%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT219^1 : 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 : n007.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 08:45:11 AM UTC 2026
% Result : Theorem 2.95s 1.64s
% Output : Refutation 2.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT219^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n007.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 06:10:38 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : DAT219^1 : TPTP v9.2.1. Released v7.0.0.
% 0.21/0.47 % Domain : Data Structures
% 0.21/0.47 % Problem : Terminated lazy lists 54
% 0.21/0.47 % Version : [Bla16] axioms : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.21/0.47 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.21/0.47 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Bla16]
% 0.21/0.47 % Names : tllist__54.p [Bla16]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.33 v9.1.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.21/0.47 % Syntax : Number of formulae : 324 ( 147 unt; 48 typ; 0 def)
% 0.21/0.47 % Number of atoms : 746 ( 296 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 13 ( 2 avg)
% 0.21/0.47 % Number of connectives : 4478 ( 103 ~; 8 |; 49 &;3972 @)
% 0.21/0.47 % ( 0 <=>; 346 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 28 ( 9 avg)
% 0.21/0.47 % Number of types : 3 ( 2 usr)
% 0.21/0.47 % Number of type conns : 402 ( 402 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 49 ( 46 usr; 4 con; 0-10 aty)
% 0.21/0.47 % Number of variables : 1285 ( 68 ^;1148 !; 5 ?;1285 :)
% 0.21/0.47 % ( 64 !>; 0 ?*; 0 @-; 0 @+)
% 0.21/0.47 % SPC : TH1_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.21/0.47 % 2016-07-13 14:49:47.576
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 %----Could-be-implicit typings (5)
% 0.21/0.47 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist,type,
% 0.21/0.47 tLList446370796tllist: $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Set_Oset,type,
% 0.21/0.47 set: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_itself,type,
% 0.21/0.47 itself: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_b,type,
% 0.21/0.47 b: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_a,type,
% 0.21/0.47 a: $tType ).
% 0.21/0.47
% 0.21/0.47 %----Explicit typings (43)
% 0.21/0.47 thf(sy_cl_HOL_Otype,type,
% 0.21/0.47 type:
% 0.21/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Obot,type,
% 0.21/0.47 bot:
% 0.21/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.21/0.47 ord:
% 0.21/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.21/0.47 order:
% 0.21/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.21/0.47 linorder:
% 0.21/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.21/0.47 preorder:
% 0.21/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.21/0.47 order_bot:
% 0.21/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Fun_Ofcomp,type,
% 0.21/0.47 fcomp:
% 0.21/0.47 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( B > C ) > A > C ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Fun_Oid,type,
% 0.21/0.47 id:
% 0.21/0.47 !>[A: $tType] : ( A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Fun_Ooverride__on,type,
% 0.21/0.47 override_on:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > B ) > ( set @ A ) > A > B ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.21/0.47 minus_minus:
% 0.21/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.21/0.47 uminus_uminus:
% 0.21/0.47 !>[A: $tType] : ( A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_HOL_Oundefined,type,
% 0.21/0.47 undefined:
% 0.21/0.47 !>[A: $tType] : A ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_If,type,
% 0.21/0.47 if:
% 0.21/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.21/0.47 inf_inf:
% 0.21/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.21/0.47 bot_bot:
% 0.21/0.47 !>[A: $tType] : A ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.21/0.47 ord_less_eq:
% 0.21/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Pure_Otype,type,
% 0.21/0.47 type2:
% 0.21/0.47 !>[A: $tType] : ( itself @ A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Relation_Oinv__imagep,type,
% 0.21/0.47 inv_imagep:
% 0.21/0.47 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_OBall,type,
% 0.21/0.47 ball:
% 0.21/0.47 !>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_OCollect,type,
% 0.21/0.47 collect:
% 0.21/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Oinsert,type,
% 0.21/0.47 insert:
% 0.21/0.47 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Ois__empty,type,
% 0.21/0.47 is_empty:
% 0.21/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Ois__singleton,type,
% 0.21/0.47 is_singleton:
% 0.21/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Opairwise,type,
% 0.21/0.47 pairwise:
% 0.21/0.47 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Othe__elem,type,
% 0.21/0.47 the_elem:
% 0.21/0.47 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Oterminal0,type,
% 0.21/0.47 tLList1825092077minal0:
% 0.21/0.47 !>[A: $tType] : A ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTCons,type,
% 0.21/0.47 tLList1992840728_TCons:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( A > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTNil,type,
% 0.21/0.47 tLList57907754e_TNil:
% 0.21/0.47 !>[B: $tType,A: $tType] : ( B > ( tLList446370796tllist @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocase__tllist,type,
% 0.21/0.47 tLList200813139tllist:
% 0.21/0.47 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > ( tLList446370796tllist @ A @ B ) > C ) > ( tLList446370796tllist @ A @ B ) > C ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocorec__tllist,type,
% 0.21/0.47 tLList1614408749tllist:
% 0.21/0.47 !>[E: $tType,B: $tType,A: $tType] : ( ( E > $o ) > ( E > B ) > ( E > A ) > ( E > $o ) > ( E > ( tLList446370796tllist @ A @ B ) ) > ( E > E ) > E > ( tLList446370796tllist @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ois__TNil,type,
% 0.21/0.47 tLList1968894004s_TNil:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Opred__tllist,type,
% 0.21/0.47 tLList11265572tllist:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( tLList446370796tllist @ A @ B ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oset2__tllist,type,
% 0.21/0.47 tLList457864275tllist:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( set @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oterminal,type,
% 0.21/0.47 tLList2110128105rminal:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > B ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Othd,type,
% 0.21/0.47 tLList_Mirabelle_thd:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otllist__all2,type,
% 0.21/0.47 tLList1380991092t_all2:
% 0.21/0.47 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otmap,type,
% 0.21/0.47 tLList1669959861e_tmap:
% 0.21/0.47 !>[A: $tType,Aa: $tType,B: $tType,Ba: $tType] : ( ( A > Aa ) > ( B > Ba ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ Aa @ Ba ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otset,type,
% 0.21/0.47 tLList1719791291e_tset:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ottl,type,
% 0.21/0.47 tLList_Mirabelle_ttl:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member,type,
% 0.21/0.47 member:
% 0.21/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_x,type,
% 0.21/0.47 x: tLList446370796tllist @ a @ b ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_x1,type,
% 0.21/0.47 x1: b ).
% 0.21/0.47
% 0.21/0.47 %----Relevant facts (255)
% 0.21/0.47 thf(fact_0_tllist_Oinject_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,X1: B,Y1: B] :
% 0.21/0.47 ( ( ( tLList57907754e_TNil @ B @ A @ X1 )
% 0.21/0.47 = ( tLList57907754e_TNil @ B @ A @ Y1 ) )
% 0.21/0.47 = ( X1 = Y1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.inject(1)
% 0.21/0.47 thf(fact_1_tllist_Ocollapse_I1_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.21/0.47 => ( ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) )
% 0.21/0.47 = Tllist ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.collapse(1)
% 0.21/0.47 thf(fact_2_tllist_Osel_I4_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,X1: B] :
% 0.21/0.47 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.21/0.47 = ( tLList57907754e_TNil @ B @ A @ X1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.sel(4)
% 0.21/0.47 thf(fact_3_tllist_Osel_I1_J,axiom,
% 0.21/0.47 ! [Aa: $tType,A: $tType,X1: A] :
% 0.21/0.47 ( ( tLList2110128105rminal @ Aa @ A @ ( tLList57907754e_TNil @ A @ Aa @ X1 ) )
% 0.21/0.47 = X1 ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.sel(1)
% 0.21/0.47 thf(fact_4_tllist_Odisc_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,X1: B] : ( tLList1968894004s_TNil @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.disc(1)
% 0.21/0.47 thf(fact_5_tllist_OdiscI_I1_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,X1: B] :
% 0.21/0.47 ( ( Tllist
% 0.21/0.47 = ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.21/0.47 => ( tLList1968894004s_TNil @ A @ B @ Tllist ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.discI(1)
% 0.21/0.47 thf(fact_6_tllist_Osimps_I5_J,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType,B: $tType,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,X1: B] :
% 0.21/0.47 ( ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.21/0.47 = ( F1 @ X1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.simps(5)
% 0.21/0.47 thf(fact_7_terminal0_Osimps,axiom,
% 0.21/0.47 ! [D: $tType,C: $tType] :
% 0.21/0.47 ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) )
% 0.21/0.47 = ( ^ [Xs: tLList446370796tllist @ C @ D] : ( if @ D @ ( tLList1968894004s_TNil @ C @ D @ Xs ) @ ( tLList200813139tllist @ D @ D @ C @ ( id @ D ) @ ( undefined @ ( C > ( tLList446370796tllist @ C @ D ) > D ) ) @ Xs ) @ ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) @ ( tLList_Mirabelle_ttl @ C @ D @ Xs ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % terminal0.simps
% 0.21/0.47 thf(fact_8_is__TNil__def,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( tLList1968894004s_TNil @ A @ B )
% 0.21/0.47 = ( ^ [Tllist2: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ? [X12: B] :
% 0.21/0.47 ( Tllist2
% 0.21/0.47 = ( tLList57907754e_TNil @ B @ A @ X12 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_TNil_def
% 0.21/0.47 thf(fact_9_terminal0_Oraw__induct,axiom,
% 0.21/0.47 ! [C: $tType,D: $tType,P: ( tLList446370796tllist @ C @ D ) > D > $o,Xs2: tLList446370796tllist @ C @ D,Y: D] :
% 0.21/0.47 ( ! [Terminal0: ( tLList446370796tllist @ C @ D ) > D] :
% 0.21/0.47 ( ! [X: tLList446370796tllist @ C @ D] :
% 0.21/0.47 ( ( ( Terminal0 @ X )
% 0.21/0.47 != ( undefined @ D ) )
% 0.21/0.47 => ( P @ X @ ( Terminal0 @ X ) ) )
% 0.21/0.47 => ! [Xs3: tLList446370796tllist @ C @ D,Xsa: D] :
% 0.21/0.47 ( ( ( ( tLList1968894004s_TNil @ C @ D @ Xs3 )
% 0.21/0.47 => ( ( tLList200813139tllist @ D @ D @ C @ ( id @ D ) @ ( undefined @ ( C > ( tLList446370796tllist @ C @ D ) > D ) ) @ Xs3 )
% 0.21/0.47 = Xsa ) )
% 0.21/0.47 & ( ~ ( tLList1968894004s_TNil @ C @ D @ Xs3 )
% 0.21/0.47 => ( ( Terminal0 @ ( tLList_Mirabelle_ttl @ C @ D @ Xs3 ) )
% 0.21/0.47 = Xsa ) ) )
% 0.21/0.47 => ( ( Xsa
% 0.21/0.47 != ( undefined @ D ) )
% 0.21/0.47 => ( P @ Xs3 @ Xsa ) ) ) )
% 0.21/0.47 => ( ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) @ Xs2 )
% 0.21/0.47 = Y )
% 0.21/0.47 => ( ( Y
% 0.21/0.47 != ( undefined @ D ) )
% 0.21/0.47 => ( P @ Xs2 @ Y ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % terminal0.raw_induct
% 0.21/0.47 thf(fact_10_id__apply,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( id @ A )
% 0.21/0.47 = ( ^ [X2: A] : X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % id_apply
% 0.21/0.47 thf(fact_11_tllist_Ocase__eq__if,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.21/0.47 ( ( tLList200813139tllist @ B @ C @ A )
% 0.21/0.47 = ( ^ [F12: B > C,F22: A > ( tLList446370796tllist @ A @ B ) > C,Tllist2: tLList446370796tllist @ A @ B] : ( if @ C @ ( tLList1968894004s_TNil @ A @ B @ Tllist2 ) @ ( F12 @ ( tLList2110128105rminal @ A @ B @ Tllist2 ) ) @ ( F22 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist2 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.case_eq_if
% 0.21/0.47 thf(fact_12_tllist_Oexpand,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.21/0.47 = ( tLList1968894004s_TNil @ A @ B @ Tllist3 ) )
% 0.21/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.21/0.47 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist3 )
% 0.21/0.47 => ( ( tLList2110128105rminal @ A @ B @ Tllist )
% 0.21/0.47 = ( tLList2110128105rminal @ A @ B @ Tllist3 ) ) ) )
% 0.21/0.47 => ( ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.21/0.47 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist3 )
% 0.21/0.47 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist )
% 0.21/0.47 = ( tLList_Mirabelle_thd @ A @ B @ Tllist3 ) )
% 0.21/0.47 & ( ( tLList_Mirabelle_ttl @ A @ B @ Tllist )
% 0.21/0.47 = ( tLList_Mirabelle_ttl @ A @ B @ Tllist3 ) ) ) ) )
% 0.21/0.47 => ( Tllist = Tllist3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.expand
% 0.21/0.47 thf(fact_13_tllist_Ocoinduct,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,R: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) > $o,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( R @ Tllist @ Tllist3 )
% 0.21/0.47 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( R @ Tllist4 @ Tllist5 )
% 0.21/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.21/0.47 = ( tLList1968894004s_TNil @ A @ B @ Tllist5 ) )
% 0.21/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.21/0.47 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 0.21/0.47 => ( ( tLList2110128105rminal @ A @ B @ Tllist4 )
% 0.21/0.47 = ( tLList2110128105rminal @ A @ B @ Tllist5 ) ) ) )
% 0.21/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.21/0.47 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 0.21/0.47 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist4 )
% 0.21/0.47 = ( tLList_Mirabelle_thd @ A @ B @ Tllist5 ) )
% 0.21/0.47 & ( R @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) ) ) ) ) ) )
% 0.21/0.47 => ( Tllist = Tllist3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.coinduct
% 0.21/0.47 thf(fact_14_tllist_Ocoinduct__strong,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,R: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) > $o,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( R @ Tllist @ Tllist3 )
% 0.21/0.47 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( R @ Tllist4 @ Tllist5 )
% 0.21/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.21/0.47 = ( tLList1968894004s_TNil @ A @ B @ Tllist5 ) )
% 0.21/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.21/0.47 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 0.21/0.47 => ( ( tLList2110128105rminal @ A @ B @ Tllist4 )
% 0.21/0.47 = ( tLList2110128105rminal @ A @ B @ Tllist5 ) ) ) )
% 0.21/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.21/0.47 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 0.21/0.47 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist4 )
% 0.21/0.47 = ( tLList_Mirabelle_thd @ A @ B @ Tllist5 ) )
% 0.21/0.47 & ( ( R @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) )
% 0.21/0.47 | ( ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 )
% 0.21/0.47 = ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) ) ) ) ) ) ) )
% 0.21/0.47 => ( Tllist = Tllist3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.coinduct_strong
% 0.21/0.47 thf(fact_15_id__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( id @ A )
% 0.21/0.47 = ( ^ [X2: A] : X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % id_def
% 0.21/0.47 thf(fact_16_eq__id__iff,axiom,
% 0.21/0.47 ! [A: $tType,F: A > A] :
% 0.21/0.47 ( ( ! [X2: A] :
% 0.21/0.47 ( ( F @ X2 )
% 0.21/0.47 = X2 ) )
% 0.21/0.47 = ( F
% 0.21/0.47 = ( id @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_id_iff
% 0.21/0.47 thf(fact_17_tllist_Osel_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,Aa: $tType,X21: Aa,X22: tLList446370796tllist @ Aa @ A] :
% 0.21/0.47 ( ( tLList2110128105rminal @ Aa @ A @ ( tLList1992840728_TCons @ Aa @ A @ X21 @ X22 ) )
% 0.21/0.47 = ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ Aa @ A ) > A ) @ X22 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.sel(2)
% 0.21/0.47 thf(fact_18_tllist_Oset__sel_I3_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.21/0.47 => ( member @ B @ ( tLList2110128105rminal @ A @ B @ A2 ) @ ( tLList457864275tllist @ A @ B @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.set_sel(3)
% 0.21/0.47 thf(fact_19_tllist_Oset__sel_I4_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,Xc: B] :
% 0.21/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.21/0.47 => ( ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) )
% 0.21/0.47 => ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.set_sel(4)
% 0.21/0.47 thf(fact_20_tllist_Oset__sel_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,X3: A] :
% 0.21/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.21/0.47 => ( ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) )
% 0.21/0.47 => ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.set_sel(2)
% 0.21/0.47 thf(fact_21_tllist_Osplit__sel,axiom,
% 0.21/0.47 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( P @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 0.21/0.47 = ( ( ( Tllist
% 0.21/0.47 = ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 0.21/0.47 => ( P @ ( F1 @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) ) )
% 0.21/0.47 & ( ( Tllist
% 0.21/0.47 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) )
% 0.21/0.47 => ( P @ ( F2 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.split_sel
% 0.21/0.47 thf(fact_22_tllist_Oinject_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B,Y21: A,Y22: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( ( tLList1992840728_TCons @ A @ B @ X21 @ X22 )
% 0.21/0.47 = ( tLList1992840728_TCons @ A @ B @ Y21 @ Y22 ) )
% 0.21/0.47 = ( ( X21 = Y21 )
% 0.21/0.47 & ( X22 = Y22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.inject(2)
% 0.21/0.47 thf(fact_23_tllist_Ocollapse_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.21/0.47 => ( ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) )
% 0.21/0.47 = Tllist ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.collapse(2)
% 0.21/0.47 thf(fact_24_tllist_Osel_I3_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.21/0.47 = X21 ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.sel(3)
% 0.21/0.47 thf(fact_25_tllist_Osimps_I23_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( tLList457864275tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.21/0.47 = ( tLList457864275tllist @ A @ B @ X22 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.simps(23)
% 0.21/0.47 thf(fact_26_tllist_Oset__cases_I1_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,E2: A,A2: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( member @ A @ E2 @ ( tLList1719791291e_tset @ A @ B @ A2 ) )
% 0.21/0.47 => ( ! [Z2: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( A2
% 0.21/0.47 != ( tLList1992840728_TCons @ A @ B @ E2 @ Z2 ) )
% 0.21/0.47 => ~ ! [Z1: A,Z2: tLList446370796tllist @ A @ B] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( tLList1992840728_TCons @ A @ B @ Z1 @ Z2 ) )
% 0.21/0.47 => ~ ( member @ A @ E2 @ ( tLList1719791291e_tset @ A @ B @ Z2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.set_cases(1)
% 0.21/0.47 thf(fact_27_tllist_Oset__induct_I1_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,X3: A,A2: tLList446370796tllist @ A @ B,P: A > ( tLList446370796tllist @ A @ B ) > $o] :
% 0.21/0.47 ( ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ A2 ) )
% 0.21/0.47 => ( ! [Z1: A,Z2: tLList446370796tllist @ A @ B] : ( P @ Z1 @ ( tLList1992840728_TCons @ A @ B @ Z1 @ Z2 ) )
% 0.21/0.47 => ( ! [Z1: A,Z2: tLList446370796tllist @ A @ B,Xa: A] :
% 0.21/0.47 ( ( member @ A @ Xa @ ( tLList1719791291e_tset @ A @ B @ Z2 ) )
% 0.21/0.47 => ( ( P @ Xa @ Z2 )
% 0.21/0.47 => ( P @ Xa @ ( tLList1992840728_TCons @ A @ B @ Z1 @ Z2 ) ) ) )
% 0.21/0.47 => ( P @ X3 @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.set_induct(1)
% 0.21/0.47 thf(fact_28_tllist_Oset__intros_I4_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,Xc: B,A2a: tLList446370796tllist @ A @ B,A1a: A] :
% 0.21/0.47 ( ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ A2a ) )
% 0.21/0.47 => ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1a @ A2a ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.set_intros(4)
% 0.21/0.47 thf(fact_29_tllist_Oset__intros_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,X3: A,A22: tLList446370796tllist @ A @ B,A1: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ A22 ) )
% 0.21/0.47 => ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1 @ A22 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.set_intros(2)
% 0.21/0.47 thf(fact_30_tllist_Oset__intros_I1_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,A1: A,A22: tLList446370796tllist @ A @ B] : ( member @ A @ A1 @ ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1 @ A22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tllist.set_intros(1)
% 0.21/0.47 thf(fact_31_tllist_Oset__induct_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,Aa: $tType,X3: A,A2: tLList446370796tllist @ Aa @ A,P: A > ( tLList446370796tllist @ Aa @ A ) > $o] :
% 0.21/0.47 ( ( member @ A @ X3 @ ( tLList457864275tllist @ Aa @ A @ A2 ) )
% 0.21/0.47 => ( ! [Z: A] : ( P @ Z @ ( tLList57907754e_TNil @ A @ Aa @ Z ) )
% 0.21/0.47 => ( ! [Z1: Aa,Z2: tLList446370796tllist @ Aa @ A,Xb: A] :
% 0.21/0.47 ( ( member @ A @ Xb @ ( tLList457864275tllist @ Aa @ A @ Z2 ) )
% 0.21/0.47 => ( ( P @ Xb @ Z2 )
% 0.21/0.47 => ( P @ Xb @ ( tLList1992840728_TCons @ Aa @ A @ Z1 @ Z2 ) ) ) )
% 0.21/0.47 => ( P @ X3 @ A2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.set_induct(2)
% 0.33/0.47 thf(fact_32_tllist_Oset__cases_I2_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,E2: B,A2: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( member @ B @ E2 @ ( tLList457864275tllist @ A @ B @ A2 ) )
% 0.33/0.47 => ( ( A2
% 0.33/0.47 != ( tLList57907754e_TNil @ B @ A @ E2 ) )
% 0.33/0.47 => ~ ! [Z1: A,Z2: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( A2
% 0.33/0.47 = ( tLList1992840728_TCons @ A @ B @ Z1 @ Z2 ) )
% 0.33/0.47 => ~ ( member @ B @ E2 @ ( tLList457864275tllist @ A @ B @ Z2 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.set_cases(2)
% 0.33/0.47 thf(fact_33_tllist_Oset__sel_I1_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.33/0.47 => ( member @ A @ ( tLList_Mirabelle_thd @ A @ B @ A2 ) @ ( tLList1719791291e_tset @ A @ B @ A2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.set_sel(1)
% 0.33/0.47 thf(fact_34_tllist_OdiscI_I2_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( Tllist
% 0.33/0.47 = ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.33/0.47 => ~ ( tLList1968894004s_TNil @ A @ B @ Tllist ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.discI(2)
% 0.33/0.47 thf(fact_35_tllist_Odisc_I2_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.disc(2)
% 0.33/0.47 thf(fact_36_tllist_Oexhaust,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,Y: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ! [X13: B] :
% 0.33/0.47 ( Y
% 0.33/0.47 != ( tLList57907754e_TNil @ B @ A @ X13 ) )
% 0.33/0.47 => ~ ! [X212: A,X222: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( Y
% 0.33/0.47 != ( tLList1992840728_TCons @ A @ B @ X212 @ X222 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.exhaust
% 0.33/0.47 thf(fact_37_tllist_Odistinct_I1_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,X1: B,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( tLList57907754e_TNil @ B @ A @ X1 )
% 0.33/0.47 != ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.distinct(1)
% 0.33/0.47 thf(fact_38_tllist_Osel_I5_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.33/0.47 = X22 ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.sel(5)
% 0.33/0.47 thf(fact_39_tllist_Osimps_I6_J,axiom,
% 0.33/0.47 ! [C: $tType,B: $tType,A: $tType,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.33/0.47 = ( F2 @ X21 @ X22 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.simps(6)
% 0.33/0.47 thf(fact_40_tllist_Oset__intros_I3_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,Aa2: B] : ( member @ B @ Aa2 @ ( tLList457864275tllist @ A @ B @ ( tLList57907754e_TNil @ B @ A @ Aa2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.set_intros(3)
% 0.33/0.47 thf(fact_41_tllist_Oexhaust__sel,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( Tllist
% 0.33/0.47 != ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 0.33/0.47 => ( Tllist
% 0.33/0.47 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.exhaust_sel
% 0.33/0.47 thf(fact_42_tllist_Osplit__sel__asm,axiom,
% 0.33/0.47 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( P @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 0.33/0.47 = ( ~ ( ( ( Tllist
% 0.33/0.47 = ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 0.33/0.47 & ~ ( P @ ( F1 @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) ) )
% 0.33/0.47 | ( ( Tllist
% 0.33/0.47 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) )
% 0.33/0.47 & ~ ( P @ ( F2 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.split_sel_asm
% 0.33/0.47 thf(fact_43_tllist_Orel__coinduct,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,P: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o,X3: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,R2: B > D > $o,R1: A > C > $o] :
% 0.33/0.47 ( ( P @ X3 @ Y )
% 0.33/0.47 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ C @ D] :
% 0.33/0.47 ( ( P @ Tllist4 @ Tllist5 )
% 0.33/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.33/0.47 = ( tLList1968894004s_TNil @ C @ D @ Tllist5 ) )
% 0.33/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.33/0.47 => ( ( tLList1968894004s_TNil @ C @ D @ Tllist5 )
% 0.33/0.47 => ( R2 @ ( tLList2110128105rminal @ A @ B @ Tllist4 ) @ ( tLList2110128105rminal @ C @ D @ Tllist5 ) ) ) )
% 0.33/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.33/0.47 => ( ~ ( tLList1968894004s_TNil @ C @ D @ Tllist5 )
% 0.33/0.47 => ( ( R1 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_thd @ C @ D @ Tllist5 ) )
% 0.33/0.47 & ( P @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ C @ D @ Tllist5 ) ) ) ) ) ) )
% 0.33/0.47 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X3 @ Y ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_coinduct
% 0.33/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.33/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.33/0.47 = ( P @ A2 ) ) ).
