25, axiom, (! [A8:$tType]: ((((finite_finite @ A8) @ (type2 @ A8)) => ((countable @ (fset @ A8)) @ (type2 @ (fset @ A8))))))).
% 2.36/1.23 thf(tcon_FSet_Ofset___Orderings_Opreorder_26, axiom, (! [A8:$tType]: (((preorder @ (fset @ A8)) @ (type2 @ (fset @ A8)))))).
% 2.36/1.23 thf(tcon_FSet_Ofset___Orderings_Oorder_27, axiom, (! [A8:$tType]: (((order @ (fset @ A8)) @ (type2 @ (fset @ A8)))))).
% 2.36/1.23 thf(tcon_FSet_Ofset___Orderings_Oord_28, axiom, (! [A8:$tType]: (((ord @ (fset @ A8)) @ (type2 @ (fset @ A8)))))).
% 2.36/1.23 thf(tcon_FSet_Ofset___Orderings_Obot_29, axiom, (! [A8:$tType]: (((bot @ (fset @ A8)) @ (type2 @ (fset @ A8)))))).
% 2.36/1.23 thf(tcon_Product__Type_Oprod___Countable_Ocountable_30, axiom, (! [A8:$tType,A9:$tType]: (((((countable @ A8) @ (type2 @ A8)) & ((countable @ A9) @ (type2 @ A9))) => ((countable @ ((product_prod @ A8) @ A9)) @ (type2 @ ((product_prod @ A8) @ A9))))))).
% 2.36/1.23 thf(help_If_3_1_T, axiom, (! [P3:$o]: (((P3 = $true) | (P3 = $false))))).
% 2.36/1.23 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 2.36/1.23 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 2.36/1.23 thf(conj_0, hypothesis, (! [Sl7:(fset @ state)]: ((((((eff @ (((product_snd @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ stepsa))) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ stepsa))) @ Sl7) & (((fmember @ state) @ (((product_fst @ state) @ rule) @ ((shd @ ((product_prod @ state) @ rule)) @ ((stl @ ((product_prod @ state) @ rule)) @ stepsa)))) @ Sl7)) => thesis)))).
% 2.36/1.23 thf(conj_1, conjecture, thesis).
% 2.36/1.23 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.VC7EeYKUxt/DTF2DTF19284.p
% 2.36/1.23 ------------------------
% 2.36/1.26 ---- Cleaned THF ---
% 2.36/1.26 thf(ty_t_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree,type,
% 2.36/1.26 abstra2103299360e_tree: $tType > $tType ).
% 2.36/1.26
% 2.36/1.26 thf(ty_t_Product__Type_Oprod,type,
% 2.36/1.26 product_prod: $tType > $tType > $tType ).
% 2.36/1.26
% 2.36/1.26 thf(ty_t_Stream_Ostream,type,
% 2.36/1.26 stream: $tType > $tType ).
% 2.36/1.26
% 2.36/1.26 thf(ty_t_FSet_Ofset,type,
% 2.36/1.26 fset: $tType > $tType ).
% 2.36/1.26
% 2.36/1.26 thf(ty_t_Set_Oset,type,
% 2.36/1.26 set: $tType > $tType ).
% 2.36/1.26
% 2.36/1.26 thf(ty_t_Nat_Onat,type,
% 2.36/1.26 nat: $tType ).
% 2.36/1.26
% 2.36/1.26 thf(ty_tf_state,type,
% 2.36/1.26 state: $tType ).
% 2.36/1.26
% 2.36/1.26 thf(ty_t_itself,type,
% 2.36/1.26 itself: $tType > $tType ).
% 2.36/1.26
% 2.36/1.26 thf(ty_tf_rule,type,
% 2.36/1.26 rule: $tType ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Finite__Set_Ofinite,type,
% 2.36/1.26 finite_finite:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_HOL_Otype,type,
% 2.36/1.26 type:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Orderings_Obot,type,
% 2.36/1.26 bot:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Orderings_Oord,type,
% 2.36/1.26 ord:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Orderings_Oorder,type,
% 2.36/1.26 order:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Orderings_Olinorder,type,
% 2.36/1.26 linorder:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Orderings_Opreorder,type,
% 2.36/1.26 preorder:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Countable_Ocountable,type,
% 2.36/1.26 countable:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.36/1.26 order_bot:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_cl_Orderings_Owellorder,type,
% 2.36/1.26 wellorder:
% 2.36/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem,type,
% 2.36/1.26 abstra1326562878System:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( set @ State ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_OminWait,type,
% 2.36/1.26 abstra1332369113inWait:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > State > nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_Oper,type,
% 2.36/1.26 abstra2096684367le_per:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( set @ State ) > Rule > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem_Opos,type,
% 2.36/1.26 abstra2097340358le_pos:
% 2.36/1.26 !>[A: $tType] : ( ( stream @ A ) > A > nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OSaturated,type,
% 2.36/1.26 abstra1209608345urated:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( stream @ ( product_prod @ State @ Rule ) ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Oenabled,type,
% 2.36/1.26 abstra1874422341nabled:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > Rule > State > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Oepath,type,
% 2.36/1.26 abstra523868654_epath:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( stream @ ( product_prod @ State @ Rule ) ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Ofair,type,
% 2.36/1.26 abstra928354080m_fair:
% 2.36/1.26 !>[Rule: $tType] : ( ( stream @ Rule ) > ( stream @ Rule ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Ofenum,type,
% 2.36/1.26 abstra1774373515_fenum:
% 2.36/1.26 !>[Rule: $tType] : ( ( stream @ Rule ) > ( stream @ Rule ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OmkTree,type,
% 2.36/1.26 abstra1225283448mkTree:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > State > ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_OpickEff,type,
% 2.36/1.26 abstra1276541928ickEff:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > Rule > State > ( fset @ State ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Osaturated,type,
% 2.36/1.26 abstra726722745urated:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > Rule > ( stream @ ( product_prod @ State @ Rule ) ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Otrim,type,
% 2.36/1.26 abstra1259602206m_trim:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > State > ( stream @ Rule ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_ORuleSystem__Defs_Owf,type,
% 2.36/1.26 abstra1874736267tem_wf:
% 2.36/1.26 !>[Rule: $tType,State: $tType] : ( ( Rule > State > ( fset @ State ) > $o ) > ( stream @ Rule ) > ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Oipath,type,
% 2.36/1.26 abstra313004635_ipath:
% 2.36/1.26 !>[A: $tType] : ( ( abstra2103299360e_tree @ A ) > ( stream @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_ONode,type,
% 2.36/1.26 abstra388494275e_Node:
% 2.36/1.26 !>[A: $tType] : ( A > ( fset @ ( abstra2103299360e_tree @ A ) ) > ( abstra2103299360e_tree @ A ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_Ocont,type,
% 2.36/1.26 abstra1749095923e_cont:
% 2.36/1.26 !>[A: $tType] : ( ( abstra2103299360e_tree @ A ) > ( fset @ ( abstra2103299360e_tree @ A ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Abstract__Completeness__Mirabelle__wdxnrclvrt_Otree_Oroot,type,
% 2.36/1.26 abstra573067619e_root:
% 2.36/1.26 !>[A: $tType] : ( ( abstra2103299360e_tree @ A ) > A ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Countable__Set_Ocountable,type,
% 2.36/1.26 countable_countable:
% 2.36/1.26 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_FSet_Ofimage,type,
% 2.36/1.26 fimage:
% 2.36/1.26 !>[A: $tType,B: $tType] : ( ( A > B ) > ( fset @ A ) > ( fset @ B ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_FSet_Ofmember,type,
% 2.36/1.26 fmember:
% 2.36/1.26 !>[A: $tType] : ( A > ( fset @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.36/1.26 minus_minus:
% 2.36/1.26 !>[A: $tType] : ( A > A > A ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_If,type,
% 2.36/1.26 if:
% 2.36/1.26 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.36/1.26 bot_bot:
% 2.36/1.26 !>[A: $tType] : A ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Orderings_Oord__class_OLeast,type,
% 2.36/1.26 ord_Least:
% 2.36/1.26 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.36/1.26 ord_less_eq:
% 2.36/1.26 !>[A: $tType] : ( A > A > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Product__Type_OPair,type,
% 2.36/1.26 product_Pair:
% 2.36/1.26 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 2.36/1.26 product_fst:
% 2.36/1.26 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 2.36/1.26 product_snd:
% 2.36/1.26 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Pure_Otype,type,
% 2.36/1.26 type2:
% 2.36/1.26 !>[A: $tType] : ( itself @ A ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Set_OCollect,type,
% 2.36/1.26 collect:
% 2.36/1.26 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Set_Oinsert,type,
% 2.36/1.26 insert:
% 2.36/1.26 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Stream_Osdrop,type,
% 2.36/1.26 sdrop:
% 2.36/1.26 !>[A: $tType] : ( nat > ( stream @ A ) > ( stream @ A ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Stream_Osdrop__while,type,
% 2.36/1.26 sdrop_while:
% 2.36/1.26 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > ( stream @ A ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Stream_Ostream_Ocase__stream,type,
% 2.36/1.26 case_stream:
% 2.36/1.26 !>[A: $tType,B: $tType] : ( ( A > ( stream @ A ) > B ) > ( stream @ A ) > B ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Stream_Ostream_Oshd,type,
% 2.36/1.26 shd:
% 2.36/1.26 !>[A: $tType] : ( ( stream @ A ) > A ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Stream_Ostream_Osset,type,
% 2.36/1.26 sset:
% 2.36/1.26 !>[A: $tType] : ( ( stream @ A ) > ( set @ A ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_Stream_Ostream_Ostl,type,
% 2.36/1.26 stl:
% 2.36/1.26 !>[A: $tType] : ( ( stream @ A ) > ( stream @ A ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_c_member,type,
% 2.36/1.26 member:
% 2.36/1.26 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_v_S,type,
% 2.36/1.26 s: set @ state ).
% 2.36/1.26
% 2.36/1.26 thf(sy_v_eff,type,
% 2.36/1.26 eff: rule > state > ( fset @ state ) > $o ).
% 2.36/1.26
% 2.36/1.26 thf(sy_v_r,type,
% 2.36/1.26 r: rule ).
% 2.36/1.26
% 2.36/1.26 thf(sy_v_rules,type,
% 2.36/1.26 rules: stream @ rule ).
% 2.36/1.26
% 2.36/1.26 thf(sy_v_steps,type,
% 2.36/1.26 steps: stream @ ( product_prod @ state @ rule ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_v_stepsa____,type,
% 2.36/1.26 stepsa: stream @ ( product_prod @ state @ rule ) ).
% 2.36/1.26
% 2.36/1.26 thf(sy_v_thesis____,type,
% 2.36/1.26 thesis: $o ).
% 2.36/1.26
% 2.36/1.26 thf(fact_0_calculation_I1_J,axiom,
% 2.36/1.26 member @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ s ).
% 2.36/1.26
% 2.36/1.26 thf(fact_1_calculation_I3_J,axiom,
% 2.36/1.26 ( ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) )
% 2.36/1.26 != r ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_2_e,axiom,
% 2.36/1.26 ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ steps )
% 2.36/1.26 & ( member @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ steps ) ) @ s ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_3_calculation_I2_J,axiom,
% 2.36/1.26 abstra1874422341nabled @ rule @ state @ eff @ r @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_4_enabled__def,axiom,
% 2.36/1.26 ! [R: rule,S: state] :
% 2.36/1.26 ( ( abstra1874422341nabled @ rule @ state @ eff @ R @ S )
% 2.36/1.26 = ( ^ [P: ( fset @ state ) > $o] :
% 2.36/1.26 ? [X: fset @ state] : ( P @ X )
% 2.36/1.26 @ ( eff @ R @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_5_epath_Ocases,axiom,
% 2.36/1.26 ! [A2: stream @ ( product_prod @ state @ rule )] :
% 2.36/1.26 ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ A2 )
% 2.36/1.26 => ~ ( ( member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ A2 ) ) @ ( sset @ rule @ rules ) )
% 2.36/1.26 => ! [Sl: fset @ state] :
% 2.36/1.26 ( ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ A2 ) ) ) @ Sl )
% 2.36/1.26 => ( ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ A2 ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ A2 ) ) @ Sl )
% 2.36/1.26 => ~ ( abstra523868654_epath @ rule @ state @ eff @ rules @ ( stl @ ( product_prod @ state @ rule ) @ A2 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_6_epath_Ocoinduct,axiom,
% 2.36/1.26 ! [X2: ( stream @ ( product_prod @ state @ rule ) ) > $o,X3: stream @ ( product_prod @ state @ rule )] :
% 2.36/1.26 ( ( X2 @ X3 )
% 2.36/1.26 => ( ! [X4: stream @ ( product_prod @ state @ rule )] :
% 2.36/1.26 ( ( X2 @ X4 )
% 2.36/1.26 => ? [Steps: stream @ ( product_prod @ state @ rule ),Sl2: fset @ state] :
% 2.36/1.26 ( ( X4 = Steps )
% 2.36/1.26 & ( member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps ) ) @ ( sset @ rule @ rules ) )
% 2.36/1.26 & ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ Steps ) ) ) @ Sl2 )
% 2.36/1.26 & ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps ) ) @ Sl2 )
% 2.36/1.26 & ( ( X2 @ ( stl @ ( product_prod @ state @ rule ) @ Steps ) )
% 2.36/1.26 | ( abstra523868654_epath @ rule @ state @ eff @ rules @ ( stl @ ( product_prod @ state @ rule ) @ Steps ) ) ) ) )
% 2.36/1.26 => ( abstra523868654_epath @ rule @ state @ eff @ rules @ X3 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_7_epath_Ointros,axiom,
% 2.36/1.26 ! [Steps2: stream @ ( product_prod @ state @ rule ),Sl3: fset @ state] :
% 2.36/1.26 ( ( member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps2 ) ) @ ( sset @ rule @ rules ) )
% 2.36/1.26 => ( ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ Steps2 ) ) ) @ Sl3 )
% 2.36/1.26 => ( ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps2 ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps2 ) ) @ Sl3 )
% 2.36/1.26 => ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ ( stl @ ( product_prod @ state @ rule ) @ Steps2 ) )
% 2.36/1.26 => ( abstra523868654_epath @ rule @ state @ eff @ rules @ Steps2 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_8_epath_Osimps,axiom,
% 2.36/1.26 ! [A2: stream @ ( product_prod @ state @ rule )] :
% 2.36/1.26 ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ A2 )
% 2.36/1.26 = ( ? [Steps3: stream @ ( product_prod @ state @ rule ),Sl4: fset @ state] :
% 2.36/1.26 ( ( A2 = Steps3 )
% 2.36/1.26 & ( member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps3 ) ) @ ( sset @ rule @ rules ) )
% 2.36/1.26 & ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ Steps3 ) ) ) @ Sl4 )
% 2.36/1.26 & ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps3 ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ Steps3 ) ) @ Sl4 )
% 2.36/1.26 & ( abstra523868654_epath @ rule @ state @ eff @ rules @ ( stl @ ( product_prod @ state @ rule ) @ Steps3 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_9_stream_Oexpand,axiom,
% 2.36/1.26 ! [A: $tType,Stream: stream @ A,Stream2: stream @ A] :
% 2.36/1.26 ( ( ( ( shd @ A @ Stream )
% 2.36/1.26 = ( shd @ A @ Stream2 ) )
% 2.36/1.26 & ( ( stl @ A @ Stream )
% 2.36/1.26 = ( stl @ A @ Stream2 ) ) )
% 2.36/1.26 => ( Stream = Stream2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_10_stream_Ocoinduct,axiom,
% 2.36/1.26 ! [A: $tType,R2: ( stream @ A ) > ( stream @ A ) > $o,Stream: stream @ A,Stream2: stream @ A] :
% 2.36/1.26 ( ( R2 @ Stream @ Stream2 )
% 2.36/1.26 => ( ! [Stream3: stream @ A,Stream4: stream @ A] :
% 2.36/1.26 ( ( R2 @ Stream3 @ Stream4 )
% 2.36/1.26 => ( ( ( shd @ A @ Stream3 )
% 2.36/1.26 = ( shd @ A @ Stream4 ) )
% 2.36/1.26 & ( R2 @ ( stl @ A @ Stream3 ) @ ( stl @ A @ Stream4 ) ) ) )
% 2.36/1.26 => ( Stream = Stream2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_11_stream_Ocoinduct__strong,axiom,
% 2.36/1.26 ! [A: $tType,R2: ( stream @ A ) > ( stream @ A ) > $o,Stream: stream @ A,Stream2: stream @ A] :
% 2.36/1.26 ( ( R2 @ Stream @ Stream2 )
% 2.36/1.26 => ( ! [Stream3: stream @ A,Stream4: stream @ A] :
% 2.36/1.26 ( ( R2 @ Stream3 @ Stream4 )
% 2.36/1.26 => ( ( ( shd @ A @ Stream3 )
% 2.36/1.26 = ( shd @ A @ Stream4 ) )
% 2.36/1.26 & ( ( R2 @ ( stl @ A @ Stream3 ) @ ( stl @ A @ Stream4 ) )
% 2.36/1.26 | ( ( stl @ A @ Stream3 )
% 2.36/1.26 = ( stl @ A @ Stream4 ) ) ) ) )
% 2.36/1.26 => ( Stream = Stream2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_12_RuleSystem__axioms,axiom,
% 2.36/1.26 abstra1326562878System @ rule @ state @ eff @ rules @ s ).