% 0.33/0.47
% 0.33/0.47 % mem_Collect_eq
% 0.33/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( collect @ A
% 0.33/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.33/0.47 = A3 ) ).
% 0.33/0.47
% 0.33/0.47 % Collect_mem_eq
% 0.33/0.47 thf(fact_46_Collect__cong,axiom,
% 0.33/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.33/0.47 ( ! [X4: A] :
% 0.33/0.47 ( ( P @ X4 )
% 0.33/0.47 = ( Q @ X4 ) )
% 0.33/0.47 => ( ( collect @ A @ P )
% 0.33/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Collect_cong
% 0.33/0.47 thf(fact_47_ext,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.33/0.47 ( ! [X4: A] :
% 0.33/0.47 ( ( F @ X4 )
% 0.33/0.47 = ( G @ X4 ) )
% 0.33/0.47 => ( F = G ) ) ).
% 0.33/0.47
% 0.33/0.47 % ext
% 0.33/0.47 thf(fact_48_tllist_Orel__sel,axiom,
% 0.33/0.47 ! [B: $tType,D: $tType,C: $tType,A: $tType] :
% 0.33/0.47 ( ( tLList1380991092t_all2 @ A @ C @ B @ D )
% 0.33/0.47 = ( ^ [R12: A > C > $o,R22: B > D > $o,A4: tLList446370796tllist @ A @ B,B2: tLList446370796tllist @ C @ D] :
% 0.33/0.47 ( ( ( tLList1968894004s_TNil @ A @ B @ A4 )
% 0.33/0.47 = ( tLList1968894004s_TNil @ C @ D @ B2 ) )
% 0.33/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ A4 )
% 0.33/0.47 => ( ( tLList1968894004s_TNil @ C @ D @ B2 )
% 0.33/0.47 => ( R22 @ ( tLList2110128105rminal @ A @ B @ A4 ) @ ( tLList2110128105rminal @ C @ D @ B2 ) ) ) )
% 0.33/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ A4 )
% 0.33/0.47 => ( ~ ( tLList1968894004s_TNil @ C @ D @ B2 )
% 0.33/0.47 => ( ( R12 @ ( tLList_Mirabelle_thd @ A @ B @ A4 ) @ ( tLList_Mirabelle_thd @ C @ D @ B2 ) )
% 0.33/0.47 & ( tLList1380991092t_all2 @ A @ C @ B @ D @ R12 @ R22 @ ( tLList_Mirabelle_ttl @ A @ B @ A4 ) @ ( tLList_Mirabelle_ttl @ C @ D @ B2 ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_sel
% 0.33/0.47 thf(fact_49_tllist_Opred__cong,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,P1: A > $o,P1a: A > $o,P2: B > $o,P2a: B > $o] :
% 0.33/0.47 ( ( X3 = Ya )
% 0.33/0.47 => ( ! [Z1: A] :
% 0.33/0.47 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 0.33/0.47 => ( ( P1 @ Z1 )
% 0.33/0.47 = ( P1a @ Z1 ) ) )
% 0.33/0.47 => ( ! [Z2: B] :
% 0.33/0.47 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 0.33/0.47 => ( ( P2 @ Z2 )
% 0.33/0.47 = ( P2a @ Z2 ) ) )
% 0.33/0.47 => ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ X3 )
% 0.33/0.47 = ( tLList11265572tllist @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.pred_cong
% 0.33/0.47 thf(fact_50_tllist_Opred__mono__strong,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,X3: tLList446370796tllist @ A @ B,P1a: A > $o,P2a: B > $o] :
% 0.33/0.47 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ X3 )
% 0.33/0.47 => ( ! [Z1: A] :
% 0.33/0.47 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 0.33/0.47 => ( ( P1 @ Z1 )
% 0.33/0.47 => ( P1a @ Z1 ) ) )
% 0.33/0.47 => ( ! [Z2: B] :
% 0.33/0.47 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 0.33/0.47 => ( ( P2 @ Z2 )
% 0.33/0.47 => ( P2a @ Z2 ) ) )
% 0.33/0.47 => ( tLList11265572tllist @ A @ B @ P1a @ P2a @ X3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.pred_mono_strong
% 0.33/0.47 thf(fact_51_tllist_Ocorec__code,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,E: $tType] :
% 0.33/0.47 ( ( tLList1614408749tllist @ E @ B @ A )
% 0.33/0.47 = ( ^ [P3: E > $o,G1: E > B,G21: E > A,Q22: E > $o,G221: E > ( tLList446370796tllist @ A @ B ),G222: E > E,A4: E] : ( if @ ( tLList446370796tllist @ A @ B ) @ ( P3 @ A4 ) @ ( tLList57907754e_TNil @ B @ A @ ( G1 @ A4 ) ) @ ( tLList1992840728_TCons @ A @ B @ ( G21 @ A4 ) @ ( if @ ( tLList446370796tllist @ A @ B ) @ ( Q22 @ A4 ) @ ( G221 @ A4 ) @ ( tLList1614408749tllist @ E @ B @ A @ P3 @ G1 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec_code
% 0.33/0.47 thf(fact_52_tllist_Osimps_I21_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.33/0.47 = ( insert @ A @ X21 @ ( tLList1719791291e_tset @ A @ B @ X22 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.simps(21)
% 0.33/0.47 thf(fact_53_tllist_Omap__cong,axiom,
% 0.33/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,F1: A > C,G12: A > C,F2: B > D,G2: B > D] :
% 0.33/0.47 ( ( X3 = Ya )
% 0.33/0.47 => ( ! [Z1: A] :
% 0.33/0.47 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 0.33/0.47 => ( ( F1 @ Z1 )
% 0.33/0.47 = ( G12 @ Z1 ) ) )
% 0.33/0.47 => ( ! [Z2: B] :
% 0.33/0.47 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 0.33/0.47 => ( ( F2 @ Z2 )
% 0.33/0.47 = ( G2 @ Z2 ) ) )
% 0.33/0.47 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X3 )
% 0.33/0.47 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G12 @ G2 @ Ya ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.map_cong
% 0.33/0.47 thf(fact_54_tllist_Omap__cong0,axiom,
% 0.33/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,F1: A > C,G12: A > C,F2: B > D,G2: B > D] :
% 0.33/0.47 ( ! [Z1: A] :
% 0.33/0.47 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 0.33/0.47 => ( ( F1 @ Z1 )
% 0.33/0.47 = ( G12 @ Z1 ) ) )
% 0.33/0.47 => ( ! [Z2: B] :
% 0.33/0.47 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 0.33/0.47 => ( ( F2 @ Z2 )
% 0.33/0.47 = ( G2 @ Z2 ) ) )
% 0.33/0.47 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X3 )
% 0.33/0.47 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G12 @ G2 @ X3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.map_cong0
% 0.33/0.47 thf(fact_55_tllist_Oinj__map__strong,axiom,
% 0.33/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,Xa2: tLList446370796tllist @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
% 0.33/0.47 ( ! [Z1: A,Z1a: A] :
% 0.33/0.47 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 0.33/0.47 => ( ( member @ A @ Z1a @ ( tLList1719791291e_tset @ A @ B @ Xa2 ) )
% 0.33/0.47 => ( ( ( F1 @ Z1 )
% 0.33/0.47 = ( F1a @ Z1a ) )
% 0.33/0.47 => ( Z1 = Z1a ) ) ) )
% 0.33/0.47 => ( ! [Z2: B,Z2a: B] :
% 0.33/0.47 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 0.33/0.47 => ( ( member @ B @ Z2a @ ( tLList457864275tllist @ A @ B @ Xa2 ) )
% 0.33/0.47 => ( ( ( F2 @ Z2 )
% 0.33/0.47 = ( F2a @ Z2a ) )
% 0.33/0.47 => ( Z2 = Z2a ) ) ) )
% 0.33/0.47 => ( ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X3 )
% 0.33/0.47 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1a @ F2a @ Xa2 ) )
% 0.33/0.47 => ( X3 = Xa2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.inj_map_strong
% 0.33/0.47 thf(fact_56_tllist_Omap__sel_I2_J,axiom,
% 0.33/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 0.33/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.33/0.47 => ( ( tLList_Mirabelle_thd @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 0.33/0.47 = ( F1 @ ( tLList_Mirabelle_thd @ A @ B @ A2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.map_sel(2)
% 0.33/0.47 thf(fact_57_tllist_Orel__inject_I2_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X21: A,X22: tLList446370796tllist @ A @ B,Y21: C,Y22: tLList446370796tllist @ C @ D] :
% 0.33/0.47 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) )
% 0.33/0.47 = ( ( R1 @ X21 @ Y21 )
% 0.33/0.47 & ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_inject(2)
% 0.33/0.47 thf(fact_58_tllist_Omap__disc__iff,axiom,
% 0.33/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,A2: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( tLList1968894004s_TNil @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 0.33/0.47 = ( tLList1968894004s_TNil @ A @ B @ A2 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.map_disc_iff
% 0.33/0.47 thf(fact_59_tllist_Orel__inject_I1_J,axiom,
% 0.33/0.47 ! [C: $tType,A: $tType,B: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,X1: B,Y1: D] :
% 0.33/0.47 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList57907754e_TNil @ D @ C @ Y1 ) )
% 0.33/0.47 = ( R2 @ X1 @ Y1 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_inject(1)
% 0.33/0.47 thf(fact_60_tllist_Ocorec__disc__iff_I2_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E,A2: E] :
% 0.33/0.47 ( ( ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) )
% 0.33/0.47 = ( ~ ( P4 @ A2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec_disc_iff(2)
% 0.33/0.47 thf(fact_61_tllist_Ocorec__disc__iff_I1_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E,A2: E] :
% 0.33/0.47 ( ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.33/0.47 = ( P4 @ A2 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec_disc_iff(1)
% 0.33/0.47 thf(fact_62_tllist_Opred__inject_I2_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,A2: A,Aa2: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ ( tLList1992840728_TCons @ A @ B @ A2 @ Aa2 ) )
% 0.33/0.47 = ( ( P1 @ A2 )
% 0.33/0.47 & ( tLList11265572tllist @ A @ B @ P1 @ P2 @ Aa2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.pred_inject(2)
% 0.33/0.47 thf(fact_63_tllist_Opred__inject_I1_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,P1: A > $o,P2: B > $o,A2: B] :
% 0.33/0.47 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ ( tLList57907754e_TNil @ B @ A @ A2 ) )
% 0.33/0.47 = ( P2 @ A2 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.pred_inject(1)
% 0.33/0.47 thf(fact_64_tllist_Orel__refl,axiom,
% 0.33/0.47 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X3: tLList446370796tllist @ C @ D] :
% 0.33/0.47 ( ! [X4: C] : ( R1a @ X4 @ X4 )
% 0.33/0.47 => ( ! [X4: D] : ( R2a @ X4 @ X4 )
% 0.33/0.47 => ( tLList1380991092t_all2 @ C @ C @ D @ D @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_refl
% 0.33/0.47 thf(fact_65_tllist_Orel__eq,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( tLList1380991092t_all2 @ A @ A @ B @ B
% 0.33/0.47 @ ^ [Y2: A,Z3: A] : ( Y2 = Z3 )
% 0.33/0.47 @ ^ [Y2: B,Z3: B] : ( Y2 = Z3 ) )
% 0.33/0.47 = ( ^ [Y2: tLList446370796tllist @ A @ B,Z3: tLList446370796tllist @ A @ B] : ( Y2 = Z3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_eq
% 0.33/0.47 thf(fact_66_tllist_Orel__intros_I2_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,X21: A,Y21: C,R2: B > D > $o,X22: tLList446370796tllist @ A @ B,Y22: tLList446370796tllist @ C @ D] :
% 0.33/0.47 ( ( R1 @ X21 @ Y21 )
% 0.33/0.47 => ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 )
% 0.33/0.47 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_intros(2)
% 0.33/0.47 thf(fact_67_tllist_Orel__intros_I1_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,C: $tType,D: $tType,R2: B > D > $o,X1: B,Y1: D,R1: A > C > $o] :
% 0.33/0.47 ( ( R2 @ X1 @ Y1 )
% 0.33/0.47 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList57907754e_TNil @ D @ C @ Y1 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_intros(1)
% 0.33/0.47 thf(fact_68_tllist_Omap__id,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,T: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( tLList1669959861e_tmap @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) @ T )
% 0.33/0.47 = T ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.map_id
% 0.33/0.47 thf(fact_69_tllist_Omap__id0,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( tLList1669959861e_tmap @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 0.33/0.47 = ( id @ ( tLList446370796tllist @ A @ B ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.map_id0
% 0.33/0.47 thf(fact_70_tllist_Osimps_I15_J,axiom,
% 0.33/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.33/0.47 = ( tLList1992840728_TCons @ C @ D @ ( F1 @ X21 ) @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X22 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.simps(15)
% 0.33/0.47 thf(fact_71_tllist_Osimps_I14_J,axiom,
% 0.33/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,F1: A > C,F2: B > D,X1: B] :
% 0.33/0.47 ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.33/0.47 = ( tLList57907754e_TNil @ D @ C @ ( F2 @ X1 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.simps(14)
% 0.33/0.47 thf(fact_72_tllist_Ocorec__disc_I2_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.33/0.47 ( ~ ( P4 @ A2 )
% 0.33/0.47 => ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec_disc(2)
% 0.33/0.47 thf(fact_73_tllist_Ocorec__disc_I1_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.33/0.47 ( ( P4 @ A2 )
% 0.33/0.47 => ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec_disc(1)
% 0.33/0.47 thf(fact_74_tllist_Ocorec_I2_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.33/0.47 ( ~ ( P4 @ A2 )
% 0.33/0.47 => ( ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.33/0.47 = ( tLList1992840728_TCons @ A @ B @ ( G212 @ A2 ) @ ( if @ ( tLList446370796tllist @ A @ B ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec(2)
% 0.33/0.47 thf(fact_75_tllist_Ocorec_I1_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.33/0.47 ( ( P4 @ A2 )
% 0.33/0.47 => ( ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.33/0.47 = ( tLList57907754e_TNil @ B @ A @ ( G12 @ A2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec(1)
% 0.33/0.47 thf(fact_76_tllist_Ocorec__sel_I3_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,Q222: E > $o,G12: E > B,G212: E > A,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.33/0.47 ( ~ ( P4 @ A2 )
% 0.33/0.47 => ( ( ( Q222 @ A2 )
% 0.33/0.47 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.33/0.47 = ( G2212 @ A2 ) ) )
% 0.33/0.47 & ( ~ ( Q222 @ A2 )
% 0.33/0.47 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.33/0.47 = ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec_sel(3)
% 0.33/0.47 thf(fact_77_tllist_Ocorec__sel_I1_J,axiom,
% 0.33/0.47 ! [Aa: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > A,G212: E > Aa,Q222: E > $o,G2212: E > ( tLList446370796tllist @ Aa @ A ),G2222: E > E] :
% 0.33/0.47 ( ( P4 @ A2 )
% 0.33/0.47 => ( ( tLList2110128105rminal @ Aa @ A @ ( tLList1614408749tllist @ E @ A @ Aa @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.33/0.47 = ( G12 @ A2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec_sel(1)
% 0.33/0.47 thf(fact_78_tllist_Ocorec__sel_I2_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.33/0.47 ( ~ ( P4 @ A2 )
% 0.33/0.47 => ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.33/0.47 = ( G212 @ A2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.corec_sel(2)
% 0.33/0.47 thf(fact_79_tllist_Orel__distinct_I2_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,Y21: A,Y22: tLList446370796tllist @ A @ B,X1: D] :
% 0.33/0.47 ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ Y21 @ Y22 ) @ ( tLList57907754e_TNil @ D @ C @ X1 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_distinct(2)
% 0.33/0.47 thf(fact_80_tllist_Orel__distinct_I1_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X1: B,Y21: C,Y22: tLList446370796tllist @ C @ D] :
% 0.33/0.47 ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_distinct(1)
% 0.33/0.47 thf(fact_81_tllist_Orel__cases,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,A2: tLList446370796tllist @ A @ B,B3: tLList446370796tllist @ C @ D] :
% 0.33/0.47 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ A2 @ B3 )
% 0.33/0.47 => ( ! [X4: B] :
% 0.33/0.47 ( ( A2
% 0.33/0.47 = ( tLList57907754e_TNil @ B @ A @ X4 ) )
% 0.33/0.47 => ! [Y3: D] :
% 0.33/0.47 ( ( B3
% 0.33/0.47 = ( tLList57907754e_TNil @ D @ C @ Y3 ) )
% 0.33/0.47 => ~ ( R2 @ X4 @ Y3 ) ) )
% 0.33/0.47 => ~ ! [X1a: A,X23: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ( A2
% 0.33/0.47 = ( tLList1992840728_TCons @ A @ B @ X1a @ X23 ) )
% 0.33/0.47 => ! [Y1a: C,Y23: tLList446370796tllist @ C @ D] :
% 0.33/0.47 ( ( B3
% 0.33/0.47 = ( tLList1992840728_TCons @ C @ D @ Y1a @ Y23 ) )
% 0.33/0.47 => ( ( R1 @ X1a @ Y1a )
% 0.33/0.47 => ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X23 @ Y23 ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_cases
% 0.33/0.47 thf(fact_82_tllist_Orel__refl__strong,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 0.33/0.47 ( ! [Z1: A] :
% 0.33/0.47 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 0.33/0.47 => ( R1a @ Z1 @ Z1 ) )
% 0.33/0.47 => ( ! [Z2: B] :
% 0.33/0.47 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 0.33/0.47 => ( R2a @ Z2 @ Z2 ) )
% 0.33/0.47 => ( tLList1380991092t_all2 @ A @ A @ B @ B @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_refl_strong
% 0.33/0.47 thf(fact_83_tllist_Orel__mono__strong,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X3: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 0.33/0.47 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X3 @ Y )
% 0.33/0.47 => ( ! [Z1: A,Y12: C] :
% 0.33/0.47 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 0.33/0.47 => ( ( member @ C @ Y12 @ ( tLList1719791291e_tset @ C @ D @ Y ) )
% 0.33/0.47 => ( ( R1 @ Z1 @ Y12 )
% 0.33/0.47 => ( R1a @ Z1 @ Y12 ) ) ) )
% 0.33/0.47 => ( ! [Z2: B,Y23: D] :
% 0.33/0.47 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 0.33/0.47 => ( ( member @ D @ Y23 @ ( tLList457864275tllist @ C @ D @ Y ) )
% 0.33/0.47 => ( ( R2 @ Z2 @ Y23 )
% 0.33/0.47 => ( R2a @ Z2 @ Y23 ) ) ) )
% 0.33/0.47 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a @ X3 @ Y ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_mono_strong
% 0.33/0.47 thf(fact_84_tllist_Orel__cong,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,X3: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,Xa2: tLList446370796tllist @ C @ D,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
% 0.33/0.47 ( ( X3 = Ya )
% 0.33/0.47 => ( ( Y = Xa2 )
% 0.33/0.47 => ( ! [Z1: A,Y12: C] :
% 0.33/0.47 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 0.33/0.47 => ( ( member @ C @ Y12 @ ( tLList1719791291e_tset @ C @ D @ Xa2 ) )
% 0.33/0.47 => ( ( R1 @ Z1 @ Y12 )
% 0.33/0.47 = ( R1a @ Z1 @ Y12 ) ) ) )
% 0.33/0.47 => ( ! [Z2: B,Y23: D] :
% 0.33/0.47 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 0.33/0.47 => ( ( member @ D @ Y23 @ ( tLList457864275tllist @ C @ D @ Xa2 ) )
% 0.33/0.47 => ( ( R2 @ Z2 @ Y23 )
% 0.33/0.47 = ( R2a @ Z2 @ Y23 ) ) ) )
% 0.33/0.47 => ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X3 @ Y )
% 0.33/0.47 = ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa2 ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_cong
% 0.33/0.47 thf(fact_85_tllist_Omap__sel_I3_J,axiom,
% 0.33/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 0.33/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.33/0.47 => ( ( tLList_Mirabelle_ttl @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 0.33/0.47 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.map_sel(3)
% 0.33/0.47 thf(fact_86_tllist_Omap__sel_I1_J,axiom,
% 0.33/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 0.33/0.47 ( ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.33/0.47 => ( ( tLList2110128105rminal @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 0.33/0.47 = ( F2 @ ( tLList2110128105rminal @ A @ B @ A2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.map_sel(1)
% 0.33/0.47 thf(fact_87_insert__absorb2,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A] :
% 0.33/0.47 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A3 ) )
% 0.33/0.47 = ( insert @ A @ X3 @ A3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_absorb2
% 0.33/0.47 thf(fact_88_insert__iff,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.33/0.47 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 0.33/0.47 = ( ( A2 = B3 )
% 0.33/0.47 | ( member @ A @ A2 @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_iff
% 0.33/0.47 thf(fact_89_insertCI,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 0.33/0.47 ( ( ~ ( member @ A @ A2 @ B4 )
% 0.33/0.47 => ( A2 = B3 ) )
% 0.33/0.47 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insertCI
% 0.33/0.47 thf(fact_90_tllist_Osimps_I22_J,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,X1: B] :
% 0.33/0.47 ( ( tLList457864275tllist @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.33/0.47 = ( insert @ B @ X1 @ ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.simps(22)
% 0.33/0.47 thf(fact_91_tllist_Opred__set,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( tLList11265572tllist @ A @ B )
% 0.33/0.47 = ( ^ [P12: A > $o,P22: B > $o,X2: tLList446370796tllist @ A @ B] :
% 0.33/0.47 ( ! [Y4: A] :
% 0.33/0.47 ( ( member @ A @ Y4 @ ( tLList1719791291e_tset @ A @ B @ X2 ) )
% 0.33/0.47 => ( P12 @ Y4 ) )
% 0.33/0.47 & ! [Y4: B] :
% 0.33/0.47 ( ( member @ B @ Y4 @ ( tLList457864275tllist @ A @ B @ X2 ) )
% 0.33/0.47 => ( P22 @ Y4 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.pred_set
% 0.33/0.47 thf(fact_92_mk__disjoint__insert,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.33/0.47 ( ( member @ A @ A2 @ A3 )
% 0.33/0.47 => ? [B5: set @ A] :
% 0.33/0.47 ( ( A3
% 0.33/0.47 = ( insert @ A @ A2 @ B5 ) )
% 0.33/0.47 & ~ ( member @ A @ A2 @ B5 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % mk_disjoint_insert
% 0.33/0.47 thf(fact_93_insert__commute,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,Y: A,A3: set @ A] :
% 0.33/0.47 ( ( insert @ A @ X3 @ ( insert @ A @ Y @ A3 ) )
% 0.33/0.47 = ( insert @ A @ Y @ ( insert @ A @ X3 @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_commute
% 0.33/0.47 thf(fact_94_empty__iff,axiom,
% 0.33/0.47 ! [A: $tType,C2: A] :
% 0.33/0.47 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % empty_iff
% 0.33/0.47 thf(fact_95_all__not__in__conv,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( ! [X2: A] :
% 0.33/0.47 ~ ( member @ A @ X2 @ A3 ) )
% 0.33/0.47 = ( A3
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % all_not_in_conv
% 0.33/0.47 thf(fact_96_Collect__empty__eq,axiom,
% 0.33/0.47 ! [A: $tType,P: A > $o] :
% 0.33/0.47 ( ( ( collect @ A @ P )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( ! [X2: A] :
% 0.33/0.47 ~ ( P @ X2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Collect_empty_eq
% 0.33/0.47 thf(fact_97_empty__Collect__eq,axiom,
% 0.33/0.47 ! [A: $tType,P: A > $o] :
% 0.33/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.33/0.47 = ( collect @ A @ P ) )
% 0.33/0.47 = ( ! [X2: A] :
% 0.33/0.47 ~ ( P @ X2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % empty_Collect_eq
% 0.33/0.47 thf(fact_98_singletonI,axiom,
% 0.33/0.47 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % singletonI
% 0.33/0.47 thf(fact_99_ball__empty,axiom,
% 0.33/0.47 ! [A: $tType,P: A > $o,X: A] :
% 0.33/0.47 ( ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 => ( P @ X ) ) ).