% 2.36/1.26
% 2.36/1.26 thf(fact_13_prod__eqI,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,P2: product_prod @ A @ B,Q: product_prod @ A @ B] :
% 2.36/1.26 ( ( ( product_fst @ A @ B @ P2 )
% 2.36/1.26 = ( product_fst @ A @ B @ Q ) )
% 2.36/1.26 => ( ( ( product_snd @ A @ B @ P2 )
% 2.36/1.26 = ( product_snd @ A @ B @ Q ) )
% 2.36/1.26 => ( P2 = Q ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_14_p,axiom,
% 2.36/1.26 abstra2096684367le_per @ rule @ state @ eff @ rules @ s @ r ).
% 2.36/1.26
% 2.36/1.26 thf(fact_15_enabled__R,axiom,
% 2.36/1.26 ! [S: state] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ? [X4: rule] :
% 2.36/1.26 ( ( member @ rule @ X4 @ ( sset @ rule @ rules ) )
% 2.36/1.26 & ? [X1: fset @ state] : ( eff @ X4 @ S @ X1 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_16_calculation_I4_J,axiom,
% 2.36/1.26 member @ rule @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ ( sset @ rule @ rules ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_17_eff__S,axiom,
% 2.36/1.26 ! [S: state,R: rule,Sl3: fset @ state,S2: state] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( member @ rule @ R @ ( sset @ rule @ rules ) )
% 2.36/1.26 => ( ( eff @ R @ S @ Sl3 )
% 2.36/1.26 => ( ( fmember @ state @ S2 @ Sl3 )
% 2.36/1.26 => ( member @ state @ S2 @ s ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_18_sset__fenum,axiom,
% 2.36/1.26 ( ( sset @ rule @ ( abstra1774373515_fenum @ rule @ rules ) )
% 2.36/1.26 = ( sset @ rule @ rules ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_19_pickEff,axiom,
% 2.36/1.26 ! [R: rule,S: state] :
% 2.36/1.26 ( ( abstra1874422341nabled @ rule @ state @ eff @ R @ S )
% 2.36/1.26 => ( eff @ R @ S @ ( abstra1276541928ickEff @ rule @ state @ eff @ R @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_20_RuleSystem_Oenabled__R,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ? [X4: Rule] :
% 2.36/1.26 ( ( member @ Rule @ X4 @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 & ? [X1: fset @ State] : ( Eff @ X4 @ S @ X1 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_21_RuleSystem__Defs_Oenabled__def,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType] :
% 2.36/1.26 ( ( abstra1874422341nabled @ Rule @ State )
% 2.36/1.26 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,R3: Rule,S4: State] :
% 2.36/1.26 ( ^ [P: ( fset @ State ) > $o] :
% 2.36/1.26 ? [X: fset @ State] : ( P @ X )
% 2.36/1.26 @ ( Eff2 @ R3 @ S4 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_22_RuleSystem_Ointro,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,S3: set @ State,Rules: stream @ Rule,Eff: Rule > State > ( fset @ State ) > $o] :
% 2.36/1.26 ( ! [S5: State] :
% 2.36/1.26 ( ( member @ State @ S5 @ S3 )
% 2.36/1.26 => ! [R4: Rule] :
% 2.36/1.26 ( ( member @ Rule @ R4 @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 => ! [Sl: fset @ State] :
% 2.36/1.26 ( ( Eff @ R4 @ S5 @ Sl )
% 2.36/1.26 => ! [S6: State] :
% 2.36/1.26 ( ( fmember @ State @ S6 @ Sl )
% 2.36/1.26 => ( member @ State @ S6 @ S3 ) ) ) ) )
% 2.36/1.26 => ( ! [S5: State] :
% 2.36/1.26 ( ( member @ State @ S5 @ S3 )
% 2.36/1.26 => ? [X5: Rule] :
% 2.36/1.26 ( ( member @ Rule @ X5 @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 & ? [X12: fset @ State] : ( Eff @ X5 @ S5 @ X12 ) ) )
% 2.36/1.26 => ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_23_RuleSystem_Oeff__S,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,R: Rule,Sl3: fset @ State,S2: State] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( member @ Rule @ R @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 => ( ( Eff @ R @ S @ Sl3 )
% 2.36/1.26 => ( ( fmember @ State @ S2 @ Sl3 )
% 2.36/1.26 => ( member @ State @ S2 @ S3 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_24_RuleSystem__def,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State )
% 2.36/1.26 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rules2: stream @ Rule,S7: set @ State] :
% 2.36/1.26 ( ! [S4: State] :
% 2.36/1.26 ( ( member @ State @ S4 @ S7 )
% 2.36/1.26 => ! [R3: Rule] :
% 2.36/1.26 ( ( member @ Rule @ R3 @ ( sset @ Rule @ Rules2 ) )
% 2.36/1.26 => ! [Sl4: fset @ State] :
% 2.36/1.26 ( ( Eff2 @ R3 @ S4 @ Sl4 )
% 2.36/1.26 => ! [S8: State] :
% 2.36/1.26 ( ( fmember @ State @ S8 @ Sl4 )
% 2.36/1.26 => ( member @ State @ S8 @ S7 ) ) ) ) )
% 2.36/1.26 & ! [S4: State] :
% 2.36/1.26 ( ( member @ State @ S4 @ S7 )
% 2.36/1.26 => ? [X6: Rule] :
% 2.36/1.26 ( ( member @ Rule @ X6 @ ( sset @ Rule @ Rules2 ) )
% 2.36/1.26 & ( ^ [P: ( fset @ State ) > $o] :
% 2.36/1.26 ? [X: fset @ State] : ( P @ X )
% 2.36/1.26 @ ( Eff2 @ X6 @ S4 ) ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_25_stl__sset,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,A2: stream @ A] :
% 2.36/1.26 ( ( member @ A @ X3 @ ( sset @ A @ ( stl @ A @ A2 ) ) )
% 2.36/1.26 => ( member @ A @ X3 @ ( sset @ A @ A2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_26_shd__sset,axiom,
% 2.36/1.26 ! [A: $tType,A2: stream @ A] : ( member @ A @ ( shd @ A @ A2 ) @ ( sset @ A @ A2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_27_sset__induct,axiom,
% 2.36/1.26 ! [A: $tType,Y: A,S: stream @ A,P3: A > ( stream @ A ) > $o] :
% 2.36/1.26 ( ( member @ A @ Y @ ( sset @ A @ S ) )
% 2.36/1.26 => ( ! [S5: stream @ A] : ( P3 @ ( shd @ A @ S5 ) @ S5 )
% 2.36/1.26 => ( ! [S5: stream @ A,Y2: A] :
% 2.36/1.26 ( ( member @ A @ Y2 @ ( sset @ A @ ( stl @ A @ S5 ) ) )
% 2.36/1.26 => ( ( P3 @ Y2 @ ( stl @ A @ S5 ) )
% 2.36/1.26 => ( P3 @ Y2 @ S5 ) ) )
% 2.36/1.26 => ( P3 @ Y @ S ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_28_RuleSystem__Defs_Oepath_Ocoinduct,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,X2: ( stream @ ( product_prod @ State @ Rule ) ) > $o,X3: stream @ ( product_prod @ State @ Rule ),Rules: stream @ Rule,Eff: Rule > State > ( fset @ State ) > $o] :
% 2.36/1.26 ( ( X2 @ X3 )
% 2.36/1.26 => ( ! [X4: stream @ ( product_prod @ State @ Rule )] :
% 2.36/1.26 ( ( X2 @ X4 )
% 2.36/1.26 => ? [Steps: stream @ ( product_prod @ State @ Rule ),Sl2: fset @ State] :
% 2.36/1.26 ( ( X4 = Steps )
% 2.36/1.26 & ( member @ Rule @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps ) ) @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 & ( fmember @ State @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ ( stl @ ( product_prod @ State @ Rule ) @ Steps ) ) ) @ Sl2 )
% 2.36/1.26 & ( Eff @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps ) ) @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps ) ) @ Sl2 )
% 2.36/1.26 & ( ( X2 @ ( stl @ ( product_prod @ State @ Rule ) @ Steps ) )
% 2.36/1.26 | ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ ( stl @ ( product_prod @ State @ Rule ) @ Steps ) ) ) ) )
% 2.36/1.26 => ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ X3 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_29_RuleSystem__Defs_Oepath_Ointros,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Steps2: stream @ ( product_prod @ State @ Rule ),Rules: stream @ Rule,Sl3: fset @ State,Eff: Rule > State > ( fset @ State ) > $o] :
% 2.36/1.26 ( ( member @ Rule @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps2 ) ) @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 => ( ( fmember @ State @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ ( stl @ ( product_prod @ State @ Rule ) @ Steps2 ) ) ) @ Sl3 )
% 2.36/1.26 => ( ( Eff @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps2 ) ) @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps2 ) ) @ Sl3 )
% 2.36/1.26 => ( ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ ( stl @ ( product_prod @ State @ Rule ) @ Steps2 ) )
% 2.36/1.26 => ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ Steps2 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_30_RuleSystem__Defs_Oepath_Osimps,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType] :
% 2.36/1.26 ( ( abstra523868654_epath @ Rule @ State )
% 2.36/1.26 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rules2: stream @ Rule,A3: stream @ ( product_prod @ State @ Rule )] :
% 2.36/1.26 ? [Steps3: stream @ ( product_prod @ State @ Rule ),Sl4: fset @ State] :
% 2.36/1.26 ( ( A3 = Steps3 )
% 2.36/1.26 & ( member @ Rule @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps3 ) ) @ ( sset @ Rule @ Rules2 ) )
% 2.36/1.26 & ( fmember @ State @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ ( stl @ ( product_prod @ State @ Rule ) @ Steps3 ) ) ) @ Sl4 )
% 2.36/1.26 & ( Eff2 @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps3 ) ) @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ Steps3 ) ) @ Sl4 )
% 2.36/1.26 & ( abstra523868654_epath @ Rule @ State @ Eff2 @ Rules2 @ ( stl @ ( product_prod @ State @ Rule ) @ Steps3 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_31_RuleSystem__Defs_Oepath_Ocases,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,A2: stream @ ( product_prod @ State @ Rule )] :
% 2.36/1.26 ( ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ A2 )
% 2.36/1.26 => ~ ( ( member @ Rule @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ A2 ) ) @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 => ! [Sl: fset @ State] :
% 2.36/1.26 ( ( fmember @ State @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ ( stl @ ( product_prod @ State @ Rule ) @ A2 ) ) ) @ Sl )
% 2.36/1.26 => ( ( Eff @ ( product_snd @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ A2 ) ) @ ( product_fst @ State @ Rule @ ( shd @ ( product_prod @ State @ Rule ) @ A2 ) ) @ Sl )
% 2.36/1.26 => ~ ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ ( stl @ ( product_prod @ State @ Rule ) @ A2 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_32_prod__eq__iff,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType] :
% 2.36/1.26 ( ( ^ [Y3: product_prod @ A @ B,Z: product_prod @ A @ B] : ( Y3 = Z ) )
% 2.36/1.26 = ( ^ [S4: product_prod @ A @ B,T: product_prod @ A @ B] :
% 2.36/1.26 ( ( ( product_fst @ A @ B @ S4 )
% 2.36/1.26 = ( product_fst @ A @ B @ T ) )
% 2.36/1.26 & ( ( product_snd @ A @ B @ S4 )
% 2.36/1.26 = ( product_snd @ A @ B @ T ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_33_prod_Oexpand,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 2.36/1.26 ( ( ( ( product_fst @ A @ B @ Prod )
% 2.36/1.26 = ( product_fst @ A @ B @ Prod2 ) )
% 2.36/1.26 & ( ( product_snd @ A @ B @ Prod )
% 2.36/1.26 = ( product_snd @ A @ B @ Prod2 ) ) )
% 2.36/1.26 => ( Prod = Prod2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_34_Saturated__def,axiom,
% 2.36/1.26 ! [Steps2: stream @ ( product_prod @ state @ rule )] :
% 2.36/1.26 ( ( abstra1209608345urated @ rule @ state @ eff @ rules @ Steps2 )
% 2.36/1.26 = ( ! [X6: rule] :
% 2.36/1.26 ( ( member @ rule @ X6 @ ( sset @ rule @ rules ) )
% 2.36/1.26 => ( abstra726722745urated @ rule @ state @ eff @ X6 @ Steps2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_35_local_Oalw,axiom,
% 2.36/1.26 ( ( abstra523868654_epath @ rule @ state @ eff @ rules @ stepsa )
% 2.36/1.26 & ( member @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ s ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_36_NE__R,axiom,
% 2.36/1.26 ( ( sset @ rule @ rules )
% 2.36/1.26 != ( bot_bot @ ( set @ rule ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_37_fair__stl,axiom,
% 2.36/1.26 ! [Rs: stream @ rule] :
% 2.36/1.26 ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( abstra928354080m_fair @ rule @ rules @ ( stl @ rule @ Rs ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_38_exE__realizer_H,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,P3: A > B > $o,P2: product_prod @ B @ A] :
% 2.36/1.26 ( ( P3 @ ( product_snd @ B @ A @ P2 ) @ ( product_fst @ B @ A @ P2 ) )
% 2.36/1.26 => ~ ! [X4: B,Y2: A] :
% 2.36/1.26 ~ ( P3 @ Y2 @ X4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_39_countable__R,axiom,
% 2.36/1.26 countable_countable @ rule @ ( sset @ rule @ rules ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_40_trim__enabled,axiom,
% 2.36/1.26 ! [S: state,Rs: stream @ rule] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_41_trim__in__R,axiom,
% 2.36/1.26 ! [S: state,Rs: stream @ rule] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( member @ rule @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ ( sset @ rule @ rules ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_42_wf__ipath__epath,axiom,
% 2.36/1.26 ! [T2: abstra2103299360e_tree @ ( product_prod @ state @ rule ),Steps2: stream @ ( product_prod @ state @ rule )] :
% 2.36/1.26 ( ( abstra1874736267tem_wf @ rule @ state @ eff @ rules @ T2 )
% 2.36/1.26 => ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ T2 @ Steps2 )
% 2.36/1.26 => ( abstra523868654_epath @ rule @ state @ eff @ rules @ Steps2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_43_minWait__ex,axiom,
% 2.36/1.26 ! [S: state,Rs: stream @ rule] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ? [N: nat] : ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ N @ Rs ) ) @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_44_trim__fair,axiom,
% 2.36/1.26 ! [S: state,Rs: stream @ rule] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( abstra928354080m_fair @ rule @ rules @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_45_mem__Collect__eq,axiom,
% 2.36/1.26 ! [A: $tType,A2: A,P3: A > $o] :
% 2.36/1.26 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 2.36/1.26 = ( P3 @ A2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_46_Collect__mem__eq,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A] :
% 2.36/1.26 ( ( collect @ A
% 2.36/1.26 @ ^ [X6: A] : ( member @ A @ X6 @ A4 ) )
% 2.36/1.26 = A4 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_47_Collect__cong,axiom,
% 2.36/1.26 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 2.36/1.26 ( ! [X4: A] :
% 2.36/1.26 ( ( P3 @ X4 )
% 2.36/1.26 = ( Q2 @ X4 ) )
% 2.36/1.26 => ( ( collect @ A @ P3 )
% 2.36/1.26 = ( collect @ A @ Q2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_48_ext,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.36/1.26 ( ! [X4: A] :
% 2.36/1.26 ( ( F @ X4 )
% 2.36/1.26 = ( G @ X4 ) )
% 2.36/1.26 => ( F = G ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_49_sdrop__fair,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,M: nat] :
% 2.36/1.26 ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( abstra928354080m_fair @ rule @ rules @ ( sdrop @ rule @ M @ Rs ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_50_fair__fenum,axiom,
% 2.36/1.26 abstra928354080m_fair @ rule @ rules @ ( abstra1774373515_fenum @ rule @ rules ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_51_RuleSystem__Defs_Osdrop__fair,axiom,
% 2.36/1.26 ! [Rule: $tType,Rules: stream @ Rule,Rs: stream @ Rule,M: nat] :
% 2.36/1.26 ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( abstra928354080m_fair @ Rule @ Rules @ ( sdrop @ Rule @ M @ Rs ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_52_RuleSystem__Defs_Ofair__fenum,axiom,
% 2.36/1.26 ! [Rule: $tType,Rules: stream @ Rule] : ( abstra928354080m_fair @ Rule @ Rules @ ( abstra1774373515_fenum @ Rule @ Rules ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_53_RuleSystem_Otrim__fair,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( abstra928354080m_fair @ Rule @ Rules @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_54_RuleSystem__Defs_Owf__ipath__epath,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,T2: abstra2103299360e_tree @ ( product_prod @ State @ Rule ),Steps2: stream @ ( product_prod @ State @ Rule )] :
% 2.36/1.26 ( ( abstra1874736267tem_wf @ Rule @ State @ Eff @ Rules @ T2 )
% 2.36/1.26 => ( ( abstra313004635_ipath @ ( product_prod @ State @ Rule ) @ T2 @ Steps2 )
% 2.36/1.26 => ( abstra523868654_epath @ Rule @ State @ Eff @ Rules @ Steps2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_55_RuleSystem__Defs_Ocountable__R,axiom,
% 2.36/1.26 ! [Rule: $tType,Rules: stream @ Rule] : ( countable_countable @ Rule @ ( sset @ Rule @ Rules ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_56_sdrop__stl,axiom,
% 2.36/1.26 ! [A: $tType,N2: nat,S: stream @ A] :
% 2.36/1.26 ( ( sdrop @ A @ N2 @ ( stl @ A @ S ) )
% 2.36/1.26 = ( stl @ A @ ( sdrop @ A @ N2 @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_57_RuleSystem__Defs_ONE__R,axiom,
% 2.36/1.26 ! [Rule: $tType,Rules: stream @ Rule] :
% 2.36/1.26 ( ( sset @ Rule @ Rules )
% 2.36/1.26 != ( bot_bot @ ( set @ Rule ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_58_RuleSystem__Defs_Ofair__stl,axiom,
% 2.36/1.26 ! [Rule: $tType,Rules: stream @ Rule,Rs: stream @ Rule] :
% 2.36/1.26 ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( abstra928354080m_fair @ Rule @ Rules @ ( stl @ Rule @ Rs ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_59_RuleSystem_OminWait__ex,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ? [N: nat] : ( abstra1874422341nabled @ Rule @ State @ Eff @ ( shd @ Rule @ ( sdrop @ Rule @ N @ Rs ) ) @ S ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_60_RuleSystem_Otrim__in__R,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( member @ Rule @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ ( sset @ Rule @ Rules ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_61_RuleSystem_Otrim__enabled,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( abstra1874422341nabled @ Rule @ State @ Eff @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ S ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_62_RuleSystem__Defs_OSaturated__def,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType] :
% 2.36/1.26 ( ( abstra1209608345urated @ Rule @ State )
% 2.36/1.26 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rules2: stream @ Rule,Steps3: stream @ ( product_prod @ State @ Rule )] :
% 2.36/1.26 ! [X6: Rule] :
% 2.36/1.26 ( ( member @ Rule @ X6 @ ( sset @ Rule @ Rules2 ) )
% 2.36/1.26 => ( abstra726722745urated @ Rule @ State @ Eff2 @ X6 @ Steps3 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_63_RuleSystem__Defs_OpickEff,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,R: Rule,S: State] :
% 2.36/1.26 ( ( abstra1874422341nabled @ Rule @ State @ Eff @ R @ S )
% 2.36/1.26 => ( Eff @ R @ S @ ( abstra1276541928ickEff @ Rule @ State @ Eff @ R @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_64_RuleSystem__Defs_Osset__fenum,axiom,
% 2.36/1.26 ! [Rule: $tType,Rules: stream @ Rule] :
% 2.36/1.26 ( ( sset @ Rule @ ( abstra1774373515_fenum @ Rule @ Rules ) )
% 2.36/1.26 = ( sset @ Rule @ Rules ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_65_trim__alt,axiom,
% 2.36/1.26 ! [S: state,Rs: stream @ rule] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S )
% 2.36/1.26 = ( sdrop @ rule @ ( abstra1332369113inWait @ rule @ state @ eff @ Rs @ S ) @ Rs ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_66_pos,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,R: rule] :
% 2.36/1.26 ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( ( member @ rule @ R @ ( sset @ rule @ rules ) )
% 2.36/1.26 => ( ( shd @ rule @ ( sdrop @ rule @ ( abstra2097340358le_pos @ rule @ Rs @ R ) @ Rs ) )
% 2.36/1.26 = R ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_67_trim__def,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,S: state] :
% 2.36/1.26 ( ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S )
% 2.36/1.26 = ( sdrop_while @ rule
% 2.36/1.26 @ ^ [R3: rule] :
% 2.36/1.26 ~ ( abstra1874422341nabled @ rule @ state @ eff @ R3 @ S )
% 2.36/1.26 @ Rs ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_68_wf__mkTree,axiom,
% 2.36/1.26 ! [S: state,Rs: stream @ rule] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( abstra1874736267tem_wf @ rule @ state @ eff @ rules @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_69_countable__empty,axiom,
% 2.36/1.26 ! [A: $tType] : ( countable_countable @ A @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_70_RuleSystem_Opos,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,Rs: stream @ Rule,R: Rule] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( ( member @ Rule @ R @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 => ( ( shd @ Rule @ ( sdrop @ Rule @ ( abstra2097340358le_pos @ Rule @ Rs @ R ) @ Rs ) )
% 2.36/1.26 = R ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_71_in__cont__mkTree,axiom,
% 2.36/1.26 ! [S: state,Rs: stream @ rule,T3: abstra2103299360e_tree @ ( product_prod @ state @ rule )] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( ( fmember @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ T3 @ ( abstra1749095923e_cont @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) ) )
% 2.36/1.26 => ? [Sl5: fset @ state,S6: state] :
% 2.36/1.26 ( ( member @ state @ S6 @ s )
% 2.36/1.26 & ( eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S @ Sl5 )
% 2.36/1.26 & ( fmember @ state @ S6 @ Sl5 )
% 2.36/1.26 & ( T3
% 2.36/1.26 = ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S6 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_72_RuleSystem_Otrim__alt,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S )
% 2.36/1.26 = ( sdrop @ Rule @ ( abstra1332369113inWait @ Rule @ State @ Eff @ Rs @ S ) @ Rs ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_73_countableI__type,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( countable @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A4: set @ A] : ( countable_countable @ A @ A4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_74_ipath__mkTree__sdrop,axiom,
% 2.36/1.26 ! [S: state,Rs: stream @ rule,Steps2: stream @ ( product_prod @ state @ rule ),M: nat] :
% 2.36/1.26 ( ( member @ state @ S @ s )
% 2.36/1.26 => ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) @ Steps2 )
% 2.36/1.26 => ? [N: nat,S6: state] :
% 2.36/1.26 ( ( member @ state @ S6 @ s )
% 2.36/1.26 & ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( sdrop @ rule @ N @ Rs ) @ S6 ) @ ( sdrop @ ( product_prod @ state @ rule ) @ M @ Steps2 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_75_sdrop__while_Osimps,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( sdrop_while @ A )
% 2.36/1.26 = ( ^ [P4: A > $o,S4: stream @ A] : ( if @ ( stream @ A ) @ ( P4 @ ( shd @ A @ S4 ) ) @ ( sdrop_while @ A @ P4 @ ( stl @ A @ S4 ) ) @ S4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_76_RuleSystem_Oin__cont__mkTree,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule,T3: abstra2103299360e_tree @ ( product_prod @ State @ Rule )] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( ( fmember @ ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) @ T3 @ ( abstra1749095923e_cont @ ( product_prod @ State @ Rule ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ Rs @ S ) ) )
% 2.36/1.26 => ? [Sl5: fset @ State,S6: State] :
% 2.36/1.26 ( ( member @ State @ S6 @ S3 )
% 2.36/1.26 & ( Eff @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ S @ Sl5 )
% 2.36/1.26 & ( fmember @ State @ S6 @ Sl5 )
% 2.36/1.26 & ( T3
% 2.36/1.26 = ( abstra1225283448mkTree @ Rule @ State @ Eff @ ( stl @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ S6 ) ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_77_RuleSystem__Defs_Otrim__def,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType] :
% 2.36/1.26 ( ( abstra1259602206m_trim @ Rule @ State )
% 2.36/1.26 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rs2: stream @ Rule,S4: State] :
% 2.36/1.26 ( sdrop_while @ Rule
% 2.36/1.26 @ ^ [R3: Rule] :
% 2.36/1.26 ~ ( abstra1874422341nabled @ Rule @ State @ Eff2 @ R3 @ S4 )
% 2.36/1.26 @ Rs2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_78_countable__Collect,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,Phi: A > $o] :
% 2.36/1.26 ( ( countable_countable @ A @ A4 )
% 2.36/1.26 => ( countable_countable @ A
% 2.36/1.26 @ ( collect @ A
% 2.36/1.26 @ ^ [A3: A] :
% 2.36/1.26 ( ( member @ A @ A3 @ A4 )
% 2.36/1.26 & ( Phi @ A3 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_79_RuleSystem_Owf__mkTree,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( abstra1874736267tem_wf @ Rule @ State @ Eff @ Rules @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ Rs @ S ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_80_RuleSystem_Oipath__mkTree__sdrop,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,S: State,Rs: stream @ Rule,Steps2: stream @ ( product_prod @ State @ Rule ),M: nat] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( member @ State @ S @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( ( abstra313004635_ipath @ ( product_prod @ State @ Rule ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ Rs @ S ) @ Steps2 )
% 2.36/1.26 => ? [N: nat,S6: State] :
% 2.36/1.26 ( ( member @ State @ S6 @ S3 )
% 2.36/1.26 & ( abstra313004635_ipath @ ( product_prod @ State @ Rule ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ ( sdrop @ Rule @ N @ Rs ) @ S6 ) @ ( sdrop @ ( product_prod @ State @ Rule ) @ M @ Steps2 ) ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_81_minWait__le__pos,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,R: rule,S: state] :
% 2.36/1.26 ( ( abstra928354080m_fair @ rule @ rules @ Rs )
% 2.36/1.26 => ( ( member @ rule @ R @ ( sset @ rule @ rules ) )
% 2.36/1.26 => ( ( abstra1874422341nabled @ rule @ state @ eff @ R @ S )
% 2.36/1.26 => ( ord_less_eq @ nat @ ( abstra1332369113inWait @ rule @ state @ eff @ Rs @ S ) @ ( abstra2097340358le_pos @ rule @ Rs @ R ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_82_minWait__def,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,S: state] :
% 2.36/1.26 ( ( abstra1332369113inWait @ rule @ state @ eff @ Rs @ S )
% 2.36/1.26 = ( ord_Least @ nat
% 2.36/1.26 @ ^ [N3: nat] : ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ N3 @ Rs ) ) @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_83_mkTree_Osimps_I2_J,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,S: state] :
% 2.36/1.26 ( ( abstra1749095923e_cont @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) )
% 2.36/1.26 = ( fimage @ state @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) @ ( abstra1276541928ickEff @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_84_minWait__least,axiom,
% 2.36/1.26 ! [N2: nat,Rs: stream @ rule,S: state] :
% 2.36/1.26 ( ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ N2 @ Rs ) ) @ S )
% 2.36/1.26 => ( ord_less_eq @ nat @ ( abstra1332369113inWait @ rule @ state @ eff @ Rs @ S ) @ N2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_85_pos__def,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( abstra2097340358le_pos @ A )
% 2.36/1.26 = ( ^ [Rs2: stream @ A,R3: A] :
% 2.36/1.26 ( ord_Least @ nat
% 2.36/1.26 @ ^ [N3: nat] :
% 2.36/1.26 ( ( shd @ A @ ( sdrop @ A @ N3 @ Rs2 ) )
% 2.36/1.26 = R3 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_86_pos__least,axiom,
% 2.36/1.26 ! [A: $tType,N2: nat,Rs: stream @ A,R: A] :
% 2.36/1.26 ( ( ( shd @ A @ ( sdrop @ A @ N2 @ Rs ) )
% 2.36/1.26 = R )
% 2.36/1.26 => ( ord_less_eq @ nat @ ( abstra2097340358le_pos @ A @ Rs @ R ) @ N2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_87_RuleSystem_Opos__least,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,A: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,N2: nat,Rs: stream @ A,R: A] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( ( shd @ A @ ( sdrop @ A @ N2 @ Rs ) )
% 2.36/1.26 = R )
% 2.36/1.26 => ( ord_less_eq @ nat @ ( abstra2097340358le_pos @ A @ Rs @ R ) @ N2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_88_RuleSystem_Opos__def,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType,A: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,Rs: stream @ A,R: A] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( abstra2097340358le_pos @ A @ Rs @ R )
% 2.36/1.26 = ( ord_Least @ nat
% 2.36/1.26 @ ^ [N3: nat] :
% 2.36/1.26 ( ( shd @ A @ ( sdrop @ A @ N3 @ Rs ) )
% 2.36/1.26 = R ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_89_RuleSystem_OminWait__least,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,N2: nat,Rs: stream @ Rule,S: State] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( abstra1874422341nabled @ Rule @ State @ Eff @ ( shd @ Rule @ ( sdrop @ Rule @ N2 @ Rs ) ) @ S )
% 2.36/1.26 => ( ord_less_eq @ nat @ ( abstra1332369113inWait @ Rule @ State @ Eff @ Rs @ S ) @ N2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_90_RuleSystem__Defs_OmkTree_Osimps_I2_J,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rs: stream @ Rule,S: State] :
% 2.36/1.26 ( ( abstra1749095923e_cont @ ( product_prod @ State @ Rule ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ Rs @ S ) )
% 2.36/1.26 = ( fimage @ State @ ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff @ ( stl @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) ) @ ( abstra1276541928ickEff @ Rule @ State @ Eff @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff @ Rs @ S ) ) @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_91_RuleSystem_OminWait__def,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,Rs: stream @ Rule,S: State] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( abstra1332369113inWait @ Rule @ State @ Eff @ Rs @ S )
% 2.36/1.26 = ( ord_Least @ nat
% 2.36/1.26 @ ^ [N3: nat] : ( abstra1874422341nabled @ Rule @ State @ Eff @ ( shd @ Rule @ ( sdrop @ Rule @ N3 @ Rs ) ) @ S ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_92_RuleSystem_OminWait__le__pos,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,Rs: stream @ Rule,R: Rule,S: State] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( abstra928354080m_fair @ Rule @ Rules @ Rs )
% 2.36/1.26 => ( ( member @ Rule @ R @ ( sset @ Rule @ Rules ) )
% 2.36/1.26 => ( ( abstra1874422341nabled @ Rule @ State @ Eff @ R @ S )
% 2.36/1.26 => ( ord_less_eq @ nat @ ( abstra1332369113inWait @ Rule @ State @ Eff @ Rs @ S ) @ ( abstra2097340358le_pos @ Rule @ Rs @ R ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_93_fimage__eqI,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,B2: A,F: B > A,X3: B,A4: fset @ B] :
% 2.36/1.26 ( ( B2
% 2.36/1.26 = ( F @ X3 ) )
% 2.36/1.26 => ( ( fmember @ B @ X3 @ A4 )
% 2.36/1.26 => ( fmember @ A @ B2 @ ( fimage @ B @ A @ F @ A4 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_94_fimage__ident,axiom,
% 2.36/1.26 ! [A: $tType,Y4: fset @ A] :
% 2.36/1.26 ( ( fimage @ A @ A
% 2.36/1.26 @ ^ [X6: A] : X6
% 2.36/1.26 @ Y4 )
% 2.36/1.26 = Y4 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_95_fset_Omap__ident,axiom,
% 2.36/1.26 ! [A: $tType,T2: fset @ A] :
% 2.36/1.26 ( ( fimage @ A @ A
% 2.36/1.26 @ ^ [X6: A] : X6
% 2.36/1.26 @ T2 )
% 2.36/1.26 = T2 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_96_per__def,axiom,
% 2.36/1.26 ! [R: rule] :
% 2.36/1.26 ( ( abstra2096684367le_per @ rule @ state @ eff @ rules @ s @ R )
% 2.36/1.26 = ( ! [S4: state,R1: rule,Sl6: fset @ state,S8: state] :
% 2.36/1.26 ( ( ( member @ state @ S4 @ s )
% 2.36/1.26 & ( abstra1874422341nabled @ rule @ state @ eff @ R @ S4 )
% 2.36/1.26 & ( member @ rule @ R1 @ ( minus_minus @ ( set @ rule ) @ ( sset @ rule @ rules ) @ ( insert @ rule @ R @ ( bot_bot @ ( set @ rule ) ) ) ) )
% 2.36/1.26 & ( eff @ R1 @ S4 @ Sl6 )
% 2.36/1.26 & ( fmember @ state @ S8 @ Sl6 ) )
% 2.36/1.26 => ( abstra1874422341nabled @ rule @ state @ eff @ R @ S8 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_97_Least__le,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o,K: A] :
% 2.36/1.26 ( ( P3 @ K )
% 2.36/1.26 => ( ord_less_eq @ A @ ( ord_Least @ A @ P3 ) @ K ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_98_mkTree_Octr,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,S: state] :
% 2.36/1.26 ( ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S )
% 2.36/1.26 = ( abstra388494275e_Node @ ( product_prod @ state @ rule ) @ ( product_Pair @ state @ rule @ S @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) @ ( fimage @ state @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) @ ( abstra1276541928ickEff @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) @ S ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_99_order__refl,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( preorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_100_old_Oprod_Oinject,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 2.36/1.26 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.36/1.26 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 2.36/1.26 = ( ( A2 = A5 )
% 2.36/1.26 & ( B2 = B3 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_101_prod_Oinject,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,X13: A,X22: B,Y1: A,Y22: B] :
% 2.36/1.26 ( ( ( product_Pair @ A @ B @ X13 @ X22 )
% 2.36/1.26 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 2.36/1.26 = ( ( X13 = Y1 )
% 2.36/1.26 & ( X22 = Y22 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_102_bot__apply,axiom,
% 2.36/1.26 ! [C: $tType,D: $tType] :
% 2.36/1.26 ( ( bot @ C @ ( type2 @ C ) )
% 2.36/1.26 => ( ( bot_bot @ ( D > C ) )
% 2.36/1.26 = ( ^ [X6: D] : ( bot_bot @ C ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_103_fsubsetI,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 2.36/1.26 ( ! [X4: A] :
% 2.36/1.26 ( ( fmember @ A @ X4 @ A4 )
% 2.36/1.26 => ( fmember @ A @ X4 @ B4 ) )
% 2.36/1.26 => ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_104_tree_Oinject,axiom,