% 0.33/0.47
% 0.33/0.47 % ball_empty
% 0.33/0.47 thf(fact_100_singleton__inject,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,B3: A] :
% 0.33/0.47 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.33/0.47 => ( A2 = B3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % singleton_inject
% 0.33/0.47 thf(fact_101_insert__not__empty,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.33/0.47 ( ( insert @ A @ A2 @ A3 )
% 0.33/0.47 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_not_empty
% 0.33/0.47 thf(fact_102_doubleton__eq__iff,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,B3: A,C2: A,D2: A] :
% 0.33/0.47 ( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.33/0.47 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.33/0.47 = ( ( ( A2 = C2 )
% 0.33/0.47 & ( B3 = D2 ) )
% 0.33/0.47 | ( ( A2 = D2 )
% 0.33/0.47 & ( B3 = C2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % doubleton_eq_iff
% 0.33/0.47 thf(fact_103_singleton__iff,axiom,
% 0.33/0.47 ! [A: $tType,B3: A,A2: A] :
% 0.33/0.47 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.33/0.47 = ( B3 = A2 ) ) ).
% 0.33/0.47
% 0.33/0.47 % singleton_iff
% 0.33/0.47 thf(fact_104_singletonD,axiom,
% 0.33/0.47 ! [A: $tType,B3: A,A2: A] :
% 0.33/0.47 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.33/0.47 => ( B3 = A2 ) ) ).
% 0.33/0.47
% 0.33/0.47 % singletonD
% 0.33/0.47 thf(fact_105_emptyE,axiom,
% 0.33/0.47 ! [A: $tType,A2: A] :
% 0.33/0.47 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % emptyE
% 0.33/0.47 thf(fact_106_Ball__def,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ball @ A )
% 0.33/0.47 = ( ^ [A5: set @ A,P5: A > $o] :
% 0.33/0.47 ! [X2: A] :
% 0.33/0.47 ( ( member @ A @ X2 @ A5 )
% 0.33/0.47 => ( P5 @ X2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Ball_def
% 0.33/0.47 thf(fact_107_equals0D,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,A2: A] :
% 0.33/0.47 ( ( A3
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % equals0D
% 0.33/0.47 thf(fact_108_equals0I,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ! [Y3: A] :
% 0.33/0.47 ~ ( member @ A @ Y3 @ A3 )
% 0.33/0.47 => ( A3
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % equals0I
% 0.33/0.47 thf(fact_109_ex__in__conv,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.33/0.47 = ( A3
% 0.33/0.47 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % ex_in_conv
% 0.33/0.47 thf(fact_110_tllist_Osimps_I20_J,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,X1: B] :
% 0.33/0.47 ( ( tLList1719791291e_tset @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.simps(20)
% 0.33/0.47 thf(fact_111_insertE,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.33/0.47 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 0.33/0.47 => ( ( A2 != B3 )
% 0.33/0.47 => ( member @ A @ A2 @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insertE
% 0.33/0.47 thf(fact_112_insertI1,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,B4: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % insertI1
% 0.33/0.47 thf(fact_113_insertI2,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 0.33/0.47 ( ( member @ A @ A2 @ B4 )
% 0.33/0.47 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insertI2
% 0.33/0.47 thf(fact_114_Set_Oset__insert,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A] :
% 0.33/0.47 ( ( member @ A @ X3 @ A3 )
% 0.33/0.47 => ~ ! [B5: set @ A] :
% 0.33/0.47 ( ( A3
% 0.33/0.47 = ( insert @ A @ X3 @ B5 ) )
% 0.33/0.47 => ( member @ A @ X3 @ B5 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Set.set_insert
% 0.33/0.47 thf(fact_115_insert__ident,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ~ ( member @ A @ X3 @ A3 )
% 0.33/0.47 => ( ~ ( member @ A @ X3 @ B4 )
% 0.33/0.47 => ( ( ( insert @ A @ X3 @ A3 )
% 0.33/0.47 = ( insert @ A @ X3 @ B4 ) )
% 0.33/0.47 = ( A3 = B4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_ident
% 0.33/0.47 thf(fact_116_insert__absorb,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.33/0.47 ( ( member @ A @ A2 @ A3 )
% 0.33/0.47 => ( ( insert @ A @ A2 @ A3 )
% 0.33/0.47 = A3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_absorb
% 0.33/0.47 thf(fact_117_insert__eq__iff,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A,B3: A,B4: set @ A] :
% 0.33/0.47 ( ~ ( member @ A @ A2 @ A3 )
% 0.33/0.47 => ( ~ ( member @ A @ B3 @ B4 )
% 0.33/0.47 => ( ( ( insert @ A @ A2 @ A3 )
% 0.33/0.47 = ( insert @ A @ B3 @ B4 ) )
% 0.33/0.47 = ( ( ( A2 = B3 )
% 0.33/0.47 => ( A3 = B4 ) )
% 0.33/0.47 & ( ( A2 != B3 )
% 0.33/0.47 => ? [C3: set @ A] :
% 0.33/0.47 ( ( A3
% 0.33/0.47 = ( insert @ A @ B3 @ C3 ) )
% 0.33/0.47 & ~ ( member @ A @ B3 @ C3 )
% 0.33/0.47 & ( B4
% 0.33/0.47 = ( insert @ A @ A2 @ C3 ) )
% 0.33/0.47 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_eq_iff
% 0.33/0.47 thf(fact_118_the__elem__eq,axiom,
% 0.33/0.47 ! [A: $tType,X3: A] :
% 0.33/0.47 ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.33/0.47 = X3 ) ).
% 0.33/0.47
% 0.33/0.47 % the_elem_eq
% 0.33/0.47 thf(fact_119_bot__apply,axiom,
% 0.33/0.47 ! [C: $tType,D: $tType] :
% 0.33/0.47 ( ( bot @ C @ ( type2 @ C ) )
% 0.33/0.47 => ( ( bot_bot @ ( D > C ) )
% 0.33/0.47 = ( ^ [X2: D] : ( bot_bot @ C ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % bot_apply
% 0.33/0.47 thf(fact_120_is__singletonI,axiom,
% 0.33/0.47 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % is_singletonI
% 0.33/0.47 thf(fact_121_override__on__emptyset,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.33/0.47 ( ( override_on @ A @ B @ F @ G @ ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = F ) ).
% 0.33/0.47
% 0.33/0.47 % override_on_emptyset
% 0.33/0.47 thf(fact_122_Set_Ois__empty__def,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( is_empty @ A )
% 0.33/0.47 = ( ^ [A5: set @ A] :
% 0.33/0.47 ( A5
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Set.is_empty_def
% 0.33/0.47 thf(fact_123_override__on__apply__notin,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,A2: A,A3: set @ A,F: A > B,G: A > B] :
% 0.33/0.47 ( ~ ( member @ A @ A2 @ A3 )
% 0.33/0.47 => ( ( override_on @ A @ B @ F @ G @ A3 @ A2 )
% 0.33/0.47 = ( F @ A2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % override_on_apply_notin
% 0.33/0.47 thf(fact_124_override__on__apply__in,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,A2: A,A3: set @ A,F: A > B,G: A > B] :
% 0.33/0.47 ( ( member @ A @ A2 @ A3 )
% 0.33/0.47 => ( ( override_on @ A @ B @ F @ G @ A3 @ A2 )
% 0.33/0.47 = ( G @ A2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % override_on_apply_in
% 0.33/0.47 thf(fact_125_bot__set__def,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.33/0.47 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % bot_set_def
% 0.33/0.47 thf(fact_126_override__on__def,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( override_on @ A @ B )
% 0.33/0.47 = ( ^ [F3: A > B,G3: A > B,A5: set @ A,A4: A] : ( if @ B @ ( member @ A @ A4 @ A5 ) @ ( G3 @ A4 ) @ ( F3 @ A4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % override_on_def
% 0.33/0.47 thf(fact_127_is__singleton__the__elem,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( is_singleton @ A )
% 0.33/0.47 = ( ^ [A5: set @ A] :
% 0.33/0.47 ( A5
% 0.33/0.47 = ( insert @ A @ ( the_elem @ A @ A5 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % is_singleton_the_elem
% 0.33/0.47 thf(fact_128_is__singletonI_H,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( A3
% 0.33/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 => ( ! [X4: A,Y3: A] :
% 0.33/0.47 ( ( member @ A @ X4 @ A3 )
% 0.33/0.47 => ( ( member @ A @ Y3 @ A3 )
% 0.33/0.47 => ( X4 = Y3 ) ) )
% 0.33/0.47 => ( is_singleton @ A @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % is_singletonI'
% 0.33/0.47 thf(fact_129_bot__fun__def,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( bot @ B @ ( type2 @ B ) )
% 0.33/0.47 => ( ( bot_bot @ ( A > B ) )
% 0.33/0.47 = ( ^ [X2: A] : ( bot_bot @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % bot_fun_def
% 0.33/0.47 thf(fact_130_is__singletonE,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( is_singleton @ A @ A3 )
% 0.33/0.47 => ~ ! [X4: A] :
% 0.33/0.47 ( A3
% 0.33/0.47 != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % is_singletonE
% 0.33/0.47 thf(fact_131_is__singleton__def,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( is_singleton @ A )
% 0.33/0.47 = ( ^ [A5: set @ A] :
% 0.33/0.47 ? [X2: A] :
% 0.33/0.47 ( A5
% 0.33/0.47 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % is_singleton_def
% 0.33/0.47 thf(fact_132_pairwise__singleton,axiom,
% 0.33/0.47 ! [A: $tType,P: A > A > $o,A3: A] : ( pairwise @ A @ P @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % pairwise_singleton
% 0.33/0.47 thf(fact_133_ball__reg,axiom,
% 0.33/0.47 ! [A: $tType,R: set @ A,P: A > $o,Q: A > $o] :
% 0.33/0.47 ( ! [X4: A] :
% 0.33/0.47 ( ( member @ A @ X4 @ R )
% 0.33/0.47 => ( ( P @ X4 )
% 0.33/0.47 => ( Q @ X4 ) ) )
% 0.33/0.47 => ( ! [X4: A] :
% 0.33/0.47 ( ( member @ A @ X4 @ R )
% 0.33/0.47 => ( P @ X4 ) )
% 0.33/0.47 => ! [X: A] :
% 0.33/0.47 ( ( member @ A @ X @ R )
% 0.33/0.47 => ( Q @ X ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % ball_reg
% 0.33/0.47 thf(fact_134_bot__empty__eq,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( bot_bot @ ( A > $o ) )
% 0.33/0.47 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % bot_empty_eq
% 0.33/0.47 thf(fact_135_Collect__empty__eq__bot,axiom,
% 0.33/0.47 ! [A: $tType,P: A > $o] :
% 0.33/0.47 ( ( ( collect @ A @ P )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( P
% 0.33/0.47 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Collect_empty_eq_bot
% 0.33/0.47 thf(fact_136_pairwise__def,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( pairwise @ A )
% 0.33/0.47 = ( ^ [R3: A > A > $o,S: set @ A] :
% 0.33/0.47 ! [X2: A] :
% 0.33/0.47 ( ( member @ A @ X2 @ S )
% 0.33/0.47 => ! [Y4: A] :
% 0.33/0.47 ( ( member @ A @ Y4 @ S )
% 0.33/0.47 => ( ( X2 != Y4 )
% 0.33/0.47 => ( R3 @ X2 @ Y4 ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % pairwise_def
% 0.33/0.47 thf(fact_137_pairwise__empty,axiom,
% 0.33/0.47 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % pairwise_empty
% 0.33/0.47 thf(fact_138_pairwise__insert,axiom,
% 0.33/0.47 ! [A: $tType,R4: A > A > $o,X3: A,S2: set @ A] :
% 0.33/0.47 ( ( pairwise @ A @ R4 @ ( insert @ A @ X3 @ S2 ) )
% 0.33/0.47 = ( ! [Y4: A] :
% 0.33/0.47 ( ( ( member @ A @ Y4 @ S2 )
% 0.33/0.47 & ( Y4 != X3 ) )
% 0.33/0.47 => ( ( R4 @ X3 @ Y4 )
% 0.33/0.47 & ( R4 @ Y4 @ X3 ) ) )
% 0.33/0.47 & ( pairwise @ A @ R4 @ S2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % pairwise_insert
% 0.33/0.47 thf(fact_139_in__inv__imagep,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( inv_imagep @ A @ B )
% 0.33/0.47 = ( ^ [R5: A > A > $o,F3: B > A,X2: B,Y4: B] : ( R5 @ ( F3 @ X2 ) @ ( F3 @ Y4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % in_inv_imagep
% 0.33/0.47 thf(fact_140_id__fcomp,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,G: A > B] :
% 0.33/0.47 ( ( fcomp @ A @ A @ B @ ( id @ A ) @ G )
% 0.33/0.47 = G ) ).
% 0.33/0.47
% 0.33/0.47 % id_fcomp
% 0.33/0.47 thf(fact_141_fcomp__id,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,F: A > B] :
% 0.33/0.47 ( ( fcomp @ A @ B @ B @ F @ ( id @ B ) )
% 0.33/0.47 = F ) ).
% 0.33/0.47
% 0.33/0.47 % fcomp_id
% 0.33/0.47 thf(fact_142_singleton__insert__inj__eq_H,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A,B3: A] :
% 0.33/0.47 ( ( ( insert @ A @ A2 @ A3 )
% 0.33/0.47 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.33/0.47 = ( ( A2 = B3 )
% 0.33/0.47 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % singleton_insert_inj_eq'
% 0.33/0.47 thf(fact_143_order__refl,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % order_refl
% 0.33/0.47 thf(fact_144_subsetI,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ! [X4: A] :
% 0.33/0.47 ( ( member @ A @ X4 @ A3 )
% 0.33/0.47 => ( member @ A @ X4 @ B4 ) )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % subsetI
% 0.33/0.47 thf(fact_145_subset__antisym,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 0.33/0.47 => ( A3 = B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_antisym
% 0.33/0.47 thf(fact_146_fcomp__apply,axiom,
% 0.33/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.33/0.47 ( ( fcomp @ B @ C @ A )
% 0.33/0.47 = ( ^ [F3: B > C,G3: C > A,X2: B] : ( G3 @ ( F3 @ X2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % fcomp_apply
% 0.33/0.47 thf(fact_147_subset__empty,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( A3
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_empty
% 0.33/0.47 thf(fact_148_empty__subsetI,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 0.33/0.47
% 0.33/0.47 % empty_subsetI
% 0.33/0.47 thf(fact_149_insert__subset,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A3 ) @ B4 )
% 0.33/0.47 = ( ( member @ A @ X3 @ B4 )
% 0.33/0.47 & ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_subset
% 0.33/0.47 thf(fact_150_singleton__insert__inj__eq,axiom,
% 0.33/0.47 ! [A: $tType,B3: A,A2: A,A3: set @ A] :
% 0.33/0.47 ( ( ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( insert @ A @ A2 @ A3 ) )
% 0.33/0.47 = ( ( A2 = B3 )
% 0.33/0.47 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % singleton_insert_inj_eq
% 0.33/0.47 thf(fact_151_bot_Oextremum,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.33/0.47
% 0.33/0.47 % bot.extremum
% 0.33/0.47 thf(fact_152_bot_Oextremum__unique,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.33/0.47 = ( A2
% 0.33/0.47 = ( bot_bot @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % bot.extremum_unique
% 0.33/0.47 thf(fact_153_bot_Oextremum__uniqueI,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.33/0.47 => ( A2
% 0.33/0.47 = ( bot_bot @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % bot.extremum_uniqueI
% 0.33/0.47 thf(fact_154_set__mp,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,X3: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ( member @ A @ X3 @ A3 )
% 0.33/0.47 => ( member @ A @ X3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % set_mp
% 0.33/0.47 thf(fact_155_in__mono,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,X3: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ( member @ A @ X3 @ A3 )
% 0.33/0.47 => ( member @ A @ X3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % in_mono
% 0.33/0.47 thf(fact_156_subsetD,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C2: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ( member @ A @ C2 @ A3 )
% 0.33/0.47 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subsetD
% 0.33/0.47 thf(fact_157_subsetCE,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C2: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ( member @ A @ C2 @ A3 )
% 0.33/0.47 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subsetCE
% 0.33/0.47 thf(fact_158_equalityE,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( A3 = B4 )
% 0.33/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % equalityE
% 0.33/0.47 thf(fact_159_subset__eq,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.33/0.47 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.33/0.47 ! [X2: A] :
% 0.33/0.47 ( ( member @ A @ X2 @ A5 )
% 0.33/0.47 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_eq
% 0.33/0.47 thf(fact_160_equalityD1,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( A3 = B4 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % equalityD1
% 0.33/0.47 thf(fact_161_equalityD2,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( A3 = B4 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % equalityD2
% 0.33/0.47 thf(fact_162_set__rev__mp,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( member @ A @ X3 @ A3 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( member @ A @ X3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % set_rev_mp
% 0.33/0.47 thf(fact_163_subset__iff,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.33/0.47 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.33/0.47 ! [T2: A] :
% 0.33/0.47 ( ( member @ A @ T2 @ A5 )
% 0.33/0.47 => ( member @ A @ T2 @ B6 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_iff
% 0.33/0.47 thf(fact_164_rev__subsetD,axiom,
% 0.33/0.47 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( member @ A @ C2 @ A3 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % rev_subsetD
% 0.33/0.47 thf(fact_165_subset__refl,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.33/0.47
% 0.33/0.47 % subset_refl
% 0.33/0.47 thf(fact_166_Collect__mono,axiom,
% 0.33/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.33/0.47 ( ! [X4: A] :
% 0.33/0.47 ( ( P @ X4 )
% 0.33/0.47 => ( Q @ X4 ) )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Collect_mono
% 0.33/0.47 thf(fact_167_subset__trans,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_trans
% 0.33/0.47 thf(fact_168_set__eq__subset,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ^ [Y2: set @ A,Z3: set @ A] : ( Y2 = Z3 ) )
% 0.33/0.47 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.33/0.47 & ( ord_less_eq @ ( set @ A ) @ B6 @ A5 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % set_eq_subset
% 0.33/0.47 thf(fact_169_contra__subsetD,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C2: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ~ ( member @ A @ C2 @ B4 )
% 0.33/0.47 => ~ ( member @ A @ C2 @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % contra_subsetD
% 0.33/0.47 thf(fact_170_Collect__mono__iff,axiom,
% 0.33/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.33/0.47 = ( ! [X2: A] :
% 0.33/0.47 ( ( P @ X2 )
% 0.33/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Collect_mono_iff
% 0.33/0.47 thf(fact_171_fcomp__def,axiom,
% 0.33/0.47 ! [C: $tType,B: $tType,A: $tType] :
% 0.33/0.47 ( ( fcomp @ A @ B @ C )
% 0.33/0.47 = ( ^ [F3: A > B,G3: B > C,X2: A] : ( G3 @ ( F3 @ X2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % fcomp_def
% 0.33/0.47 thf(fact_172_fcomp__assoc,axiom,
% 0.33/0.47 ! [A: $tType,D: $tType,B: $tType,C: $tType,F: A > D,G: D > C,H: C > B] :
% 0.33/0.47 ( ( fcomp @ A @ C @ B @ ( fcomp @ A @ D @ C @ F @ G ) @ H )
% 0.33/0.47 = ( fcomp @ A @ D @ B @ F @ ( fcomp @ D @ C @ B @ G @ H ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % fcomp_assoc
% 0.33/0.47 thf(fact_173_subset__insertI2,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,B3: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_insertI2
% 0.33/0.47 thf(fact_174_subset__insertI,axiom,
% 0.33/0.47 ! [A: $tType,B4: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B4 @ ( insert @ A @ A2 @ B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_insertI
% 0.33/0.47 thf(fact_175_subset__insert,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ~ ( member @ A @ X3 @ A3 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ B4 ) )
% 0.33/0.47 = ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_insert
% 0.33/0.47 thf(fact_176_Set_Oinsert__mono,axiom,
% 0.33/0.47 ! [A: $tType,C4: set @ A,D3: set @ A,A2: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C4 ) @ ( insert @ A @ A2 @ D3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Set.insert_mono
% 0.33/0.47 thf(fact_177_le__funD,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ! [F: A > B,G: A > B,X3: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.33/0.47 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_funD
% 0.33/0.47 thf(fact_178_le__funE,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ! [F: A > B,G: A > B,X3: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.33/0.47 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_funE
% 0.33/0.47 thf(fact_179_le__funI,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ! [F: A > B,G: A > B] :
% 0.33/0.47 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.33/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_funI
% 0.33/0.47 thf(fact_180_le__fun__def,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.33/0.47 = ( ^ [F3: A > B,G3: A > B] :
% 0.33/0.47 ! [X2: A] : ( ord_less_eq @ B @ ( F3 @ X2 ) @ ( G3 @ X2 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_fun_def
% 0.33/0.47 thf(fact_181_order__subst1,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType] :
% 0.33/0.47 ( ( ( order @ B @ ( type2 @ B ) )
% 0.33/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.33/0.47 => ! [A2: A,F: B > A,B3: B,C2: B] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 0.33/0.47 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.33/0.47 => ( ! [X4: B,Y3: B] :
% 0.33/0.47 ( ( ord_less_eq @ B @ X4 @ Y3 )
% 0.33/0.47 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.33/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % order_subst1
% 0.33/0.47 thf(fact_182_order__subst2,axiom,
% 0.33/0.47 ! [A: $tType,C: $tType] :
% 0.33/0.47 ( ( ( order @ C @ ( type2 @ C ) )
% 0.33/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.33/0.47 => ! [A2: A,B3: A,F: A > C,C2: C] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C2 )
% 0.33/0.47 => ( ! [X4: A,Y3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.33/0.47 => ( ord_less_eq @ C @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.33/0.47 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % order_subst2
% 0.33/0.47 thf(fact_183_ord__eq__le__subst,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType] :
% 0.33/0.47 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 & ( ord @ A @ ( type2 @ A ) ) )
% 0.33/0.47 => ! [A2: A,F: B > A,B3: B,C2: B] :
% 0.33/0.47 ( ( A2
% 0.33/0.47 = ( F @ B3 ) )
% 0.33/0.47 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.33/0.47 => ( ! [X4: B,Y3: B] :
% 0.33/0.47 ( ( ord_less_eq @ B @ X4 @ Y3 )
% 0.33/0.47 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.33/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % ord_eq_le_subst
% 0.33/0.47 thf(fact_184_ord__le__eq__subst,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType] :
% 0.33/0.47 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 & ( ord @ A @ ( type2 @ A ) ) )
% 0.33/0.47 => ! [A2: A,B3: A,F: A > B,C2: B] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( ( F @ B3 )
% 0.33/0.47 = C2 )
% 0.33/0.47 => ( ! [X4: A,Y3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.33/0.47 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.33/0.47 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % ord_le_eq_subst
% 0.33/0.47 thf(fact_185_eq__iff,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.33/0.47 => ( ( ^ [Y2: A,Z3: A] : ( Y2 = Z3 ) )
% 0.33/0.47 = ( ^ [X2: A,Y4: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.33/0.47 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % eq_iff
% 0.33/0.47 thf(fact_186_antisym,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X3: A,Y: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/0.47 => ( ( ord_less_eq @ A @ Y @ X3 )
% 0.33/0.47 => ( X3 = Y ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % antisym
% 0.33/0.47 thf(fact_187_linear,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X3: A,Y: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/0.47 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % linear
% 0.33/0.47 thf(fact_188_eq__refl,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X3: A,Y: A] :
% 0.33/0.47 ( ( X3 = Y )
% 0.33/0.47 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % eq_refl
% 0.33/0.47 thf(fact_189_le__cases,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X3: A,Y: A] :
% 0.33/0.47 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 0.33/0.47 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_cases
% 0.33/0.47 thf(fact_190_order_Otrans,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C2: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.33/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % order.trans
% 0.33/0.47 thf(fact_191_le__cases3,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X3: A,Y: A,Z4: A] :
% 0.33/0.47 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/0.47 => ~ ( ord_less_eq @ A @ Y @ Z4 ) )
% 0.33/0.47 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 0.33/0.47 => ~ ( ord_less_eq @ A @ X3 @ Z4 ) )
% 0.33/0.47 => ( ( ( ord_less_eq @ A @ X3 @ Z4 )
% 0.33/0.47 => ~ ( ord_less_eq @ A @ Z4 @ Y ) )
% 0.33/0.47 => ( ( ( ord_less_eq @ A @ Z4 @ Y )
% 0.33/0.47 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 0.33/0.47 => ( ( ( ord_less_eq @ A @ Y @ Z4 )
% 0.33/0.47 => ~ ( ord_less_eq @ A @ Z4 @ X3 ) )
% 0.33/0.47 => ~ ( ( ord_less_eq @ A @ Z4 @ X3 )
% 0.33/0.47 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_cases3
% 0.33/0.47 thf(fact_192_antisym__conv,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [Y: A,X3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ Y @ X3 )
% 0.33/0.47 => ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/0.47 = ( X3 = Y ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % antisym_conv
% 0.33/0.47 thf(fact_193_ord__eq__le__trans,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C2: A] :
% 0.33/0.47 ( ( A2 = B3 )
% 0.33/0.47 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.33/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % ord_eq_le_trans
% 0.33/0.47 thf(fact_194_ord__le__eq__trans,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C2: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( B3 = C2 )
% 0.33/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % ord_le_eq_trans
% 0.33/0.47 thf(fact_195_order__class_Oorder_Oantisym,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.33/0.47 => ( A2 = B3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % order_class.order.antisym
% 0.33/0.47 thf(fact_196_order__trans,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X3: A,Y: A,Z4: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/0.47 => ( ( ord_less_eq @ A @ Y @ Z4 )
% 0.33/0.47 => ( ord_less_eq @ A @ X3 @ Z4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % order_trans
% 0.33/0.47 thf(fact_197_dual__order_Orefl,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.33/0.47
% 0.33/0.47 % dual_order.refl
% 0.33/0.47 thf(fact_198_linorder__wlog,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [P: A > A > $o,A2: A,B3: A] :
% 0.33/0.47 ( ! [A6: A,B7: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A6 @ B7 )
% 0.33/0.47 => ( P @ A6 @ B7 ) )
% 0.33/0.47 => ( ! [A6: A,B7: A] :
% 0.33/0.47 ( ( P @ B7 @ A6 )
% 0.33/0.47 => ( P @ A6 @ B7 ) )
% 0.33/0.47 => ( P @ A2 @ B3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % linorder_wlog
% 0.33/0.47 thf(fact_199_dual__order_Otrans,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [B3: A,A2: A,C2: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.33/0.47 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 0.33/0.47 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % dual_order.trans
% 0.33/0.47 thf(fact_200_dual__order_Oantisym,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [B3: A,A2: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.33/0.47 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.33/0.47 => ( A2 = B3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % dual_order.antisym
% 0.33/0.47 thf(fact_201_pairwise__subset,axiom,
% 0.33/0.47 ! [A: $tType,P: A > A > $o,S3: set @ A,T3: set @ A] :
% 0.33/0.47 ( ( pairwise @ A @ P @ S3 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ T3 @ S3 )
% 0.33/0.47 => ( pairwise @ A @ P @ T3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % pairwise_subset
% 0.33/0.47 thf(fact_202_subset__singletonD,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,X3: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.33/0.47 => ( ( A3
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 | ( A3
% 0.33/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_singletonD
% 0.33/0.47 thf(fact_203_subset__singleton__iff,axiom,
% 0.33/0.47 ! [A: $tType,X5: set @ A,A2: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ X5 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.33/0.47 = ( ( X5
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 | ( X5
% 0.33/0.47 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_singleton_iff
% 0.33/0.47 thf(fact_204_Ball__Collect,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ball @ A )
% 0.33/0.47 = ( ^ [A5: set @ A,P5: A > $o] : ( ord_less_eq @ ( set @ A ) @ A5 @ ( collect @ A @ P5 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Ball_Collect
% 0.33/0.47 thf(fact_205_insert__subsetI,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A,X5: set @ A] :
% 0.33/0.47 ( ( member @ A @ X3 @ A3 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ X5 @ A3 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X5 ) @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_subsetI
% 0.33/0.47 thf(fact_206_subset__emptyI,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ! [X4: A] :
% 0.33/0.47 ~ ( member @ A @ X4 @ A3 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_emptyI
% 0.33/0.47 thf(fact_207_subset__Compl__singleton,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B3: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.33/0.47 = ( ~ ( member @ A @ B3 @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_Compl_singleton
% 0.33/0.47 thf(fact_208_Compl__eq__Compl__iff,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ( uminus_uminus @ ( set @ A ) @ A3 )
% 0.33/0.47 = ( uminus_uminus @ ( set @ A ) @ B4 ) )
% 0.33/0.47 = ( A3 = B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % Compl_eq_Compl_iff
% 0.33/0.47 thf(fact_209_Compl__iff,axiom,
% 0.33/0.47 ! [A: $tType,C2: A,A3: set @ A] :
% 0.33/0.47 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.33/0.47 = ( ~ ( member @ A @ C2 @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Compl_iff
% 0.33/0.47 thf(fact_210_ComplI,axiom,
% 0.33/0.47 ! [A: $tType,C2: A,A3: set @ A] :
% 0.33/0.47 ( ~ ( member @ A @ C2 @ A3 )
% 0.33/0.47 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % ComplI
% 0.33/0.47 thf(fact_211_Compl__anti__mono,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B4 ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Compl_anti_mono
% 0.33/0.47 thf(fact_212_Compl__subset__Compl__iff,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) @ ( uminus_uminus @ ( set @ A ) @ B4 ) )
% 0.33/0.47 = ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % Compl_subset_Compl_iff
% 0.33/0.47 thf(fact_213_tllist_Orel__mono,axiom,
% 0.33/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
% 0.33/0.47 ( ( ord_less_eq @ ( A > C > $o ) @ R1 @ R1a )
% 0.33/0.47 => ( ( ord_less_eq @ ( B > D > $o ) @ R2 @ R2a )
% 0.33/0.47 => ( ord_less_eq @ ( ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o ) @ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 ) @ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % tllist.rel_mono
% 0.33/0.47 thf(fact_214_double__complement,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.33/0.47 = A3 ) ).
% 0.33/0.47
% 0.33/0.47 % double_complement
% 0.33/0.47 thf(fact_215_ComplD,axiom,
% 0.33/0.47 ! [A: $tType,C2: A,A3: set @ A] :
% 0.33/0.47 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.33/0.47 => ~ ( member @ A @ C2 @ A3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % ComplD
% 0.33/0.47 thf(fact_216_subset__Compl__self__eq,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.33/0.47 = ( A3
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % subset_Compl_self_eq
% 0.33/0.47 thf(fact_217_Compl__insert,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A] :
% 0.33/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ X3 @ A3 ) )
% 0.33/0.47 = ( minus_minus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Compl_insert
% 0.33/0.47 thf(fact_218_disjoint__eq__subset__Compl,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( ord_less_eq @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % disjoint_eq_subset_Compl
% 0.33/0.47 thf(fact_219_IntI,axiom,
% 0.33/0.47 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( member @ A @ C2 @ A3 )
% 0.33/0.47 => ( ( member @ A @ C2 @ B4 )
% 0.33/0.47 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % IntI
% 0.33/0.47 thf(fact_220_Int__iff,axiom,
% 0.33/0.47 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.33/0.47 = ( ( member @ A @ C2 @ A3 )
% 0.33/0.47 & ( member @ A @ C2 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_iff
% 0.33/0.47 thf(fact_221_DiffI,axiom,
% 0.33/0.47 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( member @ A @ C2 @ A3 )
% 0.33/0.47 => ( ~ ( member @ A @ C2 @ B4 )
% 0.33/0.47 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % DiffI
% 0.33/0.47 thf(fact_222_Diff__iff,axiom,
% 0.33/0.47 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) )
% 0.33/0.47 = ( ( member @ A @ C2 @ A3 )
% 0.33/0.47 & ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_iff
% 0.33/0.47 thf(fact_223_Diff__idemp,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) @ B4 )
% 0.33/0.47 = ( minus_minus @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_idemp
% 0.33/0.47 thf(fact_224_predicate2I,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 0.33/0.47 ( ! [X4: A,Y3: B] :
% 0.33/0.47 ( ( P @ X4 @ Y3 )
% 0.33/0.47 => ( Q @ X4 @ Y3 ) )
% 0.33/0.47 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 0.33/0.47
% 0.33/0.47 % predicate2I
% 0.33/0.47 thf(fact_225_Int__subset__iff,axiom,
% 0.33/0.47 ! [A: $tType,C4: set @ A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.33/0.47 = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A3 )
% 0.33/0.47 & ( ord_less_eq @ ( set @ A ) @ C4 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_subset_iff
% 0.33/0.47 thf(fact_226_Diff__empty,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( minus_minus @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = A3 ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_empty
% 0.33/0.47 thf(fact_227_empty__Diff,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % empty_Diff
% 0.33/0.47 thf(fact_228_Diff__cancel,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( minus_minus @ ( set @ A ) @ A3 @ A3 )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_cancel
% 0.33/0.47 thf(fact_229_Int__insert__right__if1,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( member @ A @ A2 @ A3 )
% 0.33/0.47 => ( ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B4 ) )
% 0.33/0.47 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_insert_right_if1
% 0.33/0.47 thf(fact_230_Int__insert__right__if0,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ~ ( member @ A @ A2 @ A3 )
% 0.33/0.47 => ( ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B4 ) )
% 0.33/0.47 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_insert_right_if0
% 0.33/0.47 thf(fact_231_insert__inter__insert,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A3 ) @ ( insert @ A @ A2 @ B4 ) )
% 0.33/0.47 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_inter_insert
% 0.33/0.47 thf(fact_232_Int__insert__left__if1,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,C4: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( member @ A @ A2 @ C4 )
% 0.33/0.47 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B4 ) @ C4 )
% 0.33/0.47 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ B4 @ C4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_insert_left_if1
% 0.33/0.47 thf(fact_233_Int__insert__left__if0,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,C4: set @ A,B4: set @ A] :
% 0.33/0.47 ( ~ ( member @ A @ A2 @ C4 )
% 0.33/0.47 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B4 ) @ C4 )
% 0.33/0.47 = ( inf_inf @ ( set @ A ) @ B4 @ C4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_insert_left_if0
% 0.33/0.47 thf(fact_234_insert__Diff1,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,B4: set @ A,A3: set @ A] :
% 0.33/0.47 ( ( member @ A @ X3 @ B4 )
% 0.33/0.47 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A3 ) @ B4 )
% 0.33/0.47 = ( minus_minus @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_Diff1
% 0.33/0.47 thf(fact_235_Diff__insert0,axiom,
% 0.33/0.47 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ~ ( member @ A @ X3 @ A3 )
% 0.33/0.47 => ( ( minus_minus @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ B4 ) )
% 0.33/0.47 = ( minus_minus @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_insert0
% 0.33/0.47 thf(fact_236_insert__disjoint_I1_J,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A3 ) @ B4 )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( ~ ( member @ A @ A2 @ B4 )
% 0.33/0.47 & ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_disjoint(1)
% 0.33/0.47 thf(fact_237_insert__disjoint_I2_J,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.33/0.47 = ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A3 ) @ B4 ) )
% 0.33/0.47 = ( ~ ( member @ A @ A2 @ B4 )
% 0.33/0.47 & ( ( bot_bot @ ( set @ A ) )
% 0.33/0.47 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_disjoint(2)
% 0.33/0.47 thf(fact_238_disjoint__insert_I1_J,axiom,
% 0.33/0.47 ! [A: $tType,B4: set @ A,A2: A,A3: set @ A] :
% 0.33/0.47 ( ( ( inf_inf @ ( set @ A ) @ B4 @ ( insert @ A @ A2 @ A3 ) )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( ~ ( member @ A @ A2 @ B4 )
% 0.33/0.47 & ( ( inf_inf @ ( set @ A ) @ B4 @ A3 )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % disjoint_insert(1)
% 0.33/0.47 thf(fact_239_disjoint__insert_I2_J,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B3: A,B4: set @ A] :
% 0.33/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.33/0.47 = ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ B3 @ B4 ) ) )
% 0.33/0.47 = ( ~ ( member @ A @ B3 @ A3 )
% 0.33/0.47 & ( ( bot_bot @ ( set @ A ) )
% 0.33/0.47 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % disjoint_insert(2)
% 0.33/0.47 thf(fact_240_Diff__eq__empty__iff,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ( minus_minus @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.33/0.47 = ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_eq_empty_iff
% 0.33/0.47 thf(fact_241_insert__Diff__single,axiom,
% 0.33/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.33/0.47 ( ( insert @ A @ A2 @ ( minus_minus @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.33/0.47 = ( insert @ A @ A2 @ A3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % insert_Diff_single
% 0.33/0.47 thf(fact_242_Diff__disjoint,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( inf_inf @ ( set @ A ) @ A3 @ ( minus_minus @ ( set @ A ) @ B4 @ A3 ) )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_disjoint
% 0.33/0.47 thf(fact_243_Compl__disjoint,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( inf_inf @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Compl_disjoint
% 0.33/0.47 thf(fact_244_Compl__disjoint2,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A] :
% 0.33/0.47 ( ( inf_inf @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) @ A3 )
% 0.33/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Compl_disjoint2
% 0.33/0.47 thf(fact_245_Diff__Compl,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( minus_minus @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ B4 ) )
% 0.33/0.47 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_Compl
% 0.33/0.47 thf(fact_246_Int__mono,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,C4: set @ A,B4: set @ A,D3: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ D3 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ ( inf_inf @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_mono
% 0.33/0.47 thf(fact_247_Diff__mono,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,C4: set @ A,D3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.33/0.47 => ( ( ord_less_eq @ ( set @ A ) @ D3 @ B4 )
% 0.33/0.47 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) @ ( minus_minus @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_mono
% 0.33/0.47 thf(fact_248_Int__lower1,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ A3 ) ).
% 0.33/0.47
% 0.33/0.47 % Int_lower1
% 0.33/0.47 thf(fact_249_Int__lower2,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ B4 ) ).
% 0.33/0.47
% 0.33/0.47 % Int_lower2
% 0.33/0.47 thf(fact_250_Diff__subset,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) @ A3 ) ).
% 0.33/0.47
% 0.33/0.47 % Diff_subset
% 0.33/0.47 thf(fact_251_Int__absorb1,axiom,
% 0.33/0.47 ! [A: $tType,B4: set @ A,A3: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 0.33/0.47 => ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 = B4 ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_absorb1
% 0.33/0.47 thf(fact_252_Int__absorb2,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 => ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.47 = A3 ) ) ).
% 0.33/0.47
% 0.33/0.47 % Int_absorb2
% 0.33/0.47 thf(fact_253_double__diff,axiom,
% 0.33/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C4: set @ A] :
% 0.33/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.33/0.48 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.33/0.48 => ( ( minus_minus @ ( set @ A ) @ B4 @ ( minus_minus @ ( set @ A ) @ C4 @ A3 ) )
% 0.33/0.48 = A3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % double_diff
% 0.33/0.48 thf(fact_254_Int__greatest,axiom,
% 0.33/0.48 ! [A: $tType,C4: set @ A,A3: set @ A,B4: set @ A] :
% 0.33/0.48 ( ( ord_less_eq @ ( set @ A ) @ C4 @ A3 )
% 0.33/0.48 => ( ( ord_less_eq @ ( set @ A ) @ C4 @ B4 )
% 0.33/0.48 => ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Int_greatest
% 0.33/0.48
% 0.33/0.48 %----Type constructors (16)
% 0.33/0.48 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.33/0.48 ! [A7: $tType,A8: $tType] :
% 0.33/0.48 ( ( order_bot @ A8 @ ( type2 @ A8 ) )
% 0.33/0.48 => ( order_bot @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.33/0.48 ! [A7: $tType,A8: $tType] :
% 0.33/0.48 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 0.33/0.48 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.33/0.48 ! [A7: $tType,A8: $tType] :
% 0.33/0.48 ( ( order @ A8 @ ( type2 @ A8 ) )
% 0.33/0.48 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_fun___Orderings_Oord,axiom,
% 0.33/0.48 ! [A7: $tType,A8: $tType] :
% 0.33/0.48 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 0.33/0.48 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_fun___Orderings_Obot,axiom,
% 0.33/0.48 ! [A7: $tType,A8: $tType] :
% 0.33/0.48 ( ( bot @ A8 @ ( type2 @ A8 ) )
% 0.33/0.48 => ( bot @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_Set_Oset___Orderings_Oorder__bot_1,axiom,
% 0.33/0.48 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.33/0.48 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 0.33/0.48 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_Set_Oset___Orderings_Oord_4,axiom,
% 0.33/0.48 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_Set_Oset___Orderings_Obot_5,axiom,
% 0.33/0.48 ! [A7: $tType] : ( bot @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_HOL_Obool___Orderings_Oorder__bot_6,axiom,
% 0.33/0.48 order_bot @ $o @ ( type2 @ $o ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.33/0.48 preorder @ $o @ ( type2 @ $o ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.33/0.48 linorder @ $o @ ( type2 @ $o ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_HOL_Obool___Orderings_Oorder_8,axiom,
% 0.33/0.48 order @ $o @ ( type2 @ $o ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_HOL_Obool___Orderings_Oord_9,axiom,
% 0.33/0.48 ord @ $o @ ( type2 @ $o ) ).
% 0.33/0.48
% 0.33/0.48 thf(tcon_HOL_Obool___Orderings_Obot_10,axiom,
% 0.33/0.48 bot @ $o @ ( type2 @ $o ) ).
% 0.33/0.48
% 0.33/0.48 %----Helper facts (3)
% 0.33/0.48 thf(help_If_3_1_T,axiom,
% 0.33/0.48 ! [P: $o] :
% 0.33/0.48 ( ( P = $true )
% 0.33/0.48 | ( P = $false ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(help_If_2_1_T,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Y: A] :
% 0.33/0.48 ( ( if @ A @ $false @ X3 @ Y )
% 0.33/0.48 = Y ) ).
% 0.33/0.48
% 0.33/0.48 thf(help_If_1_1_T,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Y: A] :
% 0.33/0.48 ( ( if @ A @ $true @ X3 @ Y )
% 0.33/0.48 = X3 ) ).
% 0.33/0.48
% 0.33/0.48 %----Conjectures (2)
% 0.33/0.48 thf(conj_0,hypothesis,
% 0.33/0.48 ( x
% 0.33/0.48 = ( tLList57907754e_TNil @ b @ a @ x1 ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(conj_1,conjecture,
% 0.33/0.48 ( ( ( tLList1968894004s_TNil @ a @ b @ x )
% 0.33/0.48 => ( ( tLList200813139tllist @ b @ b @ a @ ( id @ b ) @ ( undefined @ ( a > ( tLList446370796tllist @ a @ b ) > b ) ) @ x )
% 0.33/0.48 = ( tLList2110128105rminal @ a @ b @ x ) ) )
% 0.33/0.48 & ( ~ ( tLList1968894004s_TNil @ a @ b @ x )
% 0.33/0.48 => ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ a @ b ) > b ) @ ( tLList_Mirabelle_ttl @ a @ b @ x ) )
% 0.33/0.48 = ( tLList2110128105rminal @ a @ b @ x ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 ------------------------
% 2.85/1.53 ---- Embedded in THF ---
% 2.85/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.85/1.53 %%% Generated on Tue Feb 24 06:10:39 EST 2026
% 2.85/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.85/1.53 %%% Logic specification used:
% 2.85/1.53 %%% thf(spec, logic, $$dhol).