% 2.36/1.26 ! [A: $tType,X13: A,X22: fset @ ( abstra2103299360e_tree @ A ),Y1: A,Y22: fset @ ( abstra2103299360e_tree @ A )] :
% 2.36/1.26 ( ( ( abstra388494275e_Node @ A @ X13 @ X22 )
% 2.36/1.26 = ( abstra388494275e_Node @ A @ Y1 @ Y22 ) )
% 2.36/1.26 = ( ( X13 = Y1 )
% 2.36/1.26 & ( X22 = Y22 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_105_countable__insert,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,A2: A] :
% 2.36/1.26 ( ( countable_countable @ A @ A4 )
% 2.36/1.26 => ( countable_countable @ A @ ( insert @ A @ A2 @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_106_countable__insert__eq,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,A4: set @ A] :
% 2.36/1.26 ( ( countable_countable @ A @ ( insert @ A @ X3 @ A4 ) )
% 2.36/1.26 = ( countable_countable @ A @ A4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_107_countable__Diff,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( countable_countable @ A @ A4 )
% 2.36/1.26 => ( countable_countable @ A @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_108_prod_Ocollapse,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.36/1.26 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 2.36/1.26 = Prod ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_109_countable__Diff__eq,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,X3: A] :
% 2.36/1.26 ( ( countable_countable @ A @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.36/1.26 = ( countable_countable @ A @ A4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_110_fset__mp,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A,X3: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( fmember @ A @ X3 @ A4 )
% 2.36/1.26 => ( fmember @ A @ X3 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_111_fin__mono,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A,X3: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( fmember @ A @ X3 @ A4 )
% 2.36/1.26 => ( fmember @ A @ X3 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_112_fsubsetD,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A,C2: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( fmember @ A @ C2 @ A4 )
% 2.36/1.26 => ( fmember @ A @ C2 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_113_fset__rev__mp,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,A4: fset @ A,B4: fset @ A] :
% 2.36/1.26 ( ( fmember @ A @ X3 @ A4 )
% 2.36/1.26 => ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( fmember @ A @ X3 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_114_subset__fimage__iff,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,B4: fset @ A,F: B > A,A4: fset @ B] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ B4 @ ( fimage @ B @ A @ F @ A4 ) )
% 2.36/1.26 = ( ? [AA: fset @ B] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ B ) @ AA @ A4 )
% 2.36/1.26 & ( B4
% 2.36/1.26 = ( fimage @ B @ A @ F @ AA ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_115_fimage__mono,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,A4: fset @ A,B4: fset @ A,F: A > B] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ord_less_eq @ ( fset @ B ) @ ( fimage @ A @ B @ F @ A4 ) @ ( fimage @ A @ B @ F @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_116_tree_Oexhaust,axiom,
% 2.36/1.26 ! [A: $tType,Y: abstra2103299360e_tree @ A] :
% 2.36/1.26 ~ ! [X1: A,X23: fset @ ( abstra2103299360e_tree @ A )] :
% 2.36/1.26 ( Y
% 2.36/1.26 != ( abstra388494275e_Node @ A @ X1 @ X23 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_117_old_Oprod_Oinducts,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.36/1.26 ( ! [A6: A,B5: B] : ( P3 @ ( product_Pair @ A @ B @ A6 @ B5 ) )
% 2.36/1.26 => ( P3 @ Prod ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_118_old_Oprod_Oexhaust,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.36/1.26 ~ ! [A6: A,B5: B] :
% 2.36/1.26 ( Y
% 2.36/1.26 != ( product_Pair @ A @ B @ A6 @ B5 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_119_prod__induct7,axiom,
% 2.36/1.26 ! [G2: $tType,F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 2.36/1.26 ( ! [A6: A,B5: B,C3: C,D2: D,E2: E,F3: F2,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G2 ) @ E2 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) )
% 2.36/1.26 => ( P3 @ X3 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_120_prod__induct6,axiom,
% 2.36/1.26 ! [F2: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 2.36/1.26 ( ! [A6: A,B5: B,C3: C,D2: D,E2: E,F3: F2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) )
% 2.36/1.26 => ( P3 @ X3 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_121_prod__induct5,axiom,
% 2.36/1.26 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.36/1.26 ( ! [A6: A,B5: B,C3: C,D2: D,E2: E] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 2.36/1.26 => ( P3 @ X3 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_122_prod__induct4,axiom,
% 2.36/1.26 ! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.36/1.26 ( ! [A6: A,B5: B,C3: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 2.36/1.26 => ( P3 @ X3 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_123_prod__induct3,axiom,
% 2.36/1.26 ! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.36/1.26 ( ! [A6: A,B5: B,C3: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B5 @ C3 ) ) )
% 2.36/1.26 => ( P3 @ X3 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_124_prod__cases7,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) )] :
% 2.36/1.26 ~ ! [A6: A,B5: B,C3: C,D2: D,E2: E,F3: F2,G3: G2] :
% 2.36/1.26 ( Y
% 2.36/1.26 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G2 ) @ E2 @ ( product_Pair @ F2 @ G2 @ F3 @ G3 ) ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_125_prod__cases6,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 2.36/1.26 ~ ! [A6: A,B5: B,C3: C,D2: D,E2: E,F3: F2] :
% 2.36/1.26 ( Y
% 2.36/1.26 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F3 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_126_prod__cases5,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.36/1.26 ~ ! [A6: A,B5: B,C3: C,D2: D,E2: E] :
% 2.36/1.26 ( Y
% 2.36/1.26 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_127_prod__cases4,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.36/1.26 ~ ! [A6: A,B5: B,C3: C,D2: D] :
% 2.36/1.26 ( Y
% 2.36/1.26 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_128_prod__cases3,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.36/1.26 ~ ! [A6: A,B5: B,C3: C] :
% 2.36/1.26 ( Y
% 2.36/1.26 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B5 @ C3 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_129_Pair__inject,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 2.36/1.26 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.36/1.26 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 2.36/1.26 => ~ ( ( A2 = A5 )
% 2.36/1.26 => ( B2 != B3 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_130_prod__cases,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 2.36/1.26 ( ! [A6: A,B5: B] : ( P3 @ ( product_Pair @ A @ B @ A6 @ B5 ) )
% 2.36/1.26 => ( P3 @ P2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_131_surj__pair,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 2.36/1.26 ? [X4: A,Y2: B] :
% 2.36/1.26 ( P2
% 2.36/1.26 = ( product_Pair @ A @ B @ X4 @ Y2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_132_fst__conv,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,X13: A,X22: B] :
% 2.36/1.26 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X13 @ X22 ) )
% 2.36/1.26 = X13 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_133_fst__eqD,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,X3: A,Y: B,A2: A] :
% 2.36/1.26 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 2.36/1.26 = A2 )
% 2.36/1.26 => ( X3 = A2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_134_snd__conv,axiom,
% 2.36/1.26 ! [Aa: $tType,A: $tType,X13: Aa,X22: A] :
% 2.36/1.26 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X13 @ X22 ) )
% 2.36/1.26 = X22 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_135_snd__eqD,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,X3: B,Y: A,A2: A] :
% 2.36/1.26 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) )
% 2.36/1.26 = A2 )
% 2.36/1.26 => ( Y = A2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_136_uncountable__minus__countable,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ~ ( countable_countable @ A @ A4 )
% 2.36/1.26 => ( ( countable_countable @ A @ B4 )
% 2.36/1.26 => ~ ( countable_countable @ A @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_137_countable__subset,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( countable_countable @ A @ B4 )
% 2.36/1.26 => ( countable_countable @ A @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_138_fimage__fsubsetI,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,A4: fset @ A,F: A > B,B4: fset @ B] :
% 2.36/1.26 ( ! [X4: A] :
% 2.36/1.26 ( ( fmember @ A @ X4 @ A4 )
% 2.36/1.26 => ( fmember @ B @ ( F @ X4 ) @ B4 ) )
% 2.36/1.26 => ( ord_less_eq @ ( fset @ B ) @ ( fimage @ A @ B @ F @ A4 ) @ B4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_139_tree_Osel_I2_J,axiom,
% 2.36/1.26 ! [A: $tType,X13: A,X22: fset @ ( abstra2103299360e_tree @ A )] :
% 2.36/1.26 ( ( abstra1749095923e_cont @ A @ ( abstra388494275e_Node @ A @ X13 @ X22 ) )
% 2.36/1.26 = X22 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_140_surjective__pairing,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,T2: product_prod @ A @ B] :
% 2.36/1.26 ( T2
% 2.36/1.26 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T2 ) @ ( product_snd @ A @ B @ T2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_141_prod_Oexhaust__sel,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.36/1.26 ( Prod
% 2.36/1.26 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_142_conjI__realizer,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,P3: A > $o,P2: A,Q2: B > $o,Q: B] :
% 2.36/1.26 ( ( P3 @ P2 )
% 2.36/1.26 => ( ( Q2 @ Q )
% 2.36/1.26 => ( ( P3 @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q ) ) )
% 2.36/1.26 & ( Q2 @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_143_exI__realizer,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,P3: A > B > $o,Y: A,X3: B] :
% 2.36/1.26 ( ( P3 @ Y @ X3 )
% 2.36/1.26 => ( P3 @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X3 @ Y ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_144_le__funD,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType] :
% 2.36/1.26 ( ( ord @ B @ ( type2 @ B ) )
% 2.36/1.26 => ! [F: A > B,G: A > B,X3: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.36/1.26 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_145_le__funE,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType] :
% 2.36/1.26 ( ( ord @ B @ ( type2 @ B ) )
% 2.36/1.26 => ! [F: A > B,G: A > B,X3: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.36/1.26 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_146_le__funI,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType] :
% 2.36/1.26 ( ( ord @ B @ ( type2 @ B ) )
% 2.36/1.26 => ! [F: A > B,G: A > B] :
% 2.36/1.26 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 2.36/1.26 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_147_le__fun__def,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType] :
% 2.36/1.26 ( ( ord @ B @ ( type2 @ B ) )
% 2.36/1.26 => ( ( ord_less_eq @ ( A > B ) )
% 2.36/1.26 = ( ^ [F4: A > B,G4: A > B] :
% 2.36/1.26 ! [X6: A] : ( ord_less_eq @ B @ ( F4 @ X6 ) @ ( G4 @ X6 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_148_order__subst1,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType] :
% 2.36/1.26 ( ( ( order @ B @ ( type2 @ B ) )
% 2.36/1.26 & ( order @ A @ ( type2 @ A ) ) )
% 2.36/1.26 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.36/1.26 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.36/1.26 => ( ! [X4: B,Y2: B] :
% 2.36/1.26 ( ( ord_less_eq @ B @ X4 @ Y2 )
% 2.36/1.26 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.36/1.26 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_149_order__subst2,axiom,
% 2.36/1.26 ! [A: $tType,C: $tType] :
% 2.36/1.26 ( ( ( order @ C @ ( type2 @ C ) )
% 2.36/1.26 & ( order @ A @ ( type2 @ A ) ) )
% 2.36/1.26 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.36/1.26 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 2.36/1.26 => ( ! [X4: A,Y2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ X4 @ Y2 )
% 2.36/1.26 => ( ord_less_eq @ C @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.36/1.26 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_150_ord__eq__le__subst,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType] :
% 2.36/1.26 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.36/1.26 & ( ord @ A @ ( type2 @ A ) ) )
% 2.36/1.26 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 2.36/1.26 ( ( A2
% 2.36/1.26 = ( F @ B2 ) )
% 2.36/1.26 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.36/1.26 => ( ! [X4: B,Y2: B] :
% 2.36/1.26 ( ( ord_less_eq @ B @ X4 @ Y2 )
% 2.36/1.26 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.36/1.26 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_151_ord__le__eq__subst,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType] :
% 2.36/1.26 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.36/1.26 & ( ord @ A @ ( type2 @ A ) ) )
% 2.36/1.26 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.36/1.26 => ( ( ( F @ B2 )
% 2.36/1.26 = C2 )
% 2.36/1.26 => ( ! [X4: A,Y2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ X4 @ Y2 )
% 2.36/1.26 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.36/1.26 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_152_eq__iff,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.36/1.26 = ( ^ [X6: A,Y5: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ X6 @ Y5 )
% 2.36/1.26 & ( ord_less_eq @ A @ Y5 @ X6 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_153_antisym,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [X3: A,Y: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.36/1.26 => ( ( ord_less_eq @ A @ Y @ X3 )
% 2.36/1.26 => ( X3 = Y ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_154_linear,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( linorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [X3: A,Y: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.36/1.26 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_155_eq__refl,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( preorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [X3: A,Y: A] :
% 2.36/1.26 ( ( X3 = Y )
% 2.36/1.26 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_156_le__cases,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( linorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [X3: A,Y: A] :
% 2.36/1.26 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 2.36/1.26 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_157_order_Otrans,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A2: A,B2: A,C2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.36/1.26 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.36/1.26 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_158_le__cases3,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( linorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [X3: A,Y: A,Z2: A] :
% 2.36/1.26 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 2.36/1.26 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.36/1.26 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 2.36/1.26 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 2.36/1.26 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 2.36/1.26 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.36/1.26 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.36/1.26 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 2.36/1.26 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.36/1.26 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 2.36/1.26 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 2.36/1.26 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_159_antisym__conv,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [Y: A,X3: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ Y @ X3 )
% 2.36/1.26 => ( ( ord_less_eq @ A @ X3 @ Y )
% 2.36/1.26 = ( X3 = Y ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_160_ord__eq__le__trans,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( ord @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A2: A,B2: A,C2: A] :
% 2.36/1.26 ( ( A2 = B2 )