% 2.85/1.53
% 2.85/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2DTF18945.p
% 2.85/1.53 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist, type, tLList446370796tllist: ($tType > ($tType > $tType))).
% 2.85/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.85/1.53 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.85/1.53 thf(ty_tf_b, type, b: $tType).
% 2.85/1.53 thf(ty_tf_a, type, a: $tType).
% 2.85/1.53 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_c_Fun_Ofcomp, type, fcomp: (!> [A:$tType,B:$tType,C:$tType]: (((A > B) > ((B > C) > (A > C)))))).
% 2.85/1.53 thf(sy_c_Fun_Oid, type, id: (!> [A:$tType]: ((A > A)))).
% 2.85/1.53 thf(sy_c_Fun_Ooverride__on, type, override_on: (!> [A:$tType,B:$tType]: (((A > B) > ((A > B) > ((set @ A) > (A > B))))))).
% 2.85/1.53 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.85/1.53 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.85/1.53 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.85/1.53 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.85/1.53 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.85/1.53 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.85/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.85/1.53 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.85/1.53 thf(sy_c_Relation_Oinv__imagep, type, inv_imagep: (!> [B:$tType,A:$tType]: (((B > (B > $o)) > ((A > B) > (A > (A > $o))))))).
% 2.85/1.53 thf(sy_c_Set_OBall, type, ball: (!> [A:$tType]: (((set @ A) > ((A > $o) > $o))))).
% 2.85/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.85/1.53 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.85/1.53 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.85/1.53 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.85/1.53 thf(sy_c_Set_Opairwise, type, pairwise: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.85/1.53 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Oterminal0, type, tLList1825092077minal0: (!> [A:$tType]: (A))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTCons, type, tLList1992840728_TCons: (!> [A:$tType,B:$tType]: ((A > (((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ B)))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTNil, type, tLList57907754e_TNil: (!> [B:$tType,A:$tType]: ((B > ((tLList446370796tllist @ A) @ B))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocase__tllist, type, tLList200813139tllist: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > (((tLList446370796tllist @ A) @ B) > C)) > (((tLList446370796tllist @ A) @ B) > C)))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocorec__tllist, type, tLList1614408749tllist: (!> [E:$tType,B:$tType,A:$tType]: (((E > $o) > ((E > B) > ((E > A) > ((E > $o) > ((E > ((tLList446370796tllist @ A) @ B)) > ((E > E) > (E > ((tLList446370796tllist @ A) @ B))))))))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ois__TNil, type, tLList1968894004s_TNil: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > $o)))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Opred__tllist, type, tLList11265572tllist: (!> [A:$tType,B:$tType]: (((A > $o) > ((B > $o) > (((tLList446370796tllist @ A) @ B) > $o)))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oset2__tllist, type, tLList457864275tllist: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > (set @ B))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oterminal, type, tLList2110128105rminal: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > B)))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Othd, type, tLList_Mirabelle_thd: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > A)))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otllist__all2, type, tLList1380991092t_all2: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > (((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ C) @ D) > $o))))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otmap, type, tLList1669959861e_tmap: (!> [A:$tType,Aa:$tType,B:$tType,Ba:$tType]: (((A > Aa) > ((B > Ba) > (((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ Aa) @ Ba))))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otset, type, tLList1719791291e_tset: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > (set @ A))))).
% 2.85/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ottl, type, tLList_Mirabelle_ttl: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ B))))).
% 2.85/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.85/1.53 thf(sy_v_x, type, x: ((tLList446370796tllist @ a) @ b)).
% 2.85/1.53 thf(sy_v_x1, type, x1: b).
% 2.85/1.53 thf(fact_0_tllist_Oinject_I1_J, axiom, (! [A:$tType,B:$tType,X1:B,Y1:B]: ((((((tLList57907754e_TNil @ B) @ A) @ X1) = (((tLList57907754e_TNil @ B) @ A) @ Y1)) = (X1 = Y1))))).
% 2.85/1.53 thf(fact_1_tllist_Ocollapse_I1_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ Tllist) => ((((tLList57907754e_TNil @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ Tllist)) = Tllist))))).
% 2.85/1.53 thf(fact_2_tllist_Osel_I4_J, axiom, (! [A:$tType,B:$tType,X1:B]: (((((tLList_Mirabelle_ttl @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (((tLList57907754e_TNil @ B) @ A) @ X1))))).
% 2.85/1.53 thf(fact_3_tllist_Osel_I1_J, axiom, (! [Aa:$tType,A:$tType,X1:A]: (((((tLList2110128105rminal @ Aa) @ A) @ (((tLList57907754e_TNil @ A) @ Aa) @ X1)) = X1)))).
% 2.85/1.53 thf(fact_4_tllist_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,X1:B]: ((((tLList1968894004s_TNil @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ X1))))).
% 2.85/1.53 thf(fact_5_tllist_OdiscI_I1_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B),X1:B]: (((Tllist = (((tLList57907754e_TNil @ B) @ A) @ X1)) => (((tLList1968894004s_TNil @ A) @ B) @ Tllist))))).
% 2.85/1.53 thf(fact_6_tllist_Osimps_I5_J, axiom, (! [A:$tType,C:$tType,B:$tType,F1:(B > C),F2:(A > (((tLList446370796tllist @ A) @ B) > C)),X1:B]: ((((((((tLList200813139tllist @ B) @ C) @ A) @ F1) @ F2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (F1 @ X1))))).
% 2.85/1.53 thf(fact_7_terminal0_Osimps, axiom, (! [D:$tType,C:$tType]: (((tLList1825092077minal0 @ (((tLList446370796tllist @ C) @ D) > D)) = (^ [Xs:((tLList446370796tllist @ C) @ D)]: (((((if @ D) @ (((tLList1968894004s_TNil @ C) @ D) @ Xs)) @ ((((((tLList200813139tllist @ D) @ D) @ C) @ (id @ D)) @ (undefined @ (C > (((tLList446370796tllist @ C) @ D) > D)))) @ Xs)) @ ((tLList1825092077minal0 @ (((tLList446370796tllist @ C) @ D) > D)) @ (((tLList_Mirabelle_ttl @ C) @ D) @ Xs))))))))).
% 2.85/1.53 thf(fact_8_is__TNil__def, axiom, (! [B:$tType,A:$tType]: ((((tLList1968894004s_TNil @ A) @ B) = (^ [Tllist2:((tLList446370796tllist @ A) @ B)]: ((? [X12:B]: ((Tllist2 = (((tLList57907754e_TNil @ B) @ A) @ X12)))))))))).
% 2.85/1.53 thf(fact_9_terminal0_Oraw__induct, axiom, (! [C:$tType,D:$tType,P:(((tLList446370796tllist @ C) @ D) > (D > $o)),Xs2:((tLList446370796tllist @ C) @ D),Y:D]: (((! [Terminal0:(((tLList446370796tllist @ C) @ D) > D)]: (((! [X:((tLList446370796tllist @ C) @ D)]: ((((Terminal0 @ X) != (undefined @ D)) => ((P @ X) @ (Terminal0 @ X))))) => (! [Xs3:((tLList446370796tllist @ C) @ D),Xsa:D]: (((((((tLList1968894004s_TNil @ C) @ D) @ Xs3) => (((((((tLList200813139tllist @ D) @ D) @ C) @ (id @ D)) @ (undefined @ (C > (((tLList446370796tllist @ C) @ D) > D)))) @ Xs3) = Xsa)) & ((~ ((((tLList1968894004s_TNil @ C) @ D) @ Xs3))) => ((Terminal0 @ (((tLList_Mirabelle_ttl @ C) @ D) @ Xs3)) = Xsa))) => ((Xsa != (undefined @ D)) => ((P @ Xs3) @ Xsa)))))))) => ((((tLList1825092077minal0 @ (((tLList446370796tllist @ C) @ D) > D)) @ Xs2) = Y) => ((Y != (undefined @ D)) => ((P @ Xs2) @ Y))))))).
% 2.85/1.53 thf(fact_10_id__apply, axiom, (! [A:$tType]: (((id @ A) = (^ [X2:A]: (X2)))))).
% 2.85/1.53 thf(fact_11_tllist_Ocase__eq__if, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((tLList200813139tllist @ B) @ C) @ A) = (^ [F12:(B > C),F22:(A > (((tLList446370796tllist @ A) @ B) > C)),Tllist2:((tLList446370796tllist @ A) @ B)]: (((((if @ C) @ (((tLList1968894004s_TNil @ A) @ B) @ Tllist2)) @ (F12 @ (((tLList2110128105rminal @ A) @ B) @ Tllist2))) @ ((F22 @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist2)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist2))))))))).
% 2.85/1.53 thf(fact_12_tllist_Oexpand, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B),Tllist3:((tLList446370796tllist @ A) @ B)]: ((((((tLList1968894004s_TNil @ A) @ B) @ Tllist) = (((tLList1968894004s_TNil @ A) @ B) @ Tllist3)) => (((((tLList1968894004s_TNil @ A) @ B) @ Tllist) => ((((tLList1968894004s_TNil @ A) @ B) @ Tllist3) => ((((tLList2110128105rminal @ A) @ B) @ Tllist) = (((tLList2110128105rminal @ A) @ B) @ Tllist3)))) => (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist))) => ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist3))) => (((((tLList_Mirabelle_thd @ A) @ B) @ Tllist) = (((tLList_Mirabelle_thd @ A) @ B) @ Tllist3)) & ((((tLList_Mirabelle_ttl @ A) @ B) @ Tllist) = (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist3))))) => (Tllist = Tllist3))))))).
% 2.85/1.53 thf(fact_13_tllist_Ocoinduct, axiom, (! [B:$tType,A:$tType,R:(((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ A) @ B) > $o)),Tllist:((tLList446370796tllist @ A) @ B),Tllist3:((tLList446370796tllist @ A) @ B)]: ((((R @ Tllist) @ Tllist3) => ((! [Tllist4:((tLList446370796tllist @ A) @ B),Tllist5:((tLList446370796tllist @ A) @ B)]: ((((R @ Tllist4) @ Tllist5) => (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) = (((tLList1968894004s_TNil @ A) @ B) @ Tllist5)) & (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) => ((((tLList1968894004s_TNil @ A) @ B) @ Tllist5) => ((((tLList2110128105rminal @ A) @ B) @ Tllist4) = (((tLList2110128105rminal @ A) @ B) @ Tllist5)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist4))) => ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist5))) => (((((tLList_Mirabelle_thd @ A) @ B) @ Tllist4) = (((tLList_Mirabelle_thd @ A) @ B) @ Tllist5)) & ((R @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist4)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist5)))))))))) => (Tllist = Tllist3)))))).
% 2.85/1.53 thf(fact_14_tllist_Ocoinduct__strong, axiom, (! [B:$tType,A:$tType,R:(((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ A) @ B) > $o)),Tllist:((tLList446370796tllist @ A) @ B),Tllist3:((tLList446370796tllist @ A) @ B)]: ((((R @ Tllist) @ Tllist3) => ((! [Tllist4:((tLList446370796tllist @ A) @ B),Tllist5:((tLList446370796tllist @ A) @ B)]: ((((R @ Tllist4) @ Tllist5) => (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) = (((tLList1968894004s_TNil @ A) @ B) @ Tllist5)) & (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) => ((((tLList1968894004s_TNil @ A) @ B) @ Tllist5) => ((((tLList2110128105rminal @ A) @ B) @ Tllist4) = (((tLList2110128105rminal @ A) @ B) @ Tllist5)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist4))) => ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist5))) => (((((tLList_Mirabelle_thd @ A) @ B) @ Tllist4) = (((tLList_Mirabelle_thd @ A) @ B) @ Tllist5)) & (((R @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist4)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist5)) | ((((tLList_Mirabelle_ttl @ A) @ B) @ Tllist4) = (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist5))))))))))) => (Tllist = Tllist3)))))).
% 2.85/1.53 thf(fact_15_id__def, axiom, (! [A:$tType]: (((id @ A) = (^ [X2:A]: (X2)))))).
% 2.85/1.53 thf(fact_16_eq__id__iff, axiom, (! [A:$tType,F:(A > A)]: (((! [X2:A]: (((F @ X2) = X2))) = (F = (id @ A)))))).
% 2.85/1.53 thf(fact_17_tllist_Osel_I2_J, axiom, (! [A:$tType,Aa:$tType,X21:Aa,X22:((tLList446370796tllist @ Aa) @ A)]: (((((tLList2110128105rminal @ Aa) @ A) @ ((((tLList1992840728_TCons @ Aa) @ A) @ X21) @ X22)) = ((tLList1825092077minal0 @ (((tLList446370796tllist @ Aa) @ A) > A)) @ X22))))).
% 2.85/1.53 thf(fact_18_tllist_Oset__sel_I3_J, axiom, (! [B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ A2) => (((member @ B) @ (((tLList2110128105rminal @ A) @ B) @ A2)) @ (((tLList457864275tllist @ A) @ B) @ A2)))))).
% 2.85/1.53 thf(fact_19_tllist_Oset__sel_I4_J, axiom, (! [B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),Xc:B]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => ((((member @ B) @ Xc) @ (((tLList457864275tllist @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ A2))) => (((member @ B) @ Xc) @ (((tLList457864275tllist @ A) @ B) @ A2))))))).
% 2.85/1.53 thf(fact_20_tllist_Oset__sel_I2_J, axiom, (! [B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),X3:A]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => ((((member @ A) @ X3) @ (((tLList1719791291e_tset @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ A2))) => (((member @ A) @ X3) @ (((tLList1719791291e_tset @ A) @ B) @ A2))))))).
% 2.85/1.53 thf(fact_21_tllist_Osplit__sel, axiom, (! [C:$tType,B:$tType,A:$tType,P:(C > $o),F1:(B > C),F2:(A > (((tLList446370796tllist @ A) @ B) > C)),Tllist:((tLList446370796tllist @ A) @ B)]: (((P @ ((((((tLList200813139tllist @ B) @ C) @ A) @ F1) @ F2) @ Tllist)) = (((Tllist = (((tLList57907754e_TNil @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ Tllist))) => (P @ (F1 @ (((tLList2110128105rminal @ A) @ B) @ Tllist)))) & ((Tllist = ((((tLList1992840728_TCons @ A) @ B) @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))) => (P @ ((F2 @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))))))))).
% 2.85/1.53 thf(fact_22_tllist_Oinject_I2_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B),Y21:A,Y22:((tLList446370796tllist @ A) @ B)]: (((((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22) = ((((tLList1992840728_TCons @ A) @ B) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.85/1.53 thf(fact_23_tllist_Ocollapse_I2_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist))) => (((((tLList1992840728_TCons @ A) @ B) @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist)) = Tllist))))).
% 2.85/1.53 thf(fact_24_tllist_Osel_I3_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList_Mirabelle_thd @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = X21)))).
% 2.85/1.53 thf(fact_25_tllist_Osimps_I23_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList457864275tllist @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = (((tLList457864275tllist @ A) @ B) @ X22))))).
% 2.85/1.53 thf(fact_26_tllist_Oset__cases_I1_J, axiom, (! [B:$tType,A:$tType,E2:A,A2:((tLList446370796tllist @ A) @ B)]: (((((member @ A) @ E2) @ (((tLList1719791291e_tset @ A) @ B) @ A2)) => ((! [Z2:((tLList446370796tllist @ A) @ B)]: ((A2 != ((((tLList1992840728_TCons @ A) @ B) @ E2) @ Z2)))) => (~ ((! [Z1:A,Z2:((tLList446370796tllist @ A) @ B)]: (((A2 = ((((tLList1992840728_TCons @ A) @ B) @ Z1) @ Z2)) => (~ ((((member @ A) @ E2) @ (((tLList1719791291e_tset @ A) @ B) @ Z2)))))))))))))).
% 2.85/1.53 thf(fact_27_tllist_Oset__induct_I1_J, axiom, (! [B:$tType,A:$tType,X3:A,A2:((tLList446370796tllist @ A) @ B),P:(A > (((tLList446370796tllist @ A) @ B) > $o))]: (((((member @ A) @ X3) @ (((tLList1719791291e_tset @ A) @ B) @ A2)) => ((! [Z1:A,Z2:((tLList446370796tllist @ A) @ B)]: (((P @ Z1) @ ((((tLList1992840728_TCons @ A) @ B) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:((tLList446370796tllist @ A) @ B),Xa:A]: (((((member @ A) @ Xa) @ (((tLList1719791291e_tset @ A) @ B) @ Z2)) => (((P @ Xa) @ Z2) => ((P @ Xa) @ ((((tLList1992840728_TCons @ A) @ B) @ Z1) @ Z2)))))) => ((P @ X3) @ A2))))))).
% 2.85/1.53 thf(fact_28_tllist_Oset__intros_I4_J, axiom, (! [B:$tType,A:$tType,Xc:B,A2a:((tLList446370796tllist @ A) @ B),A1a:A]: (((((member @ B) @ Xc) @ (((tLList457864275tllist @ A) @ B) @ A2a)) => (((member @ B) @ Xc) @ (((tLList457864275tllist @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ A1a) @ A2a))))))).
% 2.85/1.53 thf(fact_29_tllist_Oset__intros_I2_J, axiom, (! [B:$tType,A:$tType,X3:A,A22:((tLList446370796tllist @ A) @ B),A1:A]: (((((member @ A) @ X3) @ (((tLList1719791291e_tset @ A) @ B) @ A22)) => (((member @ A) @ X3) @ (((tLList1719791291e_tset @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ A1) @ A22))))))).
% 2.85/1.53 thf(fact_30_tllist_Oset__intros_I1_J, axiom, (! [B:$tType,A:$tType,A1:A,A22:((tLList446370796tllist @ A) @ B)]: ((((member @ A) @ A1) @ (((tLList1719791291e_tset @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ A1) @ A22)))))).
% 2.85/1.53 thf(fact_31_tllist_Oset__induct_I2_J, axiom, (! [A:$tType,Aa:$tType,X3:A,A2:((tLList446370796tllist @ Aa) @ A),P:(A > (((tLList446370796tllist @ Aa) @ A) > $o))]: (((((member @ A) @ X3) @ (((tLList457864275tllist @ Aa) @ A) @ A2)) => ((! [Z:A]: (((P @ Z) @ (((tLList57907754e_TNil @ A) @ Aa) @ Z)))) => ((! [Z1:Aa,Z2:((tLList446370796tllist @ Aa) @ A),Xb:A]: (((((member @ A) @ Xb) @ (((tLList457864275tllist @ Aa) @ A) @ Z2)) => (((P @ Xb) @ Z2) => ((P @ Xb) @ ((((tLList1992840728_TCons @ Aa) @ A) @ Z1) @ Z2)))))) => ((P @ X3) @ A2))))))).
% 2.85/1.53 thf(fact_32_tllist_Oset__cases_I2_J, axiom, (! [B:$tType,A:$tType,E2:B,A2:((tLList446370796tllist @ A) @ B)]: (((((member @ B) @ E2) @ (((tLList457864275tllist @ A) @ B) @ A2)) => ((A2 != (((tLList57907754e_TNil @ B) @ A) @ E2)) => (~ ((! [Z1:A,Z2:((tLList446370796tllist @ A) @ B)]: (((A2 = ((((tLList1992840728_TCons @ A) @ B) @ Z1) @ Z2)) => (~ ((((member @ B) @ E2) @ (((tLList457864275tllist @ A) @ B) @ Z2)))))))))))))).
% 2.85/1.53 thf(fact_33_tllist_Oset__sel_I1_J, axiom, (! [B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => (((member @ A) @ (((tLList_Mirabelle_thd @ A) @ B) @ A2)) @ (((tLList1719791291e_tset @ A) @ B) @ A2)))))).
% 2.85/1.53 thf(fact_34_tllist_OdiscI_I2_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B),X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((Tllist = ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) => (~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist))))))).
% 2.85/1.53 thf(fact_35_tllist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: ((~ ((((tLList1968894004s_TNil @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22))))))).
% 2.85/1.53 thf(fact_36_tllist_Oexhaust, axiom, (! [B:$tType,A:$tType,Y:((tLList446370796tllist @ A) @ B)]: (((! [X13:B]: ((Y != (((tLList57907754e_TNil @ B) @ A) @ X13)))) => (~ ((! [X212:A,X222:((tLList446370796tllist @ A) @ B)]: ((Y != ((((tLList1992840728_TCons @ A) @ B) @ X212) @ X222)))))))))).
% 2.85/1.53 thf(fact_37_tllist_Odistinct_I1_J, axiom, (! [B:$tType,A:$tType,X1:B,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList57907754e_TNil @ B) @ A) @ X1) != ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22))))).
% 2.85/1.53 thf(fact_38_tllist_Osel_I5_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList_Mirabelle_ttl @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = X22)))).
% 2.85/1.53 thf(fact_39_tllist_Osimps_I6_J, axiom, (! [C:$tType,B:$tType,A:$tType,F1:(B > C),F2:(A > (((tLList446370796tllist @ A) @ B) > C)),X21:A,X22:((tLList446370796tllist @ A) @ B)]: ((((((((tLList200813139tllist @ B) @ C) @ A) @ F1) @ F2) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = ((F2 @ X21) @ X22))))).
% 2.85/1.53 thf(fact_40_tllist_Oset__intros_I3_J, axiom, (! [A:$tType,B:$tType,Aa2:B]: ((((member @ B) @ Aa2) @ (((tLList457864275tllist @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ Aa2)))))).
% 2.85/1.53 thf(fact_41_tllist_Oexhaust__sel, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B)]: (((Tllist != (((tLList57907754e_TNil @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ Tllist))) => (Tllist = ((((tLList1992840728_TCons @ A) @ B) @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))))))).
% 2.85/1.53 thf(fact_42_tllist_Osplit__sel__asm, axiom, (! [C:$tType,B:$tType,A:$tType,P:(C > $o),F1:(B > C),F2:(A > (((tLList446370796tllist @ A) @ B) > C)),Tllist:((tLList446370796tllist @ A) @ B)]: (((P @ ((((((tLList200813139tllist @ B) @ C) @ A) @ F1) @ F2) @ Tllist)) = (~ ((((Tllist = (((tLList57907754e_TNil @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ Tllist))) & (~ ((P @ (F1 @ (((tLList2110128105rminal @ A) @ B) @ Tllist)))))) | ((Tllist = ((((tLList1992840728_TCons @ A) @ B) @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))) & (~ ((P @ ((F2 @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))))))))))))).
% 2.85/1.53 thf(fact_43_tllist_Orel__coinduct, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,P:(((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ C) @ D) > $o)),X3:((tLList446370796tllist @ A) @ B),Y:((tLList446370796tllist @ C) @ D),R2:(B > (D > $o)),R1:(A > (C > $o))]: ((((P @ X3) @ Y) => ((! [Tllist4:((tLList446370796tllist @ A) @ B),Tllist5:((tLList446370796tllist @ C) @ D)]: ((((P @ Tllist4) @ Tllist5) => (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) = (((tLList1968894004s_TNil @ C) @ D) @ Tllist5)) & (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) => ((((tLList1968894004s_TNil @ C) @ D) @ Tllist5) => ((R2 @ (((tLList2110128105rminal @ A) @ B) @ Tllist4)) @ (((tLList2110128105rminal @ C) @ D) @ Tllist5)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist4))) => ((~ ((((tLList1968894004s_TNil @ C) @ D) @ Tllist5))) => (((R1 @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist4)) @ (((tLList_Mirabelle_thd @ C) @ D) @ Tllist5)) & ((P @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist4)) @ (((tLList_Mirabelle_ttl @ C) @ D) @ Tllist5)))))))))) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X3) @ Y)))))).