% 2.36/1.26 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.36/1.26 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_161_ord__le__eq__trans,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( ord @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A2: A,B2: A,C2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.36/1.26 => ( ( B2 = C2 )
% 2.36/1.26 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_162_order__class_Oorder_Oantisym,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A2: A,B2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.36/1.26 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.36/1.26 => ( A2 = B2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_163_order__trans,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( preorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [X3: A,Y: A,Z2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.36/1.26 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.36/1.26 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_164_dual__order_Orefl,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_165_linorder__wlog,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( linorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > A > $o,A2: A,B2: A] :
% 2.36/1.26 ( ! [A6: A,B5: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A6 @ B5 )
% 2.36/1.26 => ( P3 @ A6 @ B5 ) )
% 2.36/1.26 => ( ! [A6: A,B5: A] :
% 2.36/1.26 ( ( P3 @ B5 @ A6 )
% 2.36/1.26 => ( P3 @ A6 @ B5 ) )
% 2.36/1.26 => ( P3 @ A2 @ B2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_166_dual__order_Otrans,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [B2: A,A2: A,C2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.36/1.26 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.36/1.26 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_167_dual__order_Oantisym,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [B2: A,A2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.36/1.26 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.36/1.26 => ( A2 = B2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_168_bot__fun__def,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType] :
% 2.36/1.26 ( ( bot @ B @ ( type2 @ B ) )
% 2.36/1.26 => ( ( bot_bot @ ( A > B ) )
% 2.36/1.26 = ( ^ [X6: A] : ( bot_bot @ B ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_169_eqfelem__imp__iff,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,Y: A,A4: fset @ A] :
% 2.36/1.26 ( ( X3 = Y )
% 2.36/1.26 => ( ( fmember @ A @ X3 @ A4 )
% 2.36/1.26 = ( fmember @ A @ Y @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_170_if__split__fmem2,axiom,
% 2.36/1.26 ! [A: $tType,A2: A,Q2: $o,X3: fset @ A,Y: fset @ A] :
% 2.36/1.26 ( ( fmember @ A @ A2 @ ( if @ ( fset @ A ) @ Q2 @ X3 @ Y ) )
% 2.36/1.26 = ( ( Q2
% 2.36/1.26 => ( fmember @ A @ A2 @ X3 ) )
% 2.36/1.26 & ( ~ Q2
% 2.36/1.26 => ( fmember @ A @ A2 @ Y ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_171_if__split__fmem1,axiom,
% 2.36/1.26 ! [A: $tType,Q2: $o,X3: A,Y: A,B2: fset @ A] :
% 2.36/1.26 ( ( fmember @ A @ ( if @ A @ Q2 @ X3 @ Y ) @ B2 )
% 2.36/1.26 = ( ( Q2
% 2.36/1.26 => ( fmember @ A @ X3 @ B2 ) )
% 2.36/1.26 & ( ~ Q2
% 2.36/1.26 => ( fmember @ A @ Y @ B2 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_172_eqfset__imp__iff,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A,X3: A] :
% 2.36/1.26 ( ( A4 = B4 )
% 2.36/1.26 => ( ( fmember @ A @ X3 @ A4 )
% 2.36/1.26 = ( fmember @ A @ X3 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_173_eq__fmem__trans,axiom,
% 2.36/1.26 ! [A: $tType,A2: A,B2: A,A4: fset @ A] :
% 2.36/1.26 ( ( A2 = B2 )
% 2.36/1.26 => ( ( fmember @ A @ B2 @ A4 )
% 2.36/1.26 => ( fmember @ A @ A2 @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_174_fset__choice,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,A4: fset @ A,P3: A > B > $o] :
% 2.36/1.26 ( ! [X4: A] :
% 2.36/1.26 ( ( fmember @ A @ X4 @ A4 )
% 2.36/1.26 => ? [X12: B] : ( P3 @ X4 @ X12 ) )
% 2.36/1.26 => ? [F3: A > B] :
% 2.36/1.26 ! [X5: A] :
% 2.36/1.26 ( ( fmember @ A @ X5 @ A4 )
% 2.36/1.26 => ( P3 @ X5 @ ( F3 @ X5 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_175_fequalityCE,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A,C2: A] :
% 2.36/1.26 ( ( A4 = B4 )
% 2.36/1.26 => ( ( ( fmember @ A @ C2 @ A4 )
% 2.36/1.26 => ~ ( fmember @ A @ C2 @ B4 ) )
% 2.36/1.26 => ~ ( ~ ( fmember @ A @ C2 @ A4 )
% 2.36/1.26 => ( fmember @ A @ C2 @ B4 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_176_fset__eqI,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 2.36/1.26 ( ! [X4: A] :
% 2.36/1.26 ( ( fmember @ A @ X4 @ A4 )
% 2.36/1.26 = ( fmember @ A @ X4 @ B4 ) )
% 2.36/1.26 => ( A4 = B4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_177_RuleSystem_Oper__def,axiom,
% 2.36/1.26 ! [Rule: $tType,State: $tType,Eff: Rule > State > ( fset @ State ) > $o,Rules: stream @ Rule,S3: set @ State,R: Rule] :
% 2.36/1.26 ( ( abstra1326562878System @ Rule @ State @ Eff @ Rules @ S3 )
% 2.36/1.26 => ( ( abstra2096684367le_per @ Rule @ State @ Eff @ Rules @ S3 @ R )
% 2.36/1.26 = ( ! [S4: State,R1: Rule,Sl6: fset @ State,S8: State] :
% 2.36/1.26 ( ( ( member @ State @ S4 @ S3 )
% 2.36/1.26 & ( abstra1874422341nabled @ Rule @ State @ Eff @ R @ S4 )
% 2.36/1.26 & ( member @ Rule @ R1 @ ( minus_minus @ ( set @ Rule ) @ ( sset @ Rule @ Rules ) @ ( insert @ Rule @ R @ ( bot_bot @ ( set @ Rule ) ) ) ) )
% 2.36/1.26 & ( Eff @ R1 @ S4 @ Sl6 )
% 2.36/1.26 & ( fmember @ State @ S8 @ Sl6 ) )
% 2.36/1.26 => ( abstra1874422341nabled @ Rule @ State @ Eff @ R @ S8 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_178_LeastI2,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o,A2: A,Q2: A > $o] :
% 2.36/1.26 ( ( P3 @ A2 )
% 2.36/1.26 => ( ! [X4: A] :
% 2.36/1.26 ( ( P3 @ X4 )
% 2.36/1.26 => ( Q2 @ X4 ) )
% 2.36/1.26 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_179_LeastI__ex,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o] :
% 2.36/1.26 ( ? [X12: A] : ( P3 @ X12 )
% 2.36/1.26 => ( P3 @ ( ord_Least @ A @ P3 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_180_LeastI2__ex,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o,Q2: A > $o] :
% 2.36/1.26 ( ? [X12: A] : ( P3 @ X12 )
% 2.36/1.26 => ( ! [X4: A] :
% 2.36/1.26 ( ( P3 @ X4 )
% 2.36/1.26 => ( Q2 @ X4 ) )
% 2.36/1.26 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_181_RuleSystem__Defs_OmkTree_Ocode,axiom,
% 2.36/1.26 ! [State: $tType,Rule: $tType] :
% 2.36/1.26 ( ( abstra1225283448mkTree @ Rule @ State )
% 2.36/1.26 = ( ^ [Eff2: Rule > State > ( fset @ State ) > $o,Rs2: stream @ Rule,S4: State] : ( abstra388494275e_Node @ ( product_prod @ State @ Rule ) @ ( product_Pair @ State @ Rule @ S4 @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff2 @ Rs2 @ S4 ) ) ) @ ( fimage @ State @ ( abstra2103299360e_tree @ ( product_prod @ State @ Rule ) ) @ ( abstra1225283448mkTree @ Rule @ State @ Eff2 @ ( stl @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff2 @ Rs2 @ S4 ) ) ) @ ( abstra1276541928ickEff @ Rule @ State @ Eff2 @ ( shd @ Rule @ ( abstra1259602206m_trim @ Rule @ State @ Eff2 @ Rs2 @ S4 ) ) @ S4 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_182_fimage__fimage,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,C: $tType,F: B > A,G: C > B,A4: fset @ C] :
% 2.36/1.26 ( ( fimage @ B @ A @ F @ ( fimage @ C @ B @ G @ A4 ) )
% 2.36/1.26 = ( fimage @ C @ A
% 2.36/1.26 @ ^ [X6: C] : ( F @ ( G @ X6 ) )
% 2.36/1.26 @ A4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_183_LeastI,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o,K: A] :
% 2.36/1.26 ( ( P3 @ K )
% 2.36/1.26 => ( P3 @ ( ord_Least @ A @ P3 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_184_bot_Oextremum,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_185_bot_Oextremum__unique,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.36/1.26 = ( A2
% 2.36/1.26 = ( bot_bot @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_186_bot_Oextremum__uniqueI,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [A2: A] :
% 2.36/1.26 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.36/1.26 => ( A2
% 2.36/1.26 = ( bot_bot @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_187_LeastI2__order,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o,X3: A,Q2: A > $o] :
% 2.36/1.26 ( ( P3 @ X3 )
% 2.36/1.26 => ( ! [Y2: A] :
% 2.36/1.26 ( ( P3 @ Y2 )
% 2.36/1.26 => ( ord_less_eq @ A @ X3 @ Y2 ) )
% 2.36/1.26 => ( ! [X4: A] :
% 2.36/1.26 ( ( P3 @ X4 )
% 2.36/1.26 => ( ! [Y6: A] :
% 2.36/1.26 ( ( P3 @ Y6 )
% 2.36/1.26 => ( ord_less_eq @ A @ X4 @ Y6 ) )
% 2.36/1.26 => ( Q2 @ X4 ) ) )
% 2.36/1.26 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_188_Least__equality,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( order @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o,X3: A] :
% 2.36/1.26 ( ( P3 @ X3 )
% 2.36/1.26 => ( ! [Y2: A] :
% 2.36/1.26 ( ( P3 @ Y2 )
% 2.36/1.26 => ( ord_less_eq @ A @ X3 @ Y2 ) )
% 2.36/1.26 => ( ( ord_Least @ A @ P3 )
% 2.36/1.26 = X3 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_189_LeastI2__wellorder,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o,A2: A,Q2: A > $o] :
% 2.36/1.26 ( ( P3 @ A2 )
% 2.36/1.26 => ( ! [A6: A] :
% 2.36/1.26 ( ( P3 @ A6 )
% 2.36/1.26 => ( ! [B6: A] :
% 2.36/1.26 ( ( P3 @ B6 )
% 2.36/1.26 => ( ord_less_eq @ A @ A6 @ B6 ) )
% 2.36/1.26 => ( Q2 @ A6 ) ) )
% 2.36/1.26 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_190_LeastI2__wellorder__ex,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.36/1.26 => ! [P3: A > $o,Q2: A > $o] :
% 2.36/1.26 ( ? [X12: A] : ( P3 @ X12 )
% 2.36/1.26 => ( ! [A6: A] :
% 2.36/1.26 ( ( P3 @ A6 )
% 2.36/1.26 => ( ! [B6: A] :
% 2.36/1.26 ( ( P3 @ B6 )
% 2.36/1.26 => ( ord_less_eq @ A @ A6 @ B6 ) )
% 2.36/1.26 => ( Q2 @ A6 ) ) )
% 2.36/1.26 => ( Q2 @ ( ord_Least @ A @ P3 ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_191_rev__fimage__eqI,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,X3: A,A4: fset @ A,B2: B,F: A > B] :
% 2.36/1.26 ( ( fmember @ A @ X3 @ A4 )
% 2.36/1.26 => ( ( B2
% 2.36/1.26 = ( F @ X3 ) )
% 2.36/1.26 => ( fmember @ B @ B2 @ ( fimage @ A @ B @ F @ A4 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_192_fimage__cong,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,M2: fset @ A,N4: fset @ A,F: A > B,G: A > B] :
% 2.36/1.26 ( ( M2 = N4 )
% 2.36/1.26 => ( ! [X4: A] :
% 2.36/1.26 ( ( fmember @ A @ X4 @ N4 )
% 2.36/1.26 => ( ( F @ X4 )
% 2.36/1.26 = ( G @ X4 ) ) )
% 2.36/1.26 => ( ( fimage @ A @ B @ F @ M2 )
% 2.36/1.26 = ( fimage @ A @ B @ G @ N4 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_193_fimageI,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,X3: A,A4: fset @ A,F: A > B] :
% 2.36/1.26 ( ( fmember @ A @ X3 @ A4 )
% 2.36/1.26 => ( fmember @ B @ ( F @ X3 ) @ ( fimage @ A @ B @ F @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_194_fimageE,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,B2: A,F: B > A,A4: fset @ B] :
% 2.36/1.26 ( ( fmember @ A @ B2 @ ( fimage @ B @ A @ F @ A4 ) )
% 2.36/1.26 => ~ ! [X4: B] :
% 2.36/1.26 ( ( B2
% 2.36/1.26 = ( F @ X4 ) )
% 2.36/1.26 => ~ ( fmember @ B @ X4 @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_195_mkTree__unfold,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,S: state] :
% 2.36/1.26 ( ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S )
% 2.36/1.26 = ( case_stream @ rule @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) )
% 2.36/1.26 @ ^ [R3: rule,S8: stream @ rule] : ( abstra388494275e_Node @ ( product_prod @ state @ rule ) @ ( product_Pair @ state @ rule @ S @ R3 ) @ ( fimage @ state @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ S8 ) @ ( abstra1276541928ickEff @ rule @ state @ eff @ R3 @ S ) ) )
% 2.36/1.26 @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_196_insert__Diff__single,axiom,
% 2.36/1.26 ! [A: $tType,A2: A,A4: set @ A] :
% 2.36/1.26 ( ( insert @ A @ A2 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.36/1.26 = ( insert @ A @ A2 @ A4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_197_singleton__conv2,axiom,
% 2.36/1.26 ! [A: $tType,A2: A] :
% 2.36/1.26 ( ( collect @ A
% 2.36/1.26 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 2.36/1.26 @ A2 ) )
% 2.36/1.26 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_198_singleton__conv,axiom,
% 2.36/1.26 ! [A: $tType,A2: A] :
% 2.36/1.26 ( ( collect @ A
% 2.36/1.26 @ ^ [X6: A] : ( X6 = A2 ) )
% 2.36/1.26 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_199_mkTree_Osimps_I1_J,axiom,
% 2.36/1.26 ! [Rs: stream @ rule,S: state] :
% 2.36/1.26 ( ( abstra573067619e_root @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ Rs @ S ) )
% 2.36/1.26 = ( product_Pair @ state @ rule @ S @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ Rs @ S ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_200_empty__Collect__eq,axiom,
% 2.36/1.26 ! [A: $tType,P3: A > $o] :
% 2.36/1.26 ( ( ( bot_bot @ ( set @ A ) )
% 2.36/1.26 = ( collect @ A @ P3 ) )
% 2.36/1.26 = ( ! [X6: A] :
% 2.36/1.26 ~ ( P3 @ X6 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_201_Collect__empty__eq,axiom,
% 2.36/1.26 ! [A: $tType,P3: A > $o] :
% 2.36/1.26 ( ( ( collect @ A @ P3 )
% 2.36/1.26 = ( bot_bot @ ( set @ A ) ) )
% 2.36/1.26 = ( ! [X6: A] :
% 2.36/1.26 ~ ( P3 @ X6 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_202_all__not__in__conv,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A] :
% 2.36/1.26 ( ( ! [X6: A] :
% 2.36/1.26 ~ ( member @ A @ X6 @ A4 ) )
% 2.36/1.26 = ( A4
% 2.36/1.26 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_203_empty__iff,axiom,
% 2.36/1.26 ! [A: $tType,C2: A] :
% 2.36/1.26 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_204_subset__antisym,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A4 )
% 2.36/1.26 => ( A4 = B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_205_subsetI,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ! [X4: A] :
% 2.36/1.26 ( ( member @ A @ X4 @ A4 )
% 2.36/1.26 => ( member @ A @ X4 @ B4 ) )
% 2.36/1.26 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_206_insert__absorb2,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,A4: set @ A] :
% 2.36/1.26 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A4 ) )
% 2.36/1.26 = ( insert @ A @ X3 @ A4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_207_insert__iff,axiom,
% 2.36/1.26 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 2.36/1.26 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 2.36/1.26 = ( ( A2 = B2 )
% 2.36/1.26 | ( member @ A @ A2 @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_208_insertCI,axiom,
% 2.36/1.26 ! [A: $tType,A2: A,B4: set @ A,B2: A] :
% 2.36/1.26 ( ( ~ ( member @ A @ A2 @ B4 )
% 2.36/1.26 => ( A2 = B2 ) )
% 2.36/1.26 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_209_Diff__idemp,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) @ B4 )
% 2.36/1.26 = ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_210_Diff__iff,axiom,
% 2.36/1.26 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) )
% 2.36/1.26 = ( ( member @ A @ C2 @ A4 )
% 2.36/1.26 & ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_211_DiffI,axiom,
% 2.36/1.26 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( member @ A @ C2 @ A4 )
% 2.36/1.26 => ( ~ ( member @ A @ C2 @ B4 )
% 2.36/1.26 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_212_fempty__iff,axiom,
% 2.36/1.26 ! [A: $tType,C2: A] :
% 2.36/1.26 ~ ( fmember @ A @ C2 @ ( bot_bot @ ( fset @ A ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_213_all__not__fin__conv,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A] :
% 2.36/1.26 ( ( ! [X6: A] :
% 2.36/1.26 ~ ( fmember @ A @ X6 @ A4 ) )
% 2.36/1.26 = ( A4
% 2.36/1.26 = ( bot_bot @ ( fset @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_214_fempty__fsubsetI,axiom,
% 2.36/1.26 ! [A: $tType,X3: fset @ A] : ( ord_less_eq @ ( fset @ A ) @ ( bot_bot @ ( fset @ A ) ) @ X3 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_215_fsubset__fempty,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ ( bot_bot @ ( fset @ A ) ) )
% 2.36/1.26 = ( A4
% 2.36/1.26 = ( bot_bot @ ( fset @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_216_fsubset__antisym,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( ord_less_eq @ ( fset @ A ) @ B4 @ A4 )
% 2.36/1.26 => ( A4 = B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_217_fimage__fempty,axiom,
% 2.36/1.26 ! [B: $tType,A: $tType,F: B > A] :
% 2.36/1.26 ( ( fimage @ B @ A @ F @ ( bot_bot @ ( fset @ B ) ) )
% 2.36/1.26 = ( bot_bot @ ( fset @ A ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_218_fempty__is__fimage,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,F: B > A,A4: fset @ B] :