% 2.85/1.53 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.85/1.53 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 2.85/1.53 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.85/1.53 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.85/1.53 thf(fact_48_tllist_Orel__sel, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType]: ((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) = (^ [R12:(A > (C > $o)),R22:(B > (D > $o)),A4:((tLList446370796tllist @ A) @ B),B2:((tLList446370796tllist @ C) @ D)]: ((((((tLList1968894004s_TNil @ A) @ B) @ A4) = (((tLList1968894004s_TNil @ C) @ D) @ B2)) & (((((tLList1968894004s_TNil @ A) @ B) @ A4) => ((((tLList1968894004s_TNil @ C) @ D) @ B2) => ((R22 @ (((tLList2110128105rminal @ A) @ B) @ A4)) @ (((tLList2110128105rminal @ C) @ D) @ B2)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ A4))) => ((~ ((((tLList1968894004s_TNil @ C) @ D) @ B2))) => (((R12 @ (((tLList_Mirabelle_thd @ A) @ B) @ A4)) @ (((tLList_Mirabelle_thd @ C) @ D) @ B2)) & ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R12) @ R22) @ (((tLList_Mirabelle_ttl @ A) @ B) @ A4)) @ (((tLList_Mirabelle_ttl @ C) @ D) @ B2))))))))))))).
% 2.85/1.53 thf(fact_49_tllist_Opred__cong, axiom, (! [B:$tType,A:$tType,X3:((tLList446370796tllist @ A) @ B),Ya:((tLList446370796tllist @ A) @ B),P1:(A > $o),P1a:(A > $o),P2:(B > $o),P2a:(B > $o)]: (((X3 = Ya) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((tLList1719791291e_tset @ A) @ B) @ Ya)) => ((P1 @ Z1) = (P1a @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((tLList457864275tllist @ A) @ B) @ Ya)) => ((P2 @ Z2) = (P2a @ Z2))))) => ((((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ X3) = (((((tLList11265572tllist @ A) @ B) @ P1a) @ P2a) @ Ya)))))))).
% 2.85/1.53 thf(fact_50_tllist_Opred__mono__strong, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P2:(B > $o),X3:((tLList446370796tllist @ A) @ B),P1a:(A > $o),P2a:(B > $o)]: (((((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ X3) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((tLList1719791291e_tset @ A) @ B) @ X3)) => ((P1 @ Z1) => (P1a @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((tLList457864275tllist @ A) @ B) @ X3)) => ((P2 @ Z2) => (P2a @ Z2))))) => (((((tLList11265572tllist @ A) @ B) @ P1a) @ P2a) @ X3))))))).
% 2.85/1.53 thf(fact_51_tllist_Ocorec__code, axiom, (! [B:$tType,A:$tType,E:$tType]: (((((tLList1614408749tllist @ E) @ B) @ A) = (^ [P3:(E > $o),G1:(E > B),G21:(E > A),Q22:(E > $o),G221:(E > ((tLList446370796tllist @ A) @ B)),G222:(E > E),A4:E]: (((((if @ ((tLList446370796tllist @ A) @ B)) @ (P3 @ A4)) @ (((tLList57907754e_TNil @ B) @ A) @ (G1 @ A4))) @ ((((tLList1992840728_TCons @ A) @ B) @ (G21 @ A4)) @ ((((if @ ((tLList446370796tllist @ A) @ B)) @ (Q22 @ A4)) @ (G221 @ A4)) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P3) @ G1) @ G21) @ Q22) @ G221) @ G222) @ (G222 @ A4))))))))))).
% 2.85/1.53 thf(fact_52_tllist_Osimps_I21_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList1719791291e_tset @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = (((insert @ A) @ X21) @ (((tLList1719791291e_tset @ A) @ B) @ X22)))))).
% 2.85/1.53 thf(fact_53_tllist_Omap__cong, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X3:((tLList446370796tllist @ A) @ B),Ya:((tLList446370796tllist @ A) @ B),F1:(A > C),G12:(A > C),F2:(B > D),G2:(B > D)]: (((X3 = Ya) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((tLList1719791291e_tset @ A) @ B) @ Ya)) => ((F1 @ Z1) = (G12 @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((tLList457864275tllist @ A) @ B) @ Ya)) => ((F2 @ Z2) = (G2 @ Z2))))) => ((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X3) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ G12) @ G2) @ Ya)))))))).
% 2.85/1.53 thf(fact_54_tllist_Omap__cong0, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X3:((tLList446370796tllist @ A) @ B),F1:(A > C),G12:(A > C),F2:(B > D),G2:(B > D)]: (((! [Z1:A]: (((((member @ A) @ Z1) @ (((tLList1719791291e_tset @ A) @ B) @ X3)) => ((F1 @ Z1) = (G12 @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((tLList457864275tllist @ A) @ B) @ X3)) => ((F2 @ Z2) = (G2 @ Z2))))) => ((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X3) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ G12) @ G2) @ X3))))))).
% 2.85/1.53 thf(fact_55_tllist_Oinj__map__strong, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,X3:((tLList446370796tllist @ A) @ B),Xa2:((tLList446370796tllist @ A) @ B),F1:(A > C),F1a:(A > C),F2:(B > D),F2a:(B > D)]: (((! [Z1:A,Z1a:A]: (((((member @ A) @ Z1) @ (((tLList1719791291e_tset @ A) @ B) @ X3)) => ((((member @ A) @ Z1a) @ (((tLList1719791291e_tset @ A) @ B) @ Xa2)) => (((F1 @ Z1) = (F1a @ Z1a)) => (Z1 = Z1a)))))) => ((! [Z2:B,Z2a:B]: (((((member @ B) @ Z2) @ (((tLList457864275tllist @ A) @ B) @ X3)) => ((((member @ B) @ Z2a) @ (((tLList457864275tllist @ A) @ B) @ Xa2)) => (((F2 @ Z2) = (F2a @ Z2a)) => (Z2 = Z2a)))))) => (((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X3) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1a) @ F2a) @ Xa2)) => (X3 = Xa2))))))).
% 2.85/1.53 thf(fact_56_tllist_Omap__sel_I2_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),F1:(A > C),F2:(B > D)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => ((((tLList_Mirabelle_thd @ C) @ D) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ A2)) = (F1 @ (((tLList_Mirabelle_thd @ A) @ B) @ A2))))))).
% 2.85/1.53 thf(fact_57_tllist_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X21:A,X22:((tLList446370796tllist @ A) @ B),Y21:C,Y22:((tLList446370796tllist @ C) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) @ ((((tLList1992840728_TCons @ C) @ D) @ Y21) @ Y22)) = (((R1 @ X21) @ Y21) & ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X22) @ Y22)))))).
% 2.85/1.53 thf(fact_58_tllist_Omap__disc__iff, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,F1:(A > C),F2:(B > D),A2:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ C) @ D) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ A2)) = (((tLList1968894004s_TNil @ A) @ B) @ A2))))).
% 2.85/1.53 thf(fact_59_tllist_Orel__inject_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X1:B,Y1:D]: ((((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) @ (((tLList57907754e_TNil @ D) @ C) @ Y1)) = ((R2 @ X1) @ Y1))))).
% 2.85/1.53 thf(fact_60_tllist_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,B:$tType,E:$tType,P4:(E > $o),G12:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E),A2:E]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))) = (~ ((P4 @ A2))))))).
% 2.85/1.53 thf(fact_61_tllist_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,B:$tType,E:$tType,P4:(E > $o),G12:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E),A2:E]: (((((tLList1968894004s_TNil @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (P4 @ A2))))).
% 2.85/1.53 thf(fact_62_tllist_Opred__inject_I2_J, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P2:(B > $o),A2:A,Aa2:((tLList446370796tllist @ A) @ B)]: (((((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ ((((tLList1992840728_TCons @ A) @ B) @ A2) @ Aa2)) = ((P1 @ A2) & (((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ Aa2)))))).
% 2.85/1.53 thf(fact_63_tllist_Opred__inject_I1_J, axiom, (! [A:$tType,B:$tType,P1:(A > $o),P2:(B > $o),A2:B]: (((((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ (((tLList57907754e_TNil @ B) @ A) @ A2)) = (P2 @ A2))))).
% 2.85/1.53 thf(fact_64_tllist_Orel__refl, axiom, (! [D:$tType,C:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X3:((tLList446370796tllist @ C) @ D)]: (((! [X4:C]: (((R1a @ X4) @ X4))) => ((! [X4:D]: (((R2a @ X4) @ X4))) => ((((((((tLList1380991092t_all2 @ C) @ C) @ D) @ D) @ R1a) @ R2a) @ X3) @ X3)))))).
% 2.85/1.53 thf(fact_65_tllist_Orel__eq, axiom, (! [B:$tType,A:$tType]: ((((((((tLList1380991092t_all2 @ A) @ A) @ B) @ B) @ (^ [Y2:A,Z3:A]: ((Y2 = Z3)))) @ (^ [Y2:B,Z3:B]: ((Y2 = Z3)))) = (^ [Y2:((tLList446370796tllist @ A) @ B),Z3:((tLList446370796tllist @ A) @ B)]: ((Y2 = Z3))))))).
% 2.85/1.53 thf(fact_66_tllist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),X21:A,Y21:C,R2:(B > (D > $o)),X22:((tLList446370796tllist @ A) @ B),Y22:((tLList446370796tllist @ C) @ D)]: ((((R1 @ X21) @ Y21) => (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X22) @ Y22) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) @ ((((tLList1992840728_TCons @ C) @ D) @ Y21) @ Y22))))))).
% 2.85/1.53 thf(fact_67_tllist_Orel__intros_I1_J, axiom, (! [B:$tType,A:$tType,C:$tType,D:$tType,R2:(B > (D > $o)),X1:B,Y1:D,R1:(A > (C > $o))]: ((((R2 @ X1) @ Y1) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) @ (((tLList57907754e_TNil @ D) @ C) @ Y1)))))).
% 2.85/1.53 thf(fact_68_tllist_Omap__id, axiom, (! [B:$tType,A:$tType,T:((tLList446370796tllist @ A) @ B)]: (((((((((tLList1669959861e_tmap @ A) @ A) @ B) @ B) @ (id @ A)) @ (id @ B)) @ T) = T)))).
% 2.85/1.53 thf(fact_69_tllist_Omap__id0, axiom, (! [B:$tType,A:$tType]: ((((((((tLList1669959861e_tmap @ A) @ A) @ B) @ B) @ (id @ A)) @ (id @ B)) = (id @ ((tLList446370796tllist @ A) @ B)))))).
% 2.85/1.53 thf(fact_70_tllist_Osimps_I15_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,F1:(A > C),F2:(B > D),X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = ((((tLList1992840728_TCons @ C) @ D) @ (F1 @ X21)) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X22)))))).
% 2.85/1.53 thf(fact_71_tllist_Osimps_I14_J, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F1:(A > C),F2:(B > D),X1:B]: (((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (((tLList57907754e_TNil @ D) @ C) @ (F2 @ X1)))))).
% 2.85/1.53 thf(fact_72_tllist_Ocorec__disc_I2_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G12:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((~ ((P4 @ A2))) => (~ ((((tLList1968894004s_TNil @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))))))).
% 2.85/1.53 thf(fact_73_tllist_Ocorec__disc_I1_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G12:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((P4 @ A2) => (((tLList1968894004s_TNil @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))))).
% 2.85/1.53 thf(fact_74_tllist_Ocorec_I2_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G12:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((~ ((P4 @ A2))) => (((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2) = ((((tLList1992840728_TCons @ A) @ B) @ (G212 @ A2)) @ ((((if @ ((tLList446370796tllist @ A) @ B)) @ (Q222 @ A2)) @ (G2212 @ A2)) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.85/1.53 thf(fact_75_tllist_Ocorec_I1_J, axiom, (! [A:$tType,B:$tType,E:$tType,P4:(E > $o),A2:E,G12:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((P4 @ A2) => (((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2) = (((tLList57907754e_TNil @ B) @ A) @ (G12 @ A2))))))).
% 2.85/1.53 thf(fact_76_tllist_Ocorec__sel_I3_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,Q222:(E > $o),G12:(E > B),G212:(E > A),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((~ ((P4 @ A2))) => (((Q222 @ A2) => ((((tLList_Mirabelle_ttl @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (G2212 @ A2))) & ((~ ((Q222 @ A2))) => ((((tLList_Mirabelle_ttl @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.85/1.53 thf(fact_77_tllist_Ocorec__sel_I1_J, axiom, (! [Aa:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G12:(E > A),G212:(E > Aa),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ Aa) @ A)),G2222:(E > E)]: (((P4 @ A2) => ((((tLList2110128105rminal @ Aa) @ A) @ ((((((((((tLList1614408749tllist @ E) @ A) @ Aa) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (G12 @ A2)))))).
% 2.85/1.53 thf(fact_78_tllist_Ocorec__sel_I2_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G12:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((~ ((P4 @ A2))) => ((((tLList_Mirabelle_thd @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G12) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (G212 @ A2)))))).
% 2.85/1.53 thf(fact_79_tllist_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),Y21:A,Y22:((tLList446370796tllist @ A) @ B),X1:D]: ((~ (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ ((((tLList1992840728_TCons @ A) @ B) @ Y21) @ Y22)) @ (((tLList57907754e_TNil @ D) @ C) @ X1))))))).
% 2.85/1.53 thf(fact_80_tllist_Orel__distinct_I1_J, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X1:B,Y21:C,Y22:((tLList446370796tllist @ C) @ D)]: ((~ (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) @ ((((tLList1992840728_TCons @ C) @ D) @ Y21) @ Y22))))))).
% 2.85/1.53 thf(fact_81_tllist_Orel__cases, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),A2:((tLList446370796tllist @ A) @ B),B3:((tLList446370796tllist @ C) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ A2) @ B3) => ((! [X4:B]: (((A2 = (((tLList57907754e_TNil @ B) @ A) @ X4)) => (! [Y3:D]: (((B3 = (((tLList57907754e_TNil @ D) @ C) @ Y3)) => (~ (((R2 @ X4) @ Y3))))))))) => (~ ((! [X1a:A,X23:((tLList446370796tllist @ A) @ B)]: (((A2 = ((((tLList1992840728_TCons @ A) @ B) @ X1a) @ X23)) => (! [Y1a:C,Y23:((tLList446370796tllist @ C) @ D)]: (((B3 = ((((tLList1992840728_TCons @ C) @ D) @ Y1a) @ Y23)) => (((R1 @ X1a) @ Y1a) => (~ (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X23) @ Y23))))))))))))))))).
% 2.85/1.53 thf(fact_82_tllist_Orel__refl__strong, axiom, (! [B:$tType,A:$tType,X3:((tLList446370796tllist @ A) @ B),R1a:(A > (A > $o)),R2a:(B > (B > $o))]: (((! [Z1:A]: (((((member @ A) @ Z1) @ (((tLList1719791291e_tset @ A) @ B) @ X3)) => ((R1a @ Z1) @ Z1)))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((tLList457864275tllist @ A) @ B) @ X3)) => ((R2a @ Z2) @ Z2)))) => ((((((((tLList1380991092t_all2 @ A) @ A) @ B) @ B) @ R1a) @ R2a) @ X3) @ X3)))))).
% 2.85/1.53 thf(fact_83_tllist_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X3:((tLList446370796tllist @ A) @ B),Y:((tLList446370796tllist @ C) @ D),R1a:(A > (C > $o)),R2a:(B > (D > $o))]: ((((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X3) @ Y) => ((! [Z1:A,Y12:C]: (((((member @ A) @ Z1) @ (((tLList1719791291e_tset @ A) @ B) @ X3)) => ((((member @ C) @ Y12) @ (((tLList1719791291e_tset @ C) @ D) @ Y)) => (((R1 @ Z1) @ Y12) => ((R1a @ Z1) @ Y12)))))) => ((! [Z2:B,Y23:D]: (((((member @ B) @ Z2) @ (((tLList457864275tllist @ A) @ B) @ X3)) => ((((member @ D) @ Y23) @ (((tLList457864275tllist @ C) @ D) @ Y)) => (((R2 @ Z2) @ Y23) => ((R2a @ Z2) @ Y23)))))) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ X3) @ Y))))))).
% 2.85/1.53 thf(fact_84_tllist_Orel__cong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,X3:((tLList446370796tllist @ A) @ B),Ya:((tLList446370796tllist @ A) @ B),Y:((tLList446370796tllist @ C) @ D),Xa2:((tLList446370796tllist @ C) @ D),R1:(A > (C > $o)),R1a:(A > (C > $o)),R2:(B > (D > $o)),R2a:(B > (D > $o))]: (((X3 = Ya) => ((Y = Xa2) => ((! [Z1:A,Y12:C]: (((((member @ A) @ Z1) @ (((tLList1719791291e_tset @ A) @ B) @ Ya)) => ((((member @ C) @ Y12) @ (((tLList1719791291e_tset @ C) @ D) @ Xa2)) => (((R1 @ Z1) @ Y12) = ((R1a @ Z1) @ Y12)))))) => ((! [Z2:B,Y23:D]: (((((member @ B) @ Z2) @ (((tLList457864275tllist @ A) @ B) @ Ya)) => ((((member @ D) @ Y23) @ (((tLList457864275tllist @ C) @ D) @ Xa2)) => (((R2 @ Z2) @ Y23) = ((R2a @ Z2) @ Y23)))))) => (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X3) @ Y) = ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ Ya) @ Xa2))))))))).
% 2.85/1.53 thf(fact_85_tllist_Omap__sel_I3_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),F1:(A > C),F2:(B > D)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => ((((tLList_Mirabelle_ttl @ C) @ D) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ A2)) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ (((tLList_Mirabelle_ttl @ A) @ B) @ A2))))))).
% 2.85/1.53 thf(fact_86_tllist_Omap__sel_I1_J, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),F1:(A > C),F2:(B > D)]: (((((tLList1968894004s_TNil @ A) @ B) @ A2) => ((((tLList2110128105rminal @ C) @ D) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ A2)) = (F2 @ (((tLList2110128105rminal @ A) @ B) @ A2))))))).
% 2.85/1.53 thf(fact_87_insert__absorb2, axiom, (! [A:$tType,X3:A,A3:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ X3) @ A3)) = (((insert @ A) @ X3) @ A3))))).
% 2.85/1.53 thf(fact_88_insert__iff, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A3)) = ((A2 = B3) | (((member @ A) @ A2) @ A3)))))).
% 2.85/1.53 thf(fact_89_insertCI, axiom, (! [A:$tType,A2:A,B4:(set @ A),B3:A]: ((((~ ((((member @ A) @ A2) @ B4))) => (A2 = B3)) => (((member @ A) @ A2) @ (((insert @ A) @ B3) @ B4)))))).
% 2.85/1.53 thf(fact_90_tllist_Osimps_I22_J, axiom, (! [A:$tType,B:$tType,X1:B]: (((((tLList457864275tllist @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (((insert @ B) @ X1) @ (bot_bot @ (set @ B))))))).
% 2.85/1.53 thf(fact_91_tllist_Opred__set, axiom, (! [B:$tType,A:$tType]: ((((tLList11265572tllist @ A) @ B) = (^ [P12:(A > $o),P22:(B > $o),X2:((tLList446370796tllist @ A) @ B)]: (((! [Y4:A]: (((((member @ A) @ Y4) @ (((tLList1719791291e_tset @ A) @ B) @ X2)) => (P12 @ Y4)))) & (! [Y4:B]: (((((member @ B) @ Y4) @ (((tLList457864275tllist @ A) @ B) @ X2)) => (P22 @ Y4))))))))))).
% 2.85/1.53 thf(fact_92_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => (? [B5:(set @ A)]: (((A3 = (((insert @ A) @ A2) @ B5)) & (~ ((((member @ A) @ A2) @ B5)))))))))).
% 2.85/1.53 thf(fact_93_insert__commute, axiom, (! [A:$tType,X3:A,Y:A,A3:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ Y) @ A3)) = (((insert @ A) @ Y) @ (((insert @ A) @ X3) @ A3)))))).
% 2.85/1.53 thf(fact_94_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.85/1.53 thf(fact_95_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X2:A]: ((~ ((((member @ A) @ X2) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_96_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 2.85/1.53 thf(fact_97_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 2.85/1.53 thf(fact_98_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_99_ball__empty, axiom, (! [A:$tType,P:(A > $o),X:A]: (((((member @ A) @ X) @ (bot_bot @ (set @ A))) => (P @ X))))).
% 2.85/1.53 thf(fact_100_singleton__inject, axiom, (! [A:$tType,A2:A,B3:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A2 = B3))))).
% 2.85/1.53 thf(fact_101_insert__not__empty, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((insert @ A) @ A2) @ A3) != (bot_bot @ (set @ A)))))).
% 2.85/1.53 thf(fact_102_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B3:A,C2:A,D2:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C2) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A2 = C2) & (B3 = D2)) | ((A2 = D2) & (B3 = C2))))))).
% 2.85/1.53 thf(fact_103_singleton__iff, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B3 = A2))))).
% 2.85/1.53 thf(fact_104_singletonD, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B3 = A2))))).
% 2.85/1.53 thf(fact_105_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.85/1.53 thf(fact_106_Ball__def, axiom, (! [A:$tType]: (((ball @ A) = (^ [A5:(set @ A),P5:(A > $o)]: ((! [X2:A]: (((((member @ A) @ X2) @ A5) => (P5 @ X2)))))))))).
% 2.85/1.53 thf(fact_107_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 2.85/1.53 thf(fact_108_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y3:A]: ((~ ((((member @ A) @ Y3) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_109_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X2:A]: ((((member @ A) @ X2) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_110_tllist_Osimps_I20_J, axiom, (! [B:$tType,A:$tType,X1:B]: (((((tLList1719791291e_tset @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (bot_bot @ (set @ A)))))).
% 2.85/1.53 thf(fact_111_insertE, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A3)) => ((A2 != B3) => (((member @ A) @ A2) @ A3)))))).
% 2.85/1.53 thf(fact_112_insertI1, axiom, (! [A:$tType,A2:A,B4:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B4))))).
% 2.85/1.53 thf(fact_113_insertI2, axiom, (! [A:$tType,A2:A,B4:(set @ A),B3:A]: (((((member @ A) @ A2) @ B4) => (((member @ A) @ A2) @ (((insert @ A) @ B3) @ B4)))))).
% 2.85/1.53 thf(fact_114_Set_Oset__insert, axiom, (! [A:$tType,X3:A,A3:(set @ A)]: (((((member @ A) @ X3) @ A3) => (~ ((! [B5:(set @ A)]: (((A3 = (((insert @ A) @ X3) @ B5)) => (((member @ A) @ X3) @ B5)))))))))).
% 2.85/1.53 thf(fact_115_insert__ident, axiom, (! [A:$tType,X3:A,A3:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ X3) @ A3))) => ((~ ((((member @ A) @ X3) @ B4))) => (((((insert @ A) @ X3) @ A3) = (((insert @ A) @ X3) @ B4)) = (A3 = B4))))))).