% 2.36/1.26 ( ( ( bot_bot @ ( fset @ A ) )
% 2.36/1.26 = ( fimage @ B @ A @ F @ A4 ) )
% 2.36/1.26 = ( A4
% 2.36/1.26 = ( bot_bot @ ( fset @ B ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_219_fimage__is__fempty,axiom,
% 2.36/1.26 ! [A: $tType,B: $tType,F: B > A,A4: fset @ B] :
% 2.36/1.26 ( ( ( fimage @ B @ A @ F @ A4 )
% 2.36/1.26 = ( bot_bot @ ( fset @ A ) ) )
% 2.36/1.26 = ( A4
% 2.36/1.26 = ( bot_bot @ ( fset @ B ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_220_empty__subsetI,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_221_subset__empty,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.36/1.26 = ( A4
% 2.36/1.26 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_222_singletonI,axiom,
% 2.36/1.26 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_223_insert__subset,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B4 )
% 2.36/1.26 = ( ( member @ A @ X3 @ B4 )
% 2.36/1.26 & ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_224_Diff__cancel,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A] :
% 2.36/1.26 ( ( minus_minus @ ( set @ A ) @ A4 @ A4 )
% 2.36/1.26 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_225_empty__Diff,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A] :
% 2.36/1.26 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 )
% 2.36/1.26 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_226_Diff__empty,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A] :
% 2.36/1.26 ( ( minus_minus @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.36/1.26 = A4 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_227_insert__Diff1,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,B4: set @ A,A4: set @ A] :
% 2.36/1.26 ( ( member @ A @ X3 @ B4 )
% 2.36/1.26 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B4 )
% 2.36/1.26 = ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_228_Diff__insert0,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ~ ( member @ A @ X3 @ A4 )
% 2.36/1.26 => ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ B4 ) )
% 2.36/1.26 = ( minus_minus @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_229_singleton__insert__inj__eq,axiom,
% 2.36/1.26 ! [A: $tType,B2: A,A2: A,A4: set @ A] :
% 2.36/1.26 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 2.36/1.26 = ( insert @ A @ A2 @ A4 ) )
% 2.36/1.26 = ( ( A2 = B2 )
% 2.36/1.26 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_230_singleton__insert__inj__eq_H,axiom,
% 2.36/1.26 ! [A: $tType,A2: A,A4: set @ A,B2: A] :
% 2.36/1.26 ( ( ( insert @ A @ A2 @ A4 )
% 2.36/1.26 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.36/1.26 = ( ( A2 = B2 )
% 2.36/1.26 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_231_Diff__eq__empty__iff,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( ( minus_minus @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 = ( bot_bot @ ( set @ A ) ) )
% 2.36/1.26 = ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_232_tree_Ocollapse,axiom,
% 2.36/1.26 ! [A: $tType,Tree: abstra2103299360e_tree @ A] :
% 2.36/1.26 ( ( abstra388494275e_Node @ A @ ( abstra573067619e_root @ A @ Tree ) @ ( abstra1749095923e_cont @ A @ Tree ) )
% 2.36/1.26 = Tree ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_233_Collect__mono__iff,axiom,
% 2.36/1.26 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q2 ) )
% 2.36/1.26 = ( ! [X6: A] :
% 2.36/1.26 ( ( P3 @ X6 )
% 2.36/1.26 => ( Q2 @ X6 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_234_fset__eq__fsubset,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( ^ [Y3: fset @ A,Z: fset @ A] : ( Y3 = Z ) )
% 2.36/1.26 = ( ^ [A7: fset @ A,B7: fset @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ A7 @ B7 )
% 2.36/1.26 & ( ord_less_eq @ ( fset @ A ) @ B7 @ A7 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_235_contra__subsetD,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ~ ( member @ A @ C2 @ B4 )
% 2.36/1.26 => ~ ( member @ A @ C2 @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_236_fsubset__trans,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A,C4: fset @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( ord_less_eq @ ( fset @ A ) @ B4 @ C4 )
% 2.36/1.26 => ( ord_less_eq @ ( fset @ A ) @ A4 @ C4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_237_set__eq__subset,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( ^ [Y3: set @ A,Z: set @ A] : ( Y3 = Z ) )
% 2.36/1.26 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 2.36/1.26 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_238_fsubset__refl,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A] : ( ord_less_eq @ ( fset @ A ) @ A4 @ A4 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_239_subset__trans,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 2.36/1.26 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_240_Collect__mono,axiom,
% 2.36/1.26 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 2.36/1.26 ( ! [X4: A] :
% 2.36/1.26 ( ( P3 @ X4 )
% 2.36/1.26 => ( Q2 @ X4 ) )
% 2.36/1.26 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q2 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_241_fequalityD2,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 2.36/1.26 ( ( A4 = B4 )
% 2.36/1.26 => ( ord_less_eq @ ( fset @ A ) @ B4 @ A4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_242_fequalityD1,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 2.36/1.26 ( ( A4 = B4 )
% 2.36/1.26 => ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_243_subset__refl,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_244_rev__subsetD,axiom,
% 2.36/1.26 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( member @ A @ C2 @ A4 )
% 2.36/1.26 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_245_fequalityE,axiom,
% 2.36/1.26 ! [A: $tType,A4: fset @ A,B4: fset @ A] :
% 2.36/1.26 ( ( A4 = B4 )
% 2.36/1.26 => ~ ( ( ord_less_eq @ ( fset @ A ) @ A4 @ B4 )
% 2.36/1.26 => ~ ( ord_less_eq @ ( fset @ A ) @ B4 @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_246_subset__iff,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) )
% 2.36/1.26 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.36/1.26 ! [T: A] :
% 2.36/1.26 ( ( member @ A @ T @ A7 )
% 2.36/1.26 => ( member @ A @ T @ B7 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_247_set__rev__mp,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( member @ A @ X3 @ A4 )
% 2.36/1.26 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( member @ A @ X3 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_248_equalityD2,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( A4 = B4 )
% 2.36/1.26 => ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_249_equalityD1,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( A4 = B4 )
% 2.36/1.26 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_250_subset__eq,axiom,
% 2.36/1.26 ! [A: $tType] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) )
% 2.36/1.26 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.36/1.26 ! [X6: A] :
% 2.36/1.26 ( ( member @ A @ X6 @ A7 )
% 2.36/1.26 => ( member @ A @ X6 @ B7 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_251_equalityE,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 2.36/1.26 ( ( A4 = B4 )
% 2.36/1.26 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_252_subsetCE,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( member @ A @ C2 @ A4 )
% 2.36/1.26 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_253_subsetD,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( member @ A @ C2 @ A4 )
% 2.36/1.26 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_254_in__mono,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A,X3: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( member @ A @ X3 @ A4 )
% 2.36/1.26 => ( member @ A @ X3 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(fact_255_set__mp,axiom,
% 2.36/1.26 ! [A: $tType,A4: set @ A,B4: set @ A,X3: A] :
% 2.36/1.26 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 2.36/1.26 => ( ( member @ A @ X3 @ A4 )
% 2.36/1.26 => ( member @ A @ X3 @ B4 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 2.36/1.26 & ( finite_finite @ A9 @ ( type2 @ A9 ) ) )
% 2.36/1.26 => ( finite_finite @ ( product_prod @ A8 @ A9 ) @ ( type2 @ ( product_prod @ A8 @ A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_FSet_Ofset___Finite__Set_Ofinite_1,axiom,
% 2.36/1.26 ! [A8: $tType] :
% 2.36/1.26 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 2.36/1.26 => ( finite_finite @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_HOL_Obool___Finite__Set_Ofinite_2,axiom,
% 2.36/1.26 finite_finite @ $o @ ( type2 @ $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Set_Oset___Finite__Set_Ofinite_3,axiom,
% 2.36/1.26 ! [A8: $tType] :
% 2.36/1.26 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 2.36/1.26 => ( finite_finite @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_fun___Finite__Set_Ofinite_4,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 2.36/1.26 & ( finite_finite @ A9 @ ( type2 @ A9 ) ) )
% 2.36/1.26 => ( finite_finite @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( order_bot @ A9 @ ( type2 @ A9 ) )
% 2.36/1.26 => ( order_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_fun___Countable_Ocountable,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 2.36/1.26 & ( countable @ A9 @ ( type2 @ A9 ) ) )
% 2.36/1.26 => ( countable @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 2.36/1.26 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( order @ A9 @ ( type2 @ A9 ) )
% 2.36/1.26 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_fun___Orderings_Oord,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 2.36/1.26 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_fun___Orderings_Obot,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 2.36/1.26 => ( bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.36/1.26 wellorder @ nat @ ( type2 @ nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Nat_Onat___Orderings_Oorder__bot_5,axiom,
% 2.36/1.26 order_bot @ nat @ ( type2 @ nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Nat_Onat___Countable_Ocountable_6,axiom,
% 2.36/1.26 countable @ nat @ ( type2 @ nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Nat_Onat___Orderings_Opreorder_7,axiom,
% 2.36/1.26 preorder @ nat @ ( type2 @ nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.36/1.26 linorder @ nat @ ( type2 @ nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Nat_Onat___Orderings_Oorder_8,axiom,
% 2.36/1.26 order @ nat @ ( type2 @ nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Nat_Onat___Orderings_Oord_9,axiom,
% 2.36/1.26 ord @ nat @ ( type2 @ nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Nat_Onat___Orderings_Obot_10,axiom,
% 2.36/1.26 bot @ nat @ ( type2 @ nat ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Set_Oset___Orderings_Oorder__bot_11,axiom,
% 2.36/1.26 ! [A8: $tType] : ( order_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Set_Oset___Countable_Ocountable_12,axiom,
% 2.36/1.26 ! [A8: $tType] :
% 2.36/1.26 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 2.36/1.26 => ( countable @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Set_Oset___Orderings_Opreorder_13,axiom,
% 2.36/1.26 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Set_Oset___Orderings_Oorder_14,axiom,
% 2.36/1.26 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Set_Oset___Orderings_Oord_15,axiom,
% 2.36/1.26 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Set_Oset___Orderings_Obot_16,axiom,
% 2.36/1.26 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_HOL_Obool___Orderings_Oorder__bot_17,axiom,
% 2.36/1.26 order_bot @ $o @ ( type2 @ $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_HOL_Obool___Countable_Ocountable_18,axiom,
% 2.36/1.26 countable @ $o @ ( type2 @ $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_HOL_Obool___Orderings_Opreorder_19,axiom,
% 2.36/1.26 preorder @ $o @ ( type2 @ $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_HOL_Obool___Orderings_Olinorder_20,axiom,
% 2.36/1.26 linorder @ $o @ ( type2 @ $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_HOL_Obool___Orderings_Oorder_21,axiom,
% 2.36/1.26 order @ $o @ ( type2 @ $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_HOL_Obool___Orderings_Oord_22,axiom,
% 2.36/1.26 ord @ $o @ ( type2 @ $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_HOL_Obool___Orderings_Obot_23,axiom,
% 2.36/1.26 bot @ $o @ ( type2 @ $o ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_FSet_Ofset___Orderings_Oorder__bot_24,axiom,
% 2.36/1.26 ! [A8: $tType] : ( order_bot @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_FSet_Ofset___Countable_Ocountable_25,axiom,
% 2.36/1.26 ! [A8: $tType] :
% 2.36/1.26 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 2.36/1.26 => ( countable @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_FSet_Ofset___Orderings_Opreorder_26,axiom,
% 2.36/1.26 ! [A8: $tType] : ( preorder @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_FSet_Ofset___Orderings_Oorder_27,axiom,
% 2.36/1.26 ! [A8: $tType] : ( order @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_FSet_Ofset___Orderings_Oord_28,axiom,
% 2.36/1.26 ! [A8: $tType] : ( ord @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_FSet_Ofset___Orderings_Obot_29,axiom,
% 2.36/1.26 ! [A8: $tType] : ( bot @ ( fset @ A8 ) @ ( type2 @ ( fset @ A8 ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(tcon_Product__Type_Oprod___Countable_Ocountable_30,axiom,
% 2.36/1.26 ! [A8: $tType,A9: $tType] :
% 2.36/1.26 ( ( ( countable @ A8 @ ( type2 @ A8 ) )
% 2.36/1.26 & ( countable @ A9 @ ( type2 @ A9 ) ) )
% 2.36/1.26 => ( countable @ ( product_prod @ A8 @ A9 ) @ ( type2 @ ( product_prod @ A8 @ A9 ) ) ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(help_If_3_1_T,axiom,
% 2.36/1.26 ! [P3: $o] :
% 2.36/1.26 ( ( P3 = $true )
% 2.36/1.26 | ( P3 = $false ) ) ).
% 2.36/1.26
% 2.36/1.26 thf(help_If_2_1_T,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,Y: A] :
% 2.36/1.26 ( ( if @ A @ $false @ X3 @ Y )
% 2.36/1.26 = Y ) ).
% 2.36/1.26
% 2.36/1.26 thf(help_If_1_1_T,axiom,
% 2.36/1.26 ! [A: $tType,X3: A,Y: A] :
% 2.36/1.26 ( ( if @ A @ $true @ X3 @ Y )
% 2.36/1.26 = X3 ) ).
% 2.36/1.26
% 2.36/1.26 thf(conj_0,hypothesis,
% 2.36/1.26 ! [Sl7: fset @ state] :
% 2.36/1.26 ( ( ( eff @ ( product_snd @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ stepsa ) ) @ Sl7 )
% 2.36/1.26 & ( fmember @ state @ ( product_fst @ state @ rule @ ( shd @ ( product_prod @ state @ rule ) @ ( stl @ ( product_prod @ state @ rule ) @ stepsa ) ) ) @ Sl7 ) )
% 2.36/1.26 => thesis ) ).
% 2.36/1.26
% 2.36/1.26 thf(conj_1,conjecture,
% 2.36/1.26 thesis ).
% 2.36/1.26 ------------------------
% 2.36/1.29 % (19503)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19284 for (2999ds/183Mi)
% 2.36/1.29 % (19507)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_19284 for (2999ds/2Mi)
% 2.36/1.29 % (19507)Instruction limit reached!
% 2.36/1.29 % (19507)------------------------------
% 2.36/1.29 % (19507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.29 % (19507)Termination reason: Unknown
% 2.36/1.29 % (19507)Termination phase: shuffling
% 2.36/1.29
% 2.36/1.29 % (19507)Memory used [KB]: 1407
% 2.36/1.29 % (19507)Time elapsed: 0.003 s
% 2.36/1.29 % (19507)Instructions burned: 3 (million)
% 2.36/1.29 % (19507)------------------------------
% 2.36/1.29 % (19507)------------------------------
% 2.36/1.29 % (19506)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19284 for (2999ds/2Mi)
% 2.36/1.29 % (19506)Instruction limit reached!
% 2.36/1.29 % (19506)------------------------------
% 2.36/1.29 % (19506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.29 % (19506)Termination reason: Unknown
% 2.36/1.29 % (19506)Termination phase: shuffling
% 2.36/1.29
% 2.36/1.29 % (19506)Memory used [KB]: 1407
% 2.36/1.29 % (19506)Time elapsed: 0.002 s
% 2.36/1.29 % (19506)Instructions burned: 2 (million)
% 2.36/1.29 % (19506)------------------------------
% 2.36/1.29 % (19506)------------------------------
% 2.36/1.29 % (19505)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_19284 for (2999ds/27Mi)
% 2.36/1.29 % (19504)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_19284 for (2999ds/4Mi)
% 2.36/1.29 % (19509)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19284 for (2999ds/18Mi)
% 2.36/1.29 % (19508)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_19284 for (2999ds/275Mi)
% 2.36/1.29 % (19504)Instruction limit reached!