% 2.85/1.53 thf(fact_116_insert__absorb, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => ((((insert @ A) @ A2) @ A3) = A3))))).
% 2.85/1.53 thf(fact_117_insert__eq__iff, axiom, (! [A:$tType,A2:A,A3:(set @ A),B3:A,B4:(set @ A)]: (((~ ((((member @ A) @ A2) @ A3))) => ((~ ((((member @ A) @ B3) @ B4))) => (((((insert @ A) @ A2) @ A3) = (((insert @ A) @ B3) @ B4)) = (((A2 = B3) => (A3 = B4)) & ((A2 != B3) => (? [C3:(set @ A)]: (((A3 = (((insert @ A) @ B3) @ C3)) & ((~ ((((member @ A) @ B3) @ C3))) & ((B4 = (((insert @ A) @ A2) @ C3)) & (~ ((((member @ A) @ A2) @ C3)))))))))))))))).
% 2.85/1.53 thf(fact_118_the__elem__eq, axiom, (! [A:$tType,X3:A]: ((((the_elem @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = X3)))).
% 2.85/1.53 thf(fact_119_bot__apply, axiom, (! [C:$tType,D:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D > C)) = (^ [X2:D]: ((bot_bot @ C)))))))).
% 2.85/1.53 thf(fact_120_is__singletonI, axiom, (! [A:$tType,X3:A]: (((is_singleton @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_121_override__on__emptyset, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((((((override_on @ A) @ B) @ F) @ G) @ (bot_bot @ (set @ A))) = F)))).
% 2.85/1.53 thf(fact_122_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A5:(set @ A)]: ((A5 = (bot_bot @ (set @ A))))))))).
% 2.85/1.53 thf(fact_123_override__on__apply__notin, axiom, (! [B:$tType,A:$tType,A2:A,A3:(set @ A),F:(A > B),G:(A > B)]: (((~ ((((member @ A) @ A2) @ A3))) => (((((((override_on @ A) @ B) @ F) @ G) @ A3) @ A2) = (F @ A2)))))).
% 2.85/1.53 thf(fact_124_override__on__apply__in, axiom, (! [B:$tType,A:$tType,A2:A,A3:(set @ A),F:(A > B),G:(A > B)]: (((((member @ A) @ A2) @ A3) => (((((((override_on @ A) @ B) @ F) @ G) @ A3) @ A2) = (G @ A2)))))).
% 2.85/1.53 thf(fact_125_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.85/1.53 thf(fact_126_override__on__def, axiom, (! [B:$tType,A:$tType]: ((((override_on @ A) @ B) = (^ [F3:(A > B),G3:(A > B),A5:(set @ A),A4:A]: (((((if @ B) @ (((member @ A) @ A4) @ A5)) @ (G3 @ A4)) @ (F3 @ A4)))))))).
% 2.85/1.53 thf(fact_127_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A5:(set @ A)]: ((A5 = (((insert @ A) @ ((the_elem @ A) @ A5)) @ (bot_bot @ (set @ A)))))))))).
% 2.85/1.53 thf(fact_128_is__singletonI_H, axiom, (! [A:$tType,A3:(set @ A)]: (((A3 != (bot_bot @ (set @ A))) => ((! [X4:A,Y3:A]: (((((member @ A) @ X4) @ A3) => ((((member @ A) @ Y3) @ A3) => (X4 = Y3))))) => ((is_singleton @ A) @ A3)))))).
% 2.85/1.53 thf(fact_129_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X2:A]: ((bot_bot @ B)))))))).
% 2.85/1.53 thf(fact_130_is__singletonE, axiom, (! [A:$tType,A3:(set @ A)]: ((((is_singleton @ A) @ A3) => (~ ((! [X4:A]: ((A3 != (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 2.85/1.53 thf(fact_131_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A5:(set @ A)]: ((? [X2:A]: ((A5 = (((insert @ A) @ X2) @ (bot_bot @ (set @ A)))))))))))).
% 2.85/1.53 thf(fact_132_pairwise__singleton, axiom, (! [A:$tType,P:(A > (A > $o)),A3:A]: ((((pairwise @ A) @ P) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_133_ball__reg, axiom, (! [A:$tType,R:(set @ A),P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ R) => ((P @ X4) => (Q @ X4))))) => ((! [X4:A]: (((((member @ A) @ X4) @ R) => (P @ X4)))) => (! [X:A]: (((((member @ A) @ X) @ R) => (Q @ X))))))))).
% 2.85/1.53 thf(fact_134_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (bot_bot @ (set @ A))))))))).
% 2.85/1.53 thf(fact_135_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.85/1.53 thf(fact_136_pairwise__def, axiom, (! [A:$tType]: (((pairwise @ A) = (^ [R3:(A > (A > $o)),S:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ S) => (! [Y4:A]: (((((member @ A) @ Y4) @ S) => ((X2 != Y4) => ((R3 @ X2) @ Y4)))))))))))))).
% 2.85/1.53 thf(fact_137_pairwise__empty, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((pairwise @ A) @ P) @ (bot_bot @ (set @ A)))))).
% 2.85/1.53 thf(fact_138_pairwise__insert, axiom, (! [A:$tType,R4:(A > (A > $o)),X3:A,S2:(set @ A)]: (((((pairwise @ A) @ R4) @ (((insert @ A) @ X3) @ S2)) = ((! [Y4:A]: ((((((member @ A) @ Y4) @ S2) & (Y4 != X3)) => (((R4 @ X3) @ Y4) & ((R4 @ Y4) @ X3))))) & (((pairwise @ A) @ R4) @ S2)))))).
% 2.85/1.53 thf(fact_139_in__inv__imagep, axiom, (! [B:$tType,A:$tType]: ((((inv_imagep @ A) @ B) = (^ [R5:(A > (A > $o)),F3:(B > A),X2:B,Y4:B]: (((R5 @ (F3 @ X2)) @ (F3 @ Y4)))))))).
% 2.85/1.53 thf(fact_140_id__fcomp, axiom, (! [B:$tType,A:$tType,G:(A > B)]: (((((((fcomp @ A) @ A) @ B) @ (id @ A)) @ G) = G)))).
% 2.85/1.53 thf(fact_141_fcomp__id, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((((fcomp @ A) @ B) @ B) @ F) @ (id @ B)) = F)))).
% 2.85/1.53 thf(fact_142_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A2:A,A3:(set @ A),B3:A]: ((((((insert @ A) @ A2) @ A3) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = ((A2 = B3) & (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A))))))))).
% 2.85/1.53 thf(fact_143_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.85/1.53 thf(fact_144_subsetI, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A3) => (((member @ A) @ X4) @ B4)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B4))))).
% 2.85/1.53 thf(fact_145_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ A3) => (A3 = B4)))))).
% 2.85/1.53 thf(fact_146_fcomp__apply, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((fcomp @ B) @ C) @ A) = (^ [F3:(B > C),G3:(C > A),X2:B]: ((G3 @ (F3 @ X2)))))))).
% 2.85/1.53 thf(fact_147_subset__empty, axiom, (! [A:$tType,A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = (A3 = (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_148_empty__subsetI, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A3)))).
% 2.85/1.53 thf(fact_149_insert__subset, axiom, (! [A:$tType,X3:A,A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ A3)) @ B4) = ((((member @ A) @ X3) @ B4) & (((ord_less_eq @ (set @ A)) @ A3) @ B4)))))).
% 2.85/1.53 thf(fact_150_singleton__insert__inj__eq, axiom, (! [A:$tType,B3:A,A2:A,A3:(set @ A)]: ((((((insert @ A) @ B3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A2) @ A3)) = ((A2 = B3) & (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A))))))))).
% 2.85/1.53 thf(fact_151_bot_Oextremum, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A2))))))).
% 2.85/1.53 thf(fact_152_bot_Oextremum__unique, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) = (A2 = (bot_bot @ A))))))))).
% 2.85/1.53 thf(fact_153_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) => (A2 = (bot_bot @ A))))))))).
% 2.85/1.53 thf(fact_154_set__mp, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((member @ A) @ X3) @ A3) => (((member @ A) @ X3) @ B4)))))).
% 2.85/1.53 thf(fact_155_in__mono, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((member @ A) @ X3) @ A3) => (((member @ A) @ X3) @ B4)))))).
% 2.85/1.53 thf(fact_156_subsetD, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B4)))))).
% 2.85/1.53 thf(fact_157_subsetCE, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B4)))))).
% 2.85/1.53 thf(fact_158_equalityE, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (~ ((((ord_less_eq @ (set @ A)) @ B4) @ A3)))))))))).
% 2.85/1.53 thf(fact_159_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A5) => (((member @ A) @ X2) @ B6)))))))))).
% 2.85/1.53 thf(fact_160_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (((ord_less_eq @ (set @ A)) @ A3) @ B4))))).
% 2.85/1.53 thf(fact_161_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A3))))).
% 2.85/1.53 thf(fact_162_set__rev__mp, axiom, (! [A:$tType,X3:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ X3) @ A3) => ((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (((member @ A) @ X3) @ B4)))))).
% 2.85/1.53 thf(fact_163_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A5) => (((member @ A) @ T2) @ B6)))))))))).
% 2.85/1.53 thf(fact_164_rev__subsetD, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A3) => ((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (((member @ A) @ C2) @ B4)))))).
% 2.85/1.53 thf(fact_165_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 2.85/1.53 thf(fact_166_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) => (Q @ X4)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.85/1.53 thf(fact_167_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C4) => (((ord_less_eq @ (set @ A)) @ A3) @ C4)))))).
% 2.85/1.53 thf(fact_168_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y2:(set @ A),Z3:(set @ A)]: ((Y2 = Z3))) = (^ [A5:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A5)))))))).
% 2.85/1.53 thf(fact_169_contra__subsetD, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((~ ((((member @ A) @ C2) @ B4))) => (~ ((((member @ A) @ C2) @ A3)))))))).
% 2.85/1.53 thf(fact_170_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 2.85/1.53 thf(fact_171_fcomp__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((fcomp @ A) @ B) @ C) = (^ [F3:(A > B),G3:(B > C),X2:A]: ((G3 @ (F3 @ X2)))))))).
% 2.85/1.53 thf(fact_172_fcomp__assoc, axiom, (! [A:$tType,D:$tType,B:$tType,C:$tType,F:(A > D),G:(D > C),H:(C > B)]: (((((((fcomp @ A) @ C) @ B) @ (((((fcomp @ A) @ D) @ C) @ F) @ G)) @ H) = (((((fcomp @ A) @ D) @ B) @ F) @ (((((fcomp @ D) @ C) @ B) @ G) @ H)))))).
% 2.85/1.53 thf(fact_173_subset__insertI2, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),B3:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B3) @ B4)))))).
% 2.85/1.53 thf(fact_174_subset__insertI, axiom, (! [A:$tType,B4:(set @ A),A2:A]: ((((ord_less_eq @ (set @ A)) @ B4) @ (((insert @ A) @ A2) @ B4))))).
% 2.85/1.53 thf(fact_175_subset__insert, axiom, (! [A:$tType,X3:A,A3:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ X3) @ A3))) => ((((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ X3) @ B4)) = (((ord_less_eq @ (set @ A)) @ A3) @ B4)))))).
% 2.85/1.53 thf(fact_176_Set_Oinsert__mono, axiom, (! [A:$tType,C4:(set @ A),D3:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ C4) @ D3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A2) @ C4)) @ (((insert @ A) @ A2) @ D3)))))).
% 2.85/1.53 thf(fact_177_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))))))))).
% 2.85/1.53 thf(fact_178_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))))))))).
% 2.85/1.53 thf(fact_179_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)))))))).
% 2.85/1.53 thf(fact_180_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F3:(A > B),G3:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F3 @ X2)) @ (G3 @ X2))))))))))).
% 2.85/1.53 thf(fact_181_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C2) => ((! [X4:B,Y3:B]: (((((ord_less_eq @ B) @ X4) @ Y3) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.85/1.53 thf(fact_182_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ C) @ (F @ B3)) @ C2) => ((! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => (((ord_less_eq @ C) @ (F @ X4)) @ (F @ Y3))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C2)))))))))).
% 2.85/1.53 thf(fact_183_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C2:B]: (((A2 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C2) => ((! [X4:B,Y3:B]: (((((ord_less_eq @ B) @ X4) @ Y3) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.85/1.53 thf(fact_184_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B3) => (((F @ B3) = C2) => ((! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => (((ord_less_eq @ B) @ (F @ X4)) @ (F @ Y3))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C2)))))))))).
% 2.85/1.53 thf(fact_185_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y2:A,Z3:A]: ((Y2 = Z3))) = (^ [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X2))))))))).
% 2.85/1.53 thf(fact_186_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ X3) => (X3 = Y))))))))).
% 2.85/1.53 thf(fact_187_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) | (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 2.85/1.53 thf(fact_188_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((X3 = Y) => (((ord_less_eq @ A) @ X3) @ Y)))))))).
% 2.85/1.53 thf(fact_189_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y))) => (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 2.85/1.53 thf(fact_190_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.85/1.53 thf(fact_191_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z4:A]: ((((((ord_less_eq @ A) @ X3) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z4)))) => (((((ord_less_eq @ A) @ Y) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z4)))) => (((((ord_less_eq @ A) @ X3) @ Z4) => (~ ((((ord_less_eq @ A) @ Z4) @ Y)))) => (((((ord_less_eq @ A) @ Z4) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X3)))) => (((((ord_less_eq @ A) @ Y) @ Z4) => (~ ((((ord_less_eq @ A) @ Z4) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z4) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y))))))))))))))))).
% 2.85/1.53 thf(fact_192_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X3:A]: (((((ord_less_eq @ A) @ Y) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y) = (X3 = Y))))))))).
% 2.85/1.53 thf(fact_193_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((A2 = B3) => ((((ord_less_eq @ A) @ B3) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.85/1.53 thf(fact_194_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((B3 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.85/1.53 thf(fact_195_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ A2) => (A2 = B3))))))))).
% 2.85/1.53 thf(fact_196_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z4:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z4) => (((ord_less_eq @ A) @ X3) @ Z4))))))))).
% 2.85/1.53 thf(fact_197_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.85/1.53 thf(fact_198_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A2:A,B3:A]: (((! [A6:A,B7:A]: (((((ord_less_eq @ A) @ A6) @ B7) => ((P @ A6) @ B7)))) => ((! [A6:A,B7:A]: ((((P @ B7) @ A6) => ((P @ A6) @ B7)))) => ((P @ A2) @ B3))))))))).
% 2.85/1.53 thf(fact_199_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C2) @ B3) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.85/1.53 thf(fact_200_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ A2) @ B3) => (A2 = B3))))))))).
% 2.85/1.53 thf(fact_201_pairwise__subset, axiom, (! [A:$tType,P:(A > (A > $o)),S3:(set @ A),T3:(set @ A)]: (((((pairwise @ A) @ P) @ S3) => ((((ord_less_eq @ (set @ A)) @ T3) @ S3) => (((pairwise @ A) @ P) @ T3)))))).
% 2.85/1.53 thf(fact_202_subset__singletonD, axiom, (! [A:$tType,A3:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) => ((A3 = (bot_bot @ (set @ A))) | (A3 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))).
% 2.85/1.53 thf(fact_203_subset__singleton__iff, axiom, (! [A:$tType,X5:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ X5) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = ((X5 = (bot_bot @ (set @ A))) | (X5 = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))))).
% 2.85/1.53 thf(fact_204_Ball__Collect, axiom, (! [A:$tType]: (((ball @ A) = (^ [A5:(set @ A),P5:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ A5) @ ((collect @ A) @ P5)))))))).
% 2.85/1.53 thf(fact_205_insert__subsetI, axiom, (! [A:$tType,X3:A,A3:(set @ A),X5:(set @ A)]: (((((member @ A) @ X3) @ A3) => ((((ord_less_eq @ (set @ A)) @ X5) @ A3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ X5)) @ A3)))))).
% 2.85/1.53 thf(fact_206_subset__emptyI, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A3))))) => (((ord_less_eq @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_207_subset__Compl__singleton, axiom, (! [A:$tType,A3:(set @ A),B3:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ ((uminus_uminus @ (set @ A)) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A))))) = (~ ((((member @ A) @ B3) @ A3))))))).
% 2.85/1.53 thf(fact_208_Compl__eq__Compl__iff, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A3) = ((uminus_uminus @ (set @ A)) @ B4)) = (A3 = B4))))).
% 2.85/1.53 thf(fact_209_Compl__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A3)) = (~ ((((member @ A) @ C2) @ A3))))))).
% 2.85/1.53 thf(fact_210_ComplI, axiom, (! [A:$tType,C2:A,A3:(set @ A)]: (((~ ((((member @ A) @ C2) @ A3))) => (((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A3)))))).
% 2.85/1.53 thf(fact_211_Compl__anti__mono, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ B4)) @ ((uminus_uminus @ (set @ A)) @ A3)))))).
% 2.85/1.53 thf(fact_212_Compl__subset__Compl__iff, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A3)) @ ((uminus_uminus @ (set @ A)) @ B4)) = (((ord_less_eq @ (set @ A)) @ B4) @ A3))))).
% 2.85/1.53 thf(fact_213_tllist_Orel__mono, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R1:(A > (C > $o)),R1a:(A > (C > $o)),R2:(B > (D > $o)),R2a:(B > (D > $o))]: (((((ord_less_eq @ (A > (C > $o))) @ R1) @ R1a) => ((((ord_less_eq @ (B > (D > $o))) @ R2) @ R2a) => (((ord_less_eq @ (((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ C) @ D) > $o))) @ ((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2)) @ ((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1a) @ R2a))))))).
% 2.85/1.53 thf(fact_214_double__complement, axiom, (! [A:$tType,A3:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A3)) = A3)))).
% 2.85/1.53 thf(fact_215_ComplD, axiom, (! [A:$tType,C2:A,A3:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A3)) => (~ ((((member @ A) @ C2) @ A3))))))).
% 2.85/1.53 thf(fact_216_subset__Compl__self__eq, axiom, (! [A:$tType,A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ ((uminus_uminus @ (set @ A)) @ A3)) = (A3 = (bot_bot @ (set @ A))))))).
% 2.85/1.53 thf(fact_217_Compl__insert, axiom, (! [A:$tType,X3:A,A3:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ (((insert @ A) @ X3) @ A3)) = (((minus_minus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A3)) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))).
% 2.85/1.53 thf(fact_218_disjoint__eq__subset__Compl, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))) = (((ord_less_eq @ (set @ A)) @ A3) @ ((uminus_uminus @ (set @ A)) @ B4)))))).
% 2.85/1.53 thf(fact_219_IntI, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A3) => ((((member @ A) @ C2) @ B4) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4))))))).
% 2.85/1.53 thf(fact_220_Int__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) = ((((member @ A) @ C2) @ A3) & (((member @ A) @ C2) @ B4)))))).
% 2.85/1.53 thf(fact_221_DiffI, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A3) => ((~ ((((member @ A) @ C2) @ B4))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A3) @ B4))))))).
% 2.85/1.53 thf(fact_222_Diff__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A3) @ B4)) = ((((member @ A) @ C2) @ A3) & (~ ((((member @ A) @ C2) @ B4)))))))).
% 2.85/1.53 thf(fact_223_Diff__idemp, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A3) @ B4)) @ B4) = (((minus_minus @ (set @ A)) @ A3) @ B4))))).
% 2.85/1.53 thf(fact_224_predicate2I, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Q:(A > (B > $o))]: (((! [X4:A,Y3:B]: ((((P @ X4) @ Y3) => ((Q @ X4) @ Y3)))) => (((ord_less_eq @ (A > (B > $o))) @ P) @ Q))))).
% 2.85/1.53 thf(fact_225_Int__subset__iff, axiom, (! [A:$tType,C4:(set @ A),A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) = ((((ord_less_eq @ (set @ A)) @ C4) @ A3) & (((ord_less_eq @ (set @ A)) @ C4) @ B4)))))).
% 2.85/1.53 thf(fact_226_Diff__empty, axiom, (! [A:$tType,A3:(set @ A)]: (((((minus_minus @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = A3)))).
% 2.85/1.53 thf(fact_227_empty__Diff, axiom, (! [A:$tType,A3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A3) = (bot_bot @ (set @ A)))))).
% 2.85/1.53 thf(fact_228_Diff__cancel, axiom, (! [A:$tType,A3:(set @ A)]: (((((minus_minus @ (set @ A)) @ A3) @ A3) = (bot_bot @ (set @ A)))))).
% 2.85/1.53 thf(fact_229_Int__insert__right__if1, axiom, (! [A:$tType,A2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ A2) @ A3) => ((((inf_inf @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ B4)) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ A3) @ B4))))))).
% 2.85/1.53 thf(fact_230_Int__insert__right__if0, axiom, (! [A:$tType,A2:A,A3:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ A2) @ A3))) => ((((inf_inf @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ B4)) = (((inf_inf @ (set @ A)) @ A3) @ B4)))))).
% 2.85/1.53 thf(fact_231_insert__inter__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A),B4:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ A3)) @ (((insert @ A) @ A2) @ B4)) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)))))).
% 2.85/1.53 thf(fact_232_Int__insert__left__if1, axiom, (! [A:$tType,A2:A,C4:(set @ A),B4:(set @ A)]: (((((member @ A) @ A2) @ C4) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ B4)) @ C4) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ B4) @ C4))))))).
% 2.85/1.53 thf(fact_233_Int__insert__left__if0, axiom, (! [A:$tType,A2:A,C4:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ A2) @ C4))) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ B4)) @ C4) = (((inf_inf @ (set @ A)) @ B4) @ C4)))))).
% 2.85/1.53 thf(fact_234_insert__Diff1, axiom, (! [A:$tType,X3:A,B4:(set @ A),A3:(set @ A)]: (((((member @ A) @ X3) @ B4) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A3)) @ B4) = (((minus_minus @ (set @ A)) @ A3) @ B4)))))).
% 2.85/1.53 thf(fact_235_Diff__insert0, axiom, (! [A:$tType,X3:A,A3:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ X3) @ A3))) => ((((minus_minus @ (set @ A)) @ A3) @ (((insert @ A) @ X3) @ B4)) = (((minus_minus @ (set @ A)) @ A3) @ B4)))))).
% 2.85/1.53 thf(fact_236_insert__disjoint_I1_J, axiom, (! [A:$tType,A2:A,A3:(set @ A),B4:(set @ A)]: ((((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ A3)) @ B4) = (bot_bot @ (set @ A))) = ((~ ((((member @ A) @ A2) @ B4))) & ((((inf_inf @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A)))))))).
% 2.85/1.53 thf(fact_237_insert__disjoint_I2_J, axiom, (! [A:$tType,A2:A,A3:(set @ A),B4:(set @ A)]: ((((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ A3)) @ B4)) = ((~ ((((member @ A) @ A2) @ B4))) & ((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A3) @ B4))))))).
% 2.85/1.53 thf(fact_238_disjoint__insert_I1_J, axiom, (! [A:$tType,B4:(set @ A),A2:A,A3:(set @ A)]: ((((((inf_inf @ (set @ A)) @ B4) @ (((insert @ A) @ A2) @ A3)) = (bot_bot @ (set @ A))) = ((~ ((((member @ A) @ A2) @ B4))) & ((((inf_inf @ (set @ A)) @ B4) @ A3) = (bot_bot @ (set @ A)))))))).