% 2.36/1.29 % (19504)------------------------------
% 2.36/1.29 % (19504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.29 % (19504)Termination reason: Unknown
% 2.36/1.29 % (19504)Termination phase: shuffling
% 2.36/1.29
% 2.36/1.29 % (19504)Memory used [KB]: 1535
% 2.36/1.29 % (19504)Time elapsed: 0.004 s
% 2.36/1.29 % (19504)Instructions burned: 5 (million)
% 2.36/1.29 % (19504)------------------------------
% 2.36/1.29 % (19504)------------------------------
% 2.43/1.30 % (19515)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19284 for (2999ds/3Mi)
% 2.43/1.30 % (19515)Instruction limit reached!
% 2.43/1.30 % (19515)------------------------------
% 2.43/1.30 % (19515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.30 % (19515)Termination reason: Unknown
% 2.43/1.30 % (19515)Termination phase: shuffling
% 2.43/1.30
% 2.43/1.30 % (19515)Memory used [KB]: 1407
% 2.43/1.30 % (19515)Time elapsed: 0.002 s
% 2.43/1.30 % (19515)Instructions burned: 3 (million)
% 2.43/1.30 % (19515)------------------------------
% 2.43/1.30 % (19515)------------------------------
% 2.43/1.30 % (19509)Instruction limit reached!
% 2.43/1.30 % (19509)------------------------------
% 2.43/1.30 % (19509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.30 % (19509)Termination reason: Unknown
% 2.43/1.30 % (19509)Termination phase: shuffling
% 2.43/1.30
% 2.43/1.30 % (19509)Memory used [KB]: 1791
% 2.43/1.30 % (19509)Time elapsed: 0.011 s
% 2.43/1.30 % (19509)Instructions burned: 19 (million)
% 2.43/1.30 % (19509)------------------------------
% 2.43/1.30 % (19509)------------------------------
% 2.43/1.31 % (19505)Instruction limit reached!
% 2.43/1.31 % (19505)------------------------------
% 2.43/1.31 % (19505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.31 % (19505)Termination reason: Unknown
% 2.43/1.31 % (19505)Termination phase: shuffling
% 2.43/1.31
% 2.43/1.31 % (19505)Memory used [KB]: 1918
% 2.43/1.31 % (19505)Time elapsed: 0.015 s
% 2.43/1.31 % (19505)Instructions burned: 27 (million)
% 2.43/1.31 % (19505)------------------------------
% 2.43/1.31 % (19505)------------------------------
% 2.43/1.31 % (19516)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_19284 for (2999ds/37Mi)
% 2.43/1.31 % (19519)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_19284 for (2999ds/3Mi)
% 2.43/1.31 % (19517)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_19284 for (2999ds/15Mi)
% 2.43/1.31 % (19519)Instruction limit reached!
% 2.43/1.31 % (19519)------------------------------
% 2.43/1.31 % (19519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.31 % (19519)Termination reason: Unknown
% 2.43/1.31 % (19519)Termination phase: shuffling
% 2.43/1.31
% 2.43/1.31 % (19519)Memory used [KB]: 1535
% 2.43/1.31 % (19519)Time elapsed: 0.003 s
% 2.43/1.31 % (19519)Instructions burned: 5 (million)
% 2.43/1.31 % (19519)------------------------------
% 2.43/1.31 % (19519)------------------------------
% 2.43/1.32 % (19520)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_19284 for (2999ds/1041Mi)
% 2.43/1.32 % (19517)Instruction limit reached!
% 2.43/1.32 % (19517)------------------------------
% 2.43/1.32 % (19517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.32 % (19517)Termination reason: Unknown
% 2.43/1.32 % (19517)Termination phase: shuffling
% 2.43/1.32
% 2.43/1.32 % (19517)Memory used [KB]: 1791
% 2.43/1.32 % (19517)Time elapsed: 0.009 s
% 2.43/1.32 % (19517)Instructions burned: 15 (million)
% 2.43/1.32 % (19517)------------------------------
% 2.43/1.32 % (19517)------------------------------
% 2.43/1.32 % (19522)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19284 for (2999ds/7Mi)
% 2.43/1.32 % (19516)Instruction limit reached!
% 2.43/1.32 % (19516)------------------------------
% 2.43/1.32 % (19516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.32 % (19516)Termination reason: Unknown
% 2.43/1.32 % (19516)Termination phase: shuffling
% 2.43/1.32
% 2.43/1.32 % (19516)Memory used [KB]: 2174
% 2.43/1.32 % (19516)Time elapsed: 0.018 s
% 2.43/1.32 % (19516)Instructions burned: 38 (million)
% 2.43/1.32 % (19516)------------------------------
% 2.43/1.32 % (19516)------------------------------
% 2.43/1.33 % (19522)Instruction limit reached!
% 2.43/1.33 % (19522)------------------------------
% 2.43/1.33 % (19522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.33 % (19522)Termination reason: Unknown
% 2.43/1.33 % (19522)Termination phase: shuffling
% 2.43/1.33
% 2.43/1.33 % (19522)Memory used [KB]: 1535
% 2.43/1.33 % (19522)Time elapsed: 0.005 s
% 2.43/1.33 % (19522)Instructions burned: 7 (million)
% 2.43/1.33 % (19522)------------------------------
% 2.43/1.33 % (19522)------------------------------
% 2.43/1.33 % (19524)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19284 for (2999ds/16Mi)
% 2.43/1.34 % (19524)Instruction limit reached!
% 2.43/1.34 % (19524)------------------------------
% 2.43/1.34 % (19524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.34 % (19524)Termination reason: Unknown
% 2.43/1.34 % (19524)Termination phase: shuffling
% 2.43/1.34
% 2.43/1.34 % (19524)Memory used [KB]: 1791
% 2.43/1.34 % (19524)Time elapsed: 0.010 s
% 2.43/1.34 % (19524)Instructions burned: 16 (million)
% 2.43/1.34 % (19524)------------------------------
% 2.43/1.34 % (19524)------------------------------
% 2.43/1.34 % (19529)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_19284 for (2999ds/3Mi)
% 2.43/1.34 % (19508)First to succeed.
% 2.43/1.34 % (19529)Instruction limit reached!
% 2.43/1.34 % (19529)------------------------------
% 2.43/1.34 % (19529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.34 % (19529)Termination reason: Unknown
% 2.43/1.34 % (19529)Termination phase: shuffling
% 2.43/1.34
% 2.43/1.34 % (19529)Memory used [KB]: 1407
% 2.43/1.34 % (19529)Time elapsed: 0.003 s
% 2.43/1.34 % (19529)Instructions burned: 3 (million)
% 2.43/1.34 % (19529)------------------------------
% 2.43/1.34 % (19529)------------------------------
% 2.43/1.34 % (19531)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19284 for (2999ds/7Mi)
% 2.43/1.34 % (19526)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_19284 for (2999ds/3Mi)
% 2.43/1.34 % (19508)Refutation found. Thanks to Tanya!
% 2.43/1.34 % SZS status Theorem for DTF2THF_19284
% 2.43/1.34 % SZS output start Proof for DTF2THF_19284
% 2.43/1.34 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.43/1.34 thf(type_def_7, type, fset: ($tType) > $tType).
% 2.43/1.34 thf(type_def_8, type, stream: ($tType) > $tType).
% 2.43/1.34 thf(type_def_9, type, set: ($tType) > $tType).
% 2.43/1.34 thf(type_def_10, type, nat: $tType).
% 2.43/1.34 thf(type_def_11, type, product_prod: ($tType * $tType) > $tType).
% 2.43/1.34 thf(type_def_12, type, abstra2103299360e_tree: ($tType) > $tType).
% 2.43/1.34 thf(type_def_13, type, state: $tType).
% 2.43/1.34 thf(type_def_14, type, rule: $tType).
% 2.43/1.34 thf(func_def_0, type, abstra2103299360e_tree: ($tType) > $tType).
% 2.43/1.34 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 2.43/1.34 thf(func_def_2, type, stream: ($tType) > $tType).
% 2.43/1.34 thf(func_def_3, type, fset: ($tType) > $tType).
% 2.43/1.34 thf(func_def_4, type, set: ($tType) > $tType).
% 2.43/1.34 thf(func_def_5, type, nat: $tType).
% 2.43/1.34 thf(func_def_6, type, state: $tType).
% 2.43/1.34 thf(func_def_7, type, itself: ($tType) > $tType).
% 2.43/1.34 thf(func_def_8, type, rule: $tType).
% 2.43/1.34 thf(func_def_9, type, finite_finite: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_10, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_11, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_12, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_13, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_14, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_15, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_16, type, countable: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_17, type, order_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_18, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.43/1.34 thf(func_def_19, type, abstra1326562878System: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > set @ X1 > $o)).
% 2.43/1.34 thf(func_def_20, type, abstra1332369113inWait: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > X1 > nat)).
% 2.43/1.34 thf(func_def_21, type, abstra2096684367le_per: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > set @ X1 > X0 > $o)).
% 2.43/1.34 thf(func_def_22, type, abstra2097340358le_pos: !>[X0: $tType]:(stream @ X0 > X0 > nat)).
% 2.43/1.34 thf(func_def_23, type, abstra1209608345urated: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > stream @ product_prod @ X1 @ X0 > $o)).
% 2.43/1.34 thf(func_def_24, type, abstra1874422341nabled: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > X0 > X1 > $o)).
% 2.43/1.34 thf(func_def_25, type, abstra523868654_epath: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > stream @ product_prod @ X1 @ X0 > $o)).
% 2.43/1.34 thf(func_def_26, type, abstra928354080m_fair: !>[X0: $tType]:(stream @ X0 > stream @ X0 > $o)).
% 2.43/1.34 thf(func_def_27, type, abstra1774373515_fenum: !>[X0: $tType]:(stream @ X0 > stream @ X0)).
% 2.43/1.34 thf(func_def_28, type, abstra1225283448mkTree: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > X1 > abstra2103299360e_tree @ product_prod @ X1 @ X0)).
% 2.43/1.34 thf(func_def_29, type, abstra1276541928ickEff: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > X0 > X1 > fset @ X1)).
% 2.43/1.34 thf(func_def_30, type, abstra726722745urated: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > X0 > stream @ product_prod @ X1 @ X0 > $o)).
% 2.43/1.34 thf(func_def_31, type, abstra1259602206m_trim: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > X1 > stream @ X0)).
% 2.43/1.34 thf(func_def_32, type, abstra1874736267tem_wf: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > abstra2103299360e_tree @ product_prod @ X1 @ X0 > $o)).
% 2.43/1.34 thf(func_def_33, type, abstra313004635_ipath: !>[X0: $tType]:(abstra2103299360e_tree @ X0 > stream @ X0 > $o)).
% 2.43/1.34 thf(func_def_34, type, abstra388494275e_Node: !>[X0: $tType]:(X0 > fset @ abstra2103299360e_tree @ X0 > abstra2103299360e_tree @ X0)).
% 2.43/1.34 thf(func_def_35, type, abstra1749095923e_cont: !>[X0: $tType]:(abstra2103299360e_tree @ X0 > fset @ abstra2103299360e_tree @ X0)).
% 2.43/1.34 thf(func_def_36, type, abstra573067619e_root: !>[X0: $tType]:(abstra2103299360e_tree @ X0 > X0)).
% 2.43/1.34 thf(func_def_37, type, countable_countable: !>[X0: $tType]:(set @ X0 > $o)).
% 2.43/1.34 thf(func_def_38, type, fimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > fset @ X0 > fset @ X1)).
% 2.43/1.34 thf(func_def_39, type, fmember: !>[X0: $tType]:(X0 > fset @ X0 > $o)).
% 2.43/1.34 thf(func_def_40, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.43/1.34 thf(func_def_41, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.43/1.34 thf(func_def_42, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.43/1.34 thf(func_def_43, type, ord_Least: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_44, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.43/1.34 thf(func_def_45, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.43/1.34 thf(func_def_46, type, product_fst: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 2.43/1.34 thf(func_def_47, type, product_snd: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 2.43/1.34 thf(func_def_48, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.43/1.34 thf(func_def_49, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.43/1.34 thf(func_def_50, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.43/1.34 thf(func_def_51, type, sdrop: !>[X0: $tType]:(nat > stream @ X0 > stream @ X0)).
% 2.43/1.34 thf(func_def_52, type, sdrop_while: !>[X0: $tType]:((X0 > $o) > stream @ X0 > stream @ X0)).
% 2.43/1.34 thf(func_def_53, type, case_stream: !>[X0: $tType, X1: $tType]:((X0 > stream @ X0 > X1) > stream @ X0 > X1)).
% 2.43/1.34 thf(func_def_54, type, shd: !>[X0: $tType]:(stream @ X0 > X0)).
% 2.43/1.34 thf(func_def_55, type, sset: !>[X0: $tType]:(stream @ X0 > set @ X0)).
% 2.43/1.34 thf(func_def_56, type, stl: !>[X0: $tType]:(stream @ X0 > stream @ X0)).
% 2.43/1.34 thf(func_def_57, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.43/1.34 thf(func_def_58, type, s: set @ state).
% 2.43/1.34 thf(func_def_59, type, eff: rule > state > fset @ state > $o).
% 2.43/1.34 thf(func_def_60, type, r: rule).
% 2.43/1.34 thf(func_def_61, type, rules: stream @ rule).
% 2.43/1.34 thf(func_def_62, type, steps: stream @ product_prod @ state @ rule).
% 2.43/1.34 thf(func_def_63, type, stepsa: stream @ product_prod @ state @ rule).
% 2.43/1.34 thf(func_def_81, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > fset @ X1 > X1 > X0)).
% 2.43/1.34 thf(func_def_82, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > fset @ X1 > X1)).
% 2.43/1.34 thf(func_def_83, type, sK2: !>[X0: $tType, X1: $tType]:(stream @ product_prod @ X1 @ X0 > stream @ X0 > (X0 > X1 > fset @ X1 > $o) > fset @ X1)).
% 2.43/1.34 thf(func_def_84, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.43/1.34 thf(func_def_85, type, sK4: !>[X0: $tType]:((stream @ X0 > stream @ X0 > $o) > stream @ X0)).
% 2.43/1.34 thf(func_def_86, type, sK5: !>[X0: $tType]:((stream @ X0 > stream @ X0 > $o) > stream @ X0)).
% 2.43/1.34 thf(func_def_87, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 2.43/1.34 thf(func_def_88, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 2.43/1.34 thf(func_def_89, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 2.43/1.34 thf(func_def_90, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 2.43/1.34 thf(func_def_91, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 2.43/1.34 thf(func_def_92, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 2.43/1.34 thf(func_def_93, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 2.43/1.34 thf(func_def_94, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 2.43/1.34 thf(func_def_95, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.43/1.34 thf(func_def_96, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.43/1.34 thf(func_def_97, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_98, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 2.43/1.34 thf(func_def_99, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 2.43/1.34 thf(func_def_100, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 2.43/1.34 thf(func_def_101, type, sK20: stream @ product_prod @ state @ rule > fset @ state).
% 2.43/1.34 thf(func_def_102, type, sK21: !>[X0: $tType]:(fset @ X0 > fset @ X0 > X0)).
% 2.43/1.34 thf(func_def_103, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 2.43/1.34 thf(func_def_104, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 2.43/1.34 thf(func_def_105, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 2.43/1.34 thf(func_def_106, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 2.43/1.34 thf(func_def_107, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 2.43/1.34 thf(func_def_108, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 2.43/1.34 thf(func_def_109, type, sK28: (stream @ product_prod @ state @ rule > $o) > stream @ product_prod @ state @ rule).
% 2.43/1.34 thf(func_def_110, type, sK29: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 2.43/1.34 thf(func_def_111, type, sK30: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 2.43/1.34 thf(func_def_112, type, sK31: stream @ rule > state > nat).
% 2.43/1.34 thf(func_def_113, type, sK32: !>[X0: $tType]:(fset @ X0 > fset @ X0 > X0)).
% 2.43/1.34 thf(func_def_114, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 2.43/1.34 thf(func_def_115, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 2.43/1.34 thf(func_def_116, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 2.43/1.34 thf(func_def_117, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 2.43/1.34 thf(func_def_118, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 2.43/1.34 thf(func_def_119, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 2.43/1.34 thf(func_def_120, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 2.43/1.34 thf(func_def_121, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 2.43/1.34 thf(func_def_122, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 2.43/1.34 thf(func_def_123, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 2.43/1.34 thf(func_def_124, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.43/1.34 thf(func_def_125, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.43/1.34 thf(func_def_126, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_127, type, sK46: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 2.43/1.34 thf(func_def_128, type, sK47: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 2.43/1.34 thf(func_def_129, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.43/1.34 thf(func_def_130, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.43/1.34 thf(func_def_131, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_132, type, sK51: !>[X0: $tType, X1: $tType]:((X0 > X1 > fset @ X1 > $o) > stream @ X0 > (stream @ product_prod @ X1 @ X0 > $o) > stream @ product_prod @ X1 @ X0)).
% 2.43/1.34 thf(func_def_133, type, sK52: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 2.43/1.34 thf(func_def_134, type, sK53: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_135, type, sK54: !>[X0: $tType]:((stream @ X0 > stream @ X0 > $o) > stream @ X0)).
% 2.43/1.34 thf(func_def_136, type, sK55: !>[X0: $tType]:((stream @ X0 > stream @ X0 > $o) > stream @ X0)).
% 2.43/1.34 thf(func_def_137, type, sK56: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 2.43/1.34 thf(func_def_138, type, sK57: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 2.43/1.34 thf(func_def_139, type, sK58: !>[X0: $tType]:((X0 > stream @ X0 > $o) > stream @ X0)).
% 2.43/1.34 thf(func_def_140, type, sK59: !>[X0: $tType]:((X0 > stream @ X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_141, type, sK60: !>[X0: $tType]:((X0 > stream @ X0 > $o) > stream @ X0)).
% 2.43/1.34 thf(func_def_142, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 2.43/1.34 thf(func_def_143, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 2.43/1.34 thf(func_def_144, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.43/1.34 thf(func_def_145, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.43/1.34 thf(func_def_146, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_147, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 2.43/1.34 thf(func_def_148, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 2.43/1.34 thf(func_def_149, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 2.43/1.34 thf(func_def_150, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 2.43/1.34 thf(func_def_151, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 2.43/1.34 thf(func_def_152, type, sK71: stream @ product_prod @ state @ rule > stream @ product_prod @ state @ rule).
% 2.43/1.34 thf(func_def_153, type, sK72: stream @ product_prod @ state @ rule > fset @ state).
% 2.43/1.34 thf(func_def_154, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 2.43/1.34 thf(func_def_155, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.43/1.34 thf(func_def_156, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.43/1.34 thf(func_def_157, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_158, type, sK77: state > rule).
% 2.43/1.34 thf(func_def_159, type, sK78: state > fset @ state).
% 2.43/1.34 thf(func_def_160, type, sK79: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 2.43/1.34 thf(func_def_161, type, sK80: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 2.43/1.34 thf(func_def_162, type, sK81: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 2.43/1.34 thf(func_def_164, type, ph83: !>[X0: $tType]:(X0)).
% 2.43/1.34 thf(f1206,plain,(
% 2.43/1.34 $false),
% 2.43/1.34 inference(avatar_sat_refutation,[status(thm)],[f1183,f1184,f1204])).
% 2.43/1.34 thf(f1204,plain,(
% 2.43/1.34 ~spl82_1),
% 2.43/1.34 inference(avatar_contradiction_clause,[status(thm)],[f1203])).
% 2.43/1.34 thf(f1203,plain,(
% 2.43/1.34 $false | ~spl82_1),
% 2.43/1.34 inference(trivial_inequality_removal,[status(thm)],[f1201])).
% 2.43/1.34 thf(f1201,plain,(
% 2.43/1.34 ($true != $true) | ~spl82_1),
% 2.43/1.34 inference(superposition,[status(thm)],[f1199,f1091])).
% 2.43/1.34 thf(f1091,plain,(
% 2.43/1.34 ((abstra523868654_epath @ rule @ state @ eff @ rules @ stepsa) = $true)),
% 2.43/1.34 inference(cnf_transformation,[status(thm)],[f540])).
% 2.43/1.34 thf(f540,plain,(
% 2.43/1.34 ((abstra523868654_epath @ rule @ state @ eff @ rules @ stepsa) = $true) & ((member @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ s) = $true)),
% 2.43/1.34 inference(fool_elimination,[status(thm)],[f539])).
% 2.43/1.34 thf(f539,plain,(
% 2.43/1.34 (member @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ s) & (abstra523868654_epath @ rule @ state @ eff @ rules @ stepsa)),
% 2.43/1.34 inference(rectify,[status(thm)],[f36])).
% 2.43/1.34 thf(f36,axiom,(
% 2.43/1.34 (member @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ s) & (abstra523868654_epath @ rule @ state @ eff @ rules @ stepsa)),
% 2.43/1.34 file('/export/starexec/sandbox/tmp/tmp.VC7EeYKUxt/DTF2THF_19284.p',fact_35_local_Oalw)).
% 2.43/1.34 thf(f1199,plain,(
% 2.43/1.34 ( ! [X0 : stream @ rule] : (($true != (abstra523868654_epath @ rule @ state @ eff @ X0 @ stepsa))) ) | ~spl82_1),
% 2.43/1.34 inference(subsumption_resolution,[status(thm)],[f1192,f1028])).
% 2.43/1.34 thf(f1028,plain,(
% 2.43/1.34 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : (((fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ (sK2 @ X0 @ X1 @ X4 @ X3 @ X2)) = $true) | ((abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ X4) != $true)) )),
% 2.43/1.34 inference(cnf_transformation,[status(thm)],[f958])).
% 2.43/1.34 thf(f958,plain,(
% 2.43/1.34 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : ((((member @ X0 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sset @ X0 @ X3)) = $true) & (($true = (abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ (stl @ product_prod @ X1 @ X0 @ X4))) & ((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sK2 @ X0 @ X1 @ X4 @ X3 @ X2)) = $true) & ((fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ (sK2 @ X0 @ X1 @ X4 @ X3 @ X2)) = $true))) | ((abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ X4) != $true))),
% 2.43/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f910,f957])).
% 2.43/1.34 thf(f957,plain,(
% 2.43/1.34 ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : (? [X5 : fset @ X1] : (($true = (abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ (stl @ product_prod @ X1 @ X0 @ X4))) & ((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ X5) = $true) & ($true = (fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ X5))) => (($true = (abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ (stl @ product_prod @ X1 @ X0 @ X4))) & ((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sK2 @ X0 @ X1 @ X4 @ X3 @ X2)) = $true) & ((fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ (sK2 @ X0 @ X1 @ X4 @ X3 @ X2)) = $true)))),
% 2.43/1.34 introduced(definition,[],[choice_axiom])).
% 2.43/1.34 thf(f910,plain,(
% 2.43/1.34 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : ((((member @ X0 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sset @ X0 @ X3)) = $true) & ? [X5 : fset @ X1] : (($true = (abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ (stl @ product_prod @ X1 @ X0 @ X4))) & ((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ X5) = $true) & ($true = (fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ X5)))) | ((abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ X4) != $true))),
% 2.43/1.34 inference(flattening,[status(thm)],[f909])).
% 2.43/1.34 thf(f909,plain,(
% 2.43/1.34 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : ((? [X5 : fset @ X1] : ((($true = (abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ (stl @ product_prod @ X1 @ X0 @ X4))) & ((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ X5) = $true)) & ($true = (fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ X5))) & ((member @ X0 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sset @ X0 @ X3)) = $true)) | ((abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ X4) != $true))),
% 2.43/1.34 inference(ennf_transformation,[status(thm)],[f842])).
% 2.43/1.34 thf(f842,plain,(
% 2.43/1.34 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : (((abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ X4) = $true) => ~(((member @ X0 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sset @ X0 @ X3)) = $true) => ! [X5 : fset @ X1] : (($true = (fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ X5)) => (((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ X5) = $true) => ($true != (abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ (stl @ product_prod @ X1 @ X0 @ X4)))))))),
% 2.43/1.34 inference(flattening,[status(thm)],[f792])).
% 2.43/1.34 thf(f792,plain,(
% 2.43/1.34 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : (((abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ X4) = $true) => ~(((member @ X0 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sset @ X0 @ X3)) = $true) => ! [X5 : fset @ X1] : (($true = (fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ X5)) => (((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ X5) = $true) => ~($true = (abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ (stl @ product_prod @ X1 @ X0 @ X4)))))))),
% 2.43/1.34 inference(fool_elimination,[status(thm)],[f791])).
% 2.43/1.34 thf(f791,plain,(
% 2.43/1.34 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : ((abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ X4) => ~((member @ X0 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sset @ X0 @ X3)) => ! [X5 : fset @ X1] : ((fmember @ X1 @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ (stl @ product_prod @ X1 @ X0 @ X4))) @ X5) => ((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ X5) => ~(abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ (stl @ product_prod @ X1 @ X0 @ X4))))))),
% 2.43/1.34 inference(rectify,[status(thm)],[f32])).
% 2.43/1.34 thf(f32,axiom,(
% 2.43/1.34 ! [X1 : $tType,X2 : $tType,X28 : X1 > X2 > fset @ X2 > $o,X29 : stream @ X1,X8 : stream @ product_prod @ X2 @ X1] : ((abstra523868654_epath @ X1 @ X2 @ X28 @ X29 @ X8) => ~((member @ X1 @ (product_snd @ X2 @ X1 @ (shd @ product_prod @ X2 @ X1 @ X8)) @ (sset @ X1 @ X29)) => ! [X9 : fset @ X2] : ((fmember @ X2 @ (product_fst @ X2 @ X1 @ (shd @ product_prod @ X2 @ X1 @ (stl @ product_prod @ X2 @ X1 @ X8))) @ X9) => ((X28 @ (product_snd @ X2 @ X1 @ (shd @ product_prod @ X2 @ X1 @ X8)) @ (product_fst @ X2 @ X1 @ (shd @ product_prod @ X2 @ X1 @ X8)) @ X9) => ~(abstra523868654_epath @ X1 @ X2 @ X28 @ X29 @ (stl @ product_prod @ X2 @ X1 @ X8))))))),
% 2.43/1.34 file('/export/starexec/sandbox/tmp/tmp.VC7EeYKUxt/DTF2THF_19284.p',fact_31_RuleSystem__Defs_Oepath_Ocases)).
% 2.43/1.34 thf(f1192,plain,(
% 2.43/1.34 ( ! [X0 : stream @ rule] : (($true != (abstra523868654_epath @ rule @ state @ eff @ X0 @ stepsa)) | ((fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ (sK2 @ rule @ state @ stepsa @ X0 @ eff)) != $true)) ) | ~spl82_1),
% 2.43/1.34 inference(trivial_inequality_removal,[status(thm)],[f1188])).
% 2.43/1.34 thf(f1188,plain,(
% 2.43/1.34 ( ! [X0 : stream @ rule] : (($true != (abstra523868654_epath @ rule @ state @ eff @ X0 @ stepsa)) | ($true != $true) | ((fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ (sK2 @ rule @ state @ stepsa @ X0 @ eff)) != $true)) ) | ~spl82_1),
% 2.43/1.34 inference(superposition,[status(thm)],[f1178,f1029])).
% 2.43/1.34 thf(f1029,plain,(
% 2.43/1.34 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > fset @ X1 > $o,X3 : stream @ X0,X4 : stream @ product_prod @ X1 @ X0] : (((X2 @ (product_snd @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (product_fst @ X1 @ X0 @ (shd @ product_prod @ X1 @ X0 @ X4)) @ (sK2 @ X0 @ X1 @ X4 @ X3 @ X2)) = $true) | ((abstra523868654_epath @ X0 @ X1 @ X2 @ X3 @ X4) != $true)) )),
% 2.43/1.34 inference(cnf_transformation,[status(thm)],[f958])).
% 2.43/1.34 thf(f1178,plain,(
% 2.43/1.34 ( ! [X0 : fset @ state] : (((eff @ (product_snd @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ X0) != $true) | ((fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ X0) != $true)) ) | ~spl82_1),
% 2.43/1.34 inference(avatar_component_clause,[status(thm)],[f1177])).
% 2.43/1.34 thf(f1177,definition,(
% 2.43/1.34 spl82_1 <=> ! [X0 : fset @ state] : (((eff @ (product_snd @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ X0) != $true) | ((fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ X0) != $true))),
% 2.43/1.34 introduced(definition,[new_symbols(naming,[spl82_1])],[avatar_definition])).
% 2.43/1.34 thf(f1184,plain,(
% 2.43/1.34 ~spl82_2),
% 2.43/1.34 inference(avatar_split_clause,[status(thm)],[f1047,f1180])).
% 2.43/1.34 thf(f1180,definition,(
% 2.43/1.34 spl82_2 <=> (thesis = $true)),
% 2.43/1.34 introduced(definition,[new_symbols(naming,[spl82_2])],[avatar_definition])).
% 2.43/1.34 thf(f1047,plain,(
% 2.43/1.34 (thesis != $true)),
% 2.43/1.34 inference(cnf_transformation,[status(thm)],[f811])).
% 2.43/1.34 thf(f811,plain,(
% 2.43/1.34 (thesis != $true)),
% 2.43/1.34 inference(flattening,[status(thm)],[f776])).
% 2.43/1.34 thf(f776,plain,(
% 2.43/1.34 ~(thesis = $true)),
% 2.43/1.34 inference(fool_elimination,[status(thm)],[f775])).
% 2.43/1.34 thf(f775,plain,(
% 2.43/1.34 ~thesis),
% 2.43/1.34 inference(rectify,[status(thm)],[f301])).
% 2.43/1.34 thf(f301,negated_conjecture,(
% 2.43/1.34 ~thesis),
% 2.43/1.34 inference(negated_conjecture,[status(cth)],[f300])).
% 2.43/1.34 thf(f300,conjecture,(
% 2.43/1.34 thesis),
% 2.43/1.34 file('/export/starexec/sandbox/tmp/tmp.VC7EeYKUxt/DTF2THF_19284.p',conj_1)).
% 2.43/1.34 thf(f1183,plain,(
% 2.43/1.34 spl82_1 | spl82_2),
% 2.43/1.34 inference(avatar_split_clause,[status(thm)],[f1032,f1180,f1177])).
% 2.43/1.34 thf(f1032,plain,(
% 2.43/1.34 ( ! [X0 : fset @ state] : (((eff @ (product_snd @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ X0) != $true) | ((fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ X0) != $true) | (thesis = $true)) )),
% 2.43/1.34 inference(cnf_transformation,[status(thm)],[f854])).
% 2.43/1.35 thf(f854,plain,(
% 2.43/1.35 ! [X0 : fset @ state] : ((thesis = $true) | ((eff @ (product_snd @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ X0) != $true) | ((fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ X0) != $true))),
% 2.43/1.35 inference(flattening,[status(thm)],[f853])).
% 2.43/1.35 thf(f853,plain,(
% 2.43/1.35 ! [X0 : fset @ state] : ((thesis = $true) | (((eff @ (product_snd @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ X0) != $true) | ((fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ X0) != $true)))),
% 2.43/1.35 inference(ennf_transformation,[status(thm)],[f748])).
% 2.43/1.35 thf(f748,plain,(
% 2.43/1.35 ! [X0 : fset @ state] : ((((eff @ (product_snd @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ X0) = $true) & ((fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ X0) = $true)) => (thesis = $true))),
% 2.43/1.35 inference(fool_elimination,[status(thm)],[f747])).
% 2.43/1.35 thf(f747,plain,(
% 2.43/1.35 ! [X0 : fset @ state] : (((eff @ (product_snd @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ X0) & (fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ X0)) => thesis)),
% 2.43/1.35 inference(rectify,[status(thm)],[f299])).
% 2.43/1.35 thf(f299,axiom,(
% 2.43/1.35 ! [X109 : fset @ state] : (((eff @ (product_snd @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ stepsa)) @ X109) & (fmember @ state @ (product_fst @ state @ rule @ (shd @ product_prod @ state @ rule @ (stl @ product_prod @ state @ rule @ stepsa))) @ X109)) => thesis)),
% 2.43/1.35 file('/export/starexec/sandbox/tmp/tmp.VC7EeYKUxt/DTF2THF_19284.p',conj_0)).
% 2.43/1.35 % SZS output end Proof for DTF2THF_19284
% 2.43/1.35 % (19508)------------------------------
% 2.43/1.35 % (19508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.35 % (19508)Termination reason: Refutation
% 2.43/1.35
% 2.43/1.35 % (19508)Memory used [KB]: 7164
% 2.43/1.35 % (19508)Time elapsed: 0.052 s
% 2.43/1.35 % (19508)Instructions burned: 99 (million)
% 2.43/1.35 % (19508)------------------------------
% 2.43/1.35 % (19508)------------------------------
% 2.43/1.35 % (19496)Success in time 0.074 s
%------------------------------------------------------------------------------