% 2.85/1.53 thf(fact_239_disjoint__insert_I2_J, axiom, (! [A:$tType,A3:(set @ A),B3:A,B4:(set @ A)]: ((((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A3) @ (((insert @ A) @ B3) @ B4))) = ((~ ((((member @ A) @ B3) @ A3))) & ((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A3) @ B4))))))).
% 2.85/1.53 thf(fact_240_Diff__eq__empty__iff, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((((minus_minus @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))) = (((ord_less_eq @ (set @ A)) @ A3) @ B4))))).
% 2.85/1.53 thf(fact_241_insert__Diff__single, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((insert @ A) @ A2) @ (((minus_minus @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))) = (((insert @ A) @ A2) @ A3))))).
% 2.85/1.53 thf(fact_242_Diff__disjoint, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (((minus_minus @ (set @ A)) @ B4) @ A3)) = (bot_bot @ (set @ A)))))).
% 2.85/1.53 thf(fact_243_Compl__disjoint, axiom, (! [A:$tType,A3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ ((uminus_uminus @ (set @ A)) @ A3)) = (bot_bot @ (set @ A)))))).
% 2.85/1.53 thf(fact_244_Compl__disjoint2, axiom, (! [A:$tType,A3:(set @ A)]: (((((inf_inf @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A3)) @ A3) = (bot_bot @ (set @ A)))))).
% 2.85/1.53 thf(fact_245_Diff__Compl, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A3) @ ((uminus_uminus @ (set @ A)) @ B4)) = (((inf_inf @ (set @ A)) @ A3) @ B4))))).
% 2.85/1.53 thf(fact_246_Int__mono, axiom, (! [A:$tType,A3:(set @ A),C4:(set @ A),B4:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C4) => ((((ord_less_eq @ (set @ A)) @ B4) @ D3) => (((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) @ (((inf_inf @ (set @ A)) @ C4) @ D3))))))).
% 2.85/1.53 thf(fact_247_Diff__mono, axiom, (! [A:$tType,A3:(set @ A),C4:(set @ A),D3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C4) => ((((ord_less_eq @ (set @ A)) @ D3) @ B4) => (((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A3) @ B4)) @ (((minus_minus @ (set @ A)) @ C4) @ D3))))))).
% 2.85/1.53 thf(fact_248_Int__lower1, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) @ A3)))).
% 2.85/1.53 thf(fact_249_Int__lower2, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) @ B4)))).
% 2.85/1.53 thf(fact_250_Diff__subset, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A3) @ B4)) @ A3)))).
% 2.85/1.53 thf(fact_251_Int__absorb1, axiom, (! [A:$tType,B4:(set @ A),A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B4) @ A3) => ((((inf_inf @ (set @ A)) @ A3) @ B4) = B4))))).
% 2.85/1.53 thf(fact_252_Int__absorb2, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((inf_inf @ (set @ A)) @ A3) @ B4) = A3))))).
% 2.85/1.53 thf(fact_253_double__diff, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C4) => ((((minus_minus @ (set @ A)) @ B4) @ (((minus_minus @ (set @ A)) @ C4) @ A3)) = A3)))))).
% 2.85/1.53 thf(fact_254_Int__greatest, axiom, (! [A:$tType,C4:(set @ A),A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ A3) => ((((ord_less_eq @ (set @ A)) @ C4) @ B4) => (((ord_less_eq @ (set @ A)) @ C4) @ (((inf_inf @ (set @ A)) @ A3) @ B4))))))).
% 2.85/1.53 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A7:$tType,A8:$tType]: ((((order_bot @ A8) @ (type2 @ A8)) => ((order_bot @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.85/1.53 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: ((((preorder @ A8) @ (type2 @ A8)) => ((preorder @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.85/1.53 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: ((((order @ A8) @ (type2 @ A8)) => ((order @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.85/1.53 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: ((((ord @ A8) @ (type2 @ A8)) => ((ord @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.85/1.53 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A8:$tType]: ((((bot @ A8) @ (type2 @ A8)) => ((bot @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.85/1.53 thf(tcon_Set_Oset___Orderings_Oorder__bot_1, axiom, (! [A7:$tType]: (((order_bot @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.85/1.53 thf(tcon_Set_Oset___Orderings_Opreorder_2, axiom, (! [A7:$tType]: (((preorder @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.85/1.53 thf(tcon_Set_Oset___Orderings_Oorder_3, axiom, (! [A7:$tType]: (((order @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.85/1.53 thf(tcon_Set_Oset___Orderings_Oord_4, axiom, (! [A7:$tType]: (((ord @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.85/1.53 thf(tcon_Set_Oset___Orderings_Obot_5, axiom, (! [A7:$tType]: (((bot @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.85/1.53 thf(tcon_HOL_Obool___Orderings_Oorder__bot_6, axiom, ((order_bot @ $o) @ (type2 @ $o))).
% 2.85/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_7, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.85/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.85/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_8, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.85/1.53 thf(tcon_HOL_Obool___Orderings_Oord_9, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.85/1.53 thf(tcon_HOL_Obool___Orderings_Obot_10, axiom, ((bot @ $o) @ (type2 @ $o))).
% 2.85/1.53 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.85/1.53 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 2.85/1.53 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 2.85/1.53 thf(conj_0, hypothesis, (x = (((tLList57907754e_TNil @ b) @ a) @ x1))).
% 2.85/1.53 thf(conj_1, conjecture, (((((tLList1968894004s_TNil @ a) @ b) @ x) => (((((((tLList200813139tllist @ b) @ b) @ a) @ (id @ b)) @ (undefined @ (a > (((tLList446370796tllist @ a) @ b) > b)))) @ x) = (((tLList2110128105rminal @ a) @ b) @ x))) & ((~ ((((tLList1968894004s_TNil @ a) @ b) @ x))) => (((tLList1825092077minal0 @ (((tLList446370796tllist @ a) @ b) > b)) @ (((tLList_Mirabelle_ttl @ a) @ b) @ x)) = (((tLList2110128105rminal @ a) @ b) @ x))))).
% 2.85/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2DTF18945.p
% 2.85/1.53 ------------------------
% 2.85/1.56 ---- Cleaned THF ---
% 2.85/1.56 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist,type,
% 2.85/1.56 tLList446370796tllist: $tType > $tType > $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_t_Set_Oset,type,
% 2.85/1.56 set: $tType > $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_t_itself,type,
% 2.85/1.56 itself: $tType > $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_tf_b,type,
% 2.85/1.56 b: $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_tf_a,type,
% 2.85/1.56 a: $tType ).
% 2.85/1.56
% 2.85/1.56 thf(sy_cl_HOL_Otype,type,
% 2.85/1.56 type:
% 2.85/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_cl_Orderings_Obot,type,
% 2.85/1.56 bot:
% 2.85/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_cl_Orderings_Oord,type,
% 2.85/1.56 ord:
% 2.85/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_cl_Orderings_Oorder,type,
% 2.85/1.56 order:
% 2.85/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_cl_Orderings_Olinorder,type,
% 2.85/1.56 linorder:
% 2.85/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_cl_Orderings_Opreorder,type,
% 2.85/1.56 preorder:
% 2.85/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.85/1.56 order_bot:
% 2.85/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Fun_Ofcomp,type,
% 2.85/1.56 fcomp:
% 2.85/1.56 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( B > C ) > A > C ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Fun_Oid,type,
% 2.85/1.56 id:
% 2.85/1.56 !>[A: $tType] : ( A > A ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Fun_Ooverride__on,type,
% 2.85/1.56 override_on:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > B ) > ( set @ A ) > A > B ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.85/1.56 minus_minus:
% 2.85/1.56 !>[A: $tType] : ( A > A > A ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.85/1.56 uminus_uminus:
% 2.85/1.56 !>[A: $tType] : ( A > A ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_HOL_Oundefined,type,
% 2.85/1.56 undefined:
% 2.85/1.56 !>[A: $tType] : A ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_If,type,
% 2.85/1.56 if:
% 2.85/1.56 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.85/1.56 inf_inf:
% 2.85/1.56 !>[A: $tType] : ( A > A > A ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.85/1.56 bot_bot:
% 2.85/1.56 !>[A: $tType] : A ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.85/1.56 ord_less_eq:
% 2.85/1.56 !>[A: $tType] : ( A > A > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Pure_Otype,type,
% 2.85/1.56 type2:
% 2.85/1.56 !>[A: $tType] : ( itself @ A ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Relation_Oinv__imagep,type,
% 2.85/1.56 inv_imagep:
% 2.85/1.56 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_OBall,type,
% 2.85/1.56 ball:
% 2.85/1.56 !>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_OCollect,type,
% 2.85/1.56 collect:
% 2.85/1.56 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Oinsert,type,
% 2.85/1.56 insert:
% 2.85/1.56 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Ois__empty,type,
% 2.85/1.56 is_empty:
% 2.85/1.56 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Ois__singleton,type,
% 2.85/1.56 is_singleton:
% 2.85/1.56 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Opairwise,type,
% 2.85/1.56 pairwise:
% 2.85/1.56 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Othe__elem,type,
% 2.85/1.56 the_elem:
% 2.85/1.56 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Oterminal0,type,
% 2.85/1.56 tLList1825092077minal0:
% 2.85/1.56 !>[A: $tType] : A ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTCons,type,
% 2.85/1.56 tLList1992840728_TCons:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( A > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTNil,type,
% 2.85/1.56 tLList57907754e_TNil:
% 2.85/1.56 !>[B: $tType,A: $tType] : ( B > ( tLList446370796tllist @ A @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocase__tllist,type,
% 2.85/1.56 tLList200813139tllist:
% 2.85/1.56 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > ( tLList446370796tllist @ A @ B ) > C ) > ( tLList446370796tllist @ A @ B ) > C ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocorec__tllist,type,
% 2.85/1.56 tLList1614408749tllist:
% 2.85/1.56 !>[E: $tType,B: $tType,A: $tType] : ( ( E > $o ) > ( E > B ) > ( E > A ) > ( E > $o ) > ( E > ( tLList446370796tllist @ A @ B ) ) > ( E > E ) > E > ( tLList446370796tllist @ A @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ois__TNil,type,
% 2.85/1.56 tLList1968894004s_TNil:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Opred__tllist,type,
% 2.85/1.56 tLList11265572tllist:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( tLList446370796tllist @ A @ B ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oset2__tllist,type,
% 2.85/1.56 tLList457864275tllist:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( set @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oterminal,type,
% 2.85/1.56 tLList2110128105rminal:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > B ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Othd,type,
% 2.85/1.56 tLList_Mirabelle_thd:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > A ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otllist__all2,type,
% 2.85/1.56 tLList1380991092t_all2:
% 2.85/1.56 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otmap,type,
% 2.85/1.56 tLList1669959861e_tmap:
% 2.85/1.56 !>[A: $tType,Aa: $tType,B: $tType,Ba: $tType] : ( ( A > Aa ) > ( B > Ba ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ Aa @ Ba ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otset,type,
% 2.85/1.56 tLList1719791291e_tset:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( set @ A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ottl,type,
% 2.85/1.56 tLList_Mirabelle_ttl:
% 2.85/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_member,type,
% 2.85/1.56 member:
% 2.85/1.56 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.85/1.56
% 2.85/1.56 thf(sy_v_x,type,
% 2.85/1.56 x: tLList446370796tllist @ a @ b ).
% 2.85/1.56
% 2.85/1.56 thf(sy_v_x1,type,
% 2.85/1.56 x1: b ).
% 2.85/1.56
% 2.85/1.56 thf(fact_0_tllist_Oinject_I1_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,X1: B,Y1: B] :
% 2.85/1.56 ( ( ( tLList57907754e_TNil @ B @ A @ X1 )
% 2.85/1.56 = ( tLList57907754e_TNil @ B @ A @ Y1 ) )
% 2.85/1.56 = ( X1 = Y1 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_1_tllist_Ocollapse_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.85/1.56 => ( ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) )
% 2.85/1.56 = Tllist ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_2_tllist_Osel_I4_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,X1: B] :
% 2.85/1.56 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.85/1.56 = ( tLList57907754e_TNil @ B @ A @ X1 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_3_tllist_Osel_I1_J,axiom,
% 2.85/1.56 ! [Aa: $tType,A: $tType,X1: A] :
% 2.85/1.56 ( ( tLList2110128105rminal @ Aa @ A @ ( tLList57907754e_TNil @ A @ Aa @ X1 ) )
% 2.85/1.56 = X1 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_4_tllist_Odisc_I1_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,X1: B] : ( tLList1968894004s_TNil @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_5_tllist_OdiscI_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,X1: B] :
% 2.85/1.56 ( ( Tllist
% 2.85/1.56 = ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.85/1.56 => ( tLList1968894004s_TNil @ A @ B @ Tllist ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_6_tllist_Osimps_I5_J,axiom,
% 2.85/1.56 ! [A: $tType,C: $tType,B: $tType,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,X1: B] :
% 2.85/1.56 ( ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.85/1.56 = ( F1 @ X1 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_7_terminal0_Osimps,axiom,
% 2.85/1.56 ! [D: $tType,C: $tType] :
% 2.85/1.56 ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) )
% 2.85/1.56 = ( ^ [Xs: tLList446370796tllist @ C @ D] : ( if @ D @ ( tLList1968894004s_TNil @ C @ D @ Xs ) @ ( tLList200813139tllist @ D @ D @ C @ ( id @ D ) @ ( undefined @ ( C > ( tLList446370796tllist @ C @ D ) > D ) ) @ Xs ) @ ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) @ ( tLList_Mirabelle_ttl @ C @ D @ Xs ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_8_is__TNil__def,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType] :
% 2.85/1.56 ( ( tLList1968894004s_TNil @ A @ B )
% 2.85/1.56 = ( ^ [Tllist2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ? [X12: B] :
% 2.85/1.56 ( Tllist2
% 2.85/1.56 = ( tLList57907754e_TNil @ B @ A @ X12 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_9_terminal0_Oraw__induct,axiom,
% 2.85/1.56 ! [C: $tType,D: $tType,P: ( tLList446370796tllist @ C @ D ) > D > $o,Xs2: tLList446370796tllist @ C @ D,Y: D] :
% 2.85/1.56 ( ! [Terminal0: ( tLList446370796tllist @ C @ D ) > D] :
% 2.85/1.56 ( ! [X: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ( ( ( Terminal0 @ X )
% 2.85/1.56 != ( undefined @ D ) )
% 2.85/1.56 => ( P @ X @ ( Terminal0 @ X ) ) )
% 2.85/1.56 => ! [Xs3: tLList446370796tllist @ C @ D,Xsa: D] :
% 2.85/1.56 ( ( ( ( tLList1968894004s_TNil @ C @ D @ Xs3 )
% 2.85/1.56 => ( ( tLList200813139tllist @ D @ D @ C @ ( id @ D ) @ ( undefined @ ( C > ( tLList446370796tllist @ C @ D ) > D ) ) @ Xs3 )
% 2.85/1.56 = Xsa ) )
% 2.85/1.56 & ( ~ ( tLList1968894004s_TNil @ C @ D @ Xs3 )
% 2.85/1.56 => ( ( Terminal0 @ ( tLList_Mirabelle_ttl @ C @ D @ Xs3 ) )
% 2.85/1.56 = Xsa ) ) )
% 2.85/1.56 => ( ( Xsa
% 2.85/1.56 != ( undefined @ D ) )
% 2.85/1.56 => ( P @ Xs3 @ Xsa ) ) ) )
% 2.85/1.56 => ( ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) @ Xs2 )
% 2.85/1.56 = Y )
% 2.85/1.56 => ( ( Y
% 2.85/1.56 != ( undefined @ D ) )
% 2.85/1.56 => ( P @ Xs2 @ Y ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_10_id__apply,axiom,
% 2.85/1.56 ! [A: $tType] :
% 2.85/1.56 ( ( id @ A )
% 2.85/1.56 = ( ^ [X2: A] : X2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_11_tllist_Ocase__eq__if,axiom,
% 2.85/1.56 ! [A: $tType,C: $tType,B: $tType] :
% 2.85/1.56 ( ( tLList200813139tllist @ B @ C @ A )
% 2.85/1.56 = ( ^ [F12: B > C,F22: A > ( tLList446370796tllist @ A @ B ) > C,Tllist2: tLList446370796tllist @ A @ B] : ( if @ C @ ( tLList1968894004s_TNil @ A @ B @ Tllist2 ) @ ( F12 @ ( tLList2110128105rminal @ A @ B @ Tllist2 ) ) @ ( F22 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist2 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist2 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_12_tllist_Oexpand,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.85/1.56 = ( tLList1968894004s_TNil @ A @ B @ Tllist3 ) )
% 2.85/1.56 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.85/1.56 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist3 )
% 2.85/1.56 => ( ( tLList2110128105rminal @ A @ B @ Tllist )
% 2.85/1.56 = ( tLList2110128105rminal @ A @ B @ Tllist3 ) ) ) )
% 2.85/1.56 => ( ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.85/1.56 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist3 )
% 2.85/1.56 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist )
% 2.85/1.56 = ( tLList_Mirabelle_thd @ A @ B @ Tllist3 ) )
% 2.85/1.56 & ( ( tLList_Mirabelle_ttl @ A @ B @ Tllist )
% 2.85/1.56 = ( tLList_Mirabelle_ttl @ A @ B @ Tllist3 ) ) ) ) )
% 2.85/1.56 => ( Tllist = Tllist3 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_13_tllist_Ocoinduct,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,R: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) > $o,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( R @ Tllist @ Tllist3 )
% 2.85/1.56 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( R @ Tllist4 @ Tllist5 )
% 2.85/1.56 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 = ( tLList1968894004s_TNil @ A @ B @ Tllist5 ) )
% 2.85/1.56 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 2.85/1.56 => ( ( tLList2110128105rminal @ A @ B @ Tllist4 )
% 2.85/1.56 = ( tLList2110128105rminal @ A @ B @ Tllist5 ) ) ) )
% 2.85/1.56 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 2.85/1.56 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist4 )
% 2.85/1.56 = ( tLList_Mirabelle_thd @ A @ B @ Tllist5 ) )
% 2.85/1.56 & ( R @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) ) ) ) ) ) )
% 2.85/1.56 => ( Tllist = Tllist3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_14_tllist_Ocoinduct__strong,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,R: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) > $o,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( R @ Tllist @ Tllist3 )
% 2.85/1.56 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( R @ Tllist4 @ Tllist5 )
% 2.85/1.56 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 = ( tLList1968894004s_TNil @ A @ B @ Tllist5 ) )
% 2.85/1.56 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 2.85/1.56 => ( ( tLList2110128105rminal @ A @ B @ Tllist4 )
% 2.85/1.56 = ( tLList2110128105rminal @ A @ B @ Tllist5 ) ) ) )
% 2.85/1.56 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 2.85/1.56 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist4 )
% 2.85/1.56 = ( tLList_Mirabelle_thd @ A @ B @ Tllist5 ) )
% 2.85/1.56 & ( ( R @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) )
% 2.85/1.56 | ( ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 )
% 2.85/1.56 = ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) ) ) ) ) ) ) )
% 2.85/1.56 => ( Tllist = Tllist3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_15_id__def,axiom,
% 2.85/1.56 ! [A: $tType] :
% 2.85/1.56 ( ( id @ A )
% 2.85/1.56 = ( ^ [X2: A] : X2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_16_eq__id__iff,axiom,
% 2.85/1.56 ! [A: $tType,F: A > A] :
% 2.85/1.56 ( ( ! [X2: A] :
% 2.85/1.56 ( ( F @ X2 )
% 2.85/1.56 = X2 ) )
% 2.85/1.56 = ( F
% 2.85/1.56 = ( id @ A ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_17_tllist_Osel_I2_J,axiom,
% 2.85/1.56 ! [A: $tType,Aa: $tType,X21: Aa,X22: tLList446370796tllist @ Aa @ A] :
% 2.85/1.56 ( ( tLList2110128105rminal @ Aa @ A @ ( tLList1992840728_TCons @ Aa @ A @ X21 @ X22 ) )
% 2.85/1.56 = ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ Aa @ A ) > A ) @ X22 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_18_tllist_Oset__sel_I3_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.85/1.56 => ( member @ B @ ( tLList2110128105rminal @ A @ B @ A2 ) @ ( tLList457864275tllist @ A @ B @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_19_tllist_Oset__sel_I4_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,Xc: B] :
% 2.85/1.56 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.85/1.56 => ( ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) )
% 2.85/1.56 => ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ A2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_20_tllist_Oset__sel_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,X3: A] :
% 2.85/1.56 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.85/1.56 => ( ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) )
% 2.85/1.56 => ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ A2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_21_tllist_Osplit__sel,axiom,
% 2.85/1.56 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( P @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 2.85/1.56 = ( ( ( Tllist
% 2.85/1.56 = ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 2.85/1.56 => ( P @ ( F1 @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) ) )
% 2.85/1.56 & ( ( Tllist
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) )
% 2.85/1.56 => ( P @ ( F2 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_22_tllist_Oinject_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B,Y21: A,Y22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( ( tLList1992840728_TCons @ A @ B @ X21 @ X22 )
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ Y21 @ Y22 ) )
% 2.85/1.56 = ( ( X21 = Y21 )
% 2.85/1.56 & ( X22 = Y22 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_23_tllist_Ocollapse_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.85/1.56 => ( ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) )
% 2.85/1.56 = Tllist ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_24_tllist_Osel_I3_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.85/1.56 = X21 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_25_tllist_Osimps_I23_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList457864275tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.85/1.56 = ( tLList457864275tllist @ A @ B @ X22 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_26_tllist_Oset__cases_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,E2: A,A2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( member @ A @ E2 @ ( tLList1719791291e_tset @ A @ B @ A2 ) )
% 2.85/1.56 => ( ! [Z2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( A2
% 2.85/1.56 != ( tLList1992840728_TCons @ A @ B @ E2 @ Z2 ) )
% 2.85/1.56 => ~ ! [Z1: A,Z2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ Z1 @ Z2 ) )
% 2.85/1.56 => ~ ( member @ A @ E2 @ ( tLList1719791291e_tset @ A @ B @ Z2 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_27_tllist_Oset__induct_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X3: A,A2: tLList446370796tllist @ A @ B,P: A > ( tLList446370796tllist @ A @ B ) > $o] :
% 2.85/1.56 ( ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ A2 ) )
% 2.85/1.56 => ( ! [Z1: A,Z2: tLList446370796tllist @ A @ B] : ( P @ Z1 @ ( tLList1992840728_TCons @ A @ B @ Z1 @ Z2 ) )
% 2.85/1.56 => ( ! [Z1: A,Z2: tLList446370796tllist @ A @ B,Xa: A] :
% 2.85/1.56 ( ( member @ A @ Xa @ ( tLList1719791291e_tset @ A @ B @ Z2 ) )
% 2.85/1.56 => ( ( P @ Xa @ Z2 )
% 2.85/1.56 => ( P @ Xa @ ( tLList1992840728_TCons @ A @ B @ Z1 @ Z2 ) ) ) )
% 2.85/1.56 => ( P @ X3 @ A2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_28_tllist_Oset__intros_I4_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,Xc: B,A2a: tLList446370796tllist @ A @ B,A1a: A] :
% 2.85/1.56 ( ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ A2a ) )
% 2.85/1.56 => ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1a @ A2a ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_29_tllist_Oset__intros_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X3: A,A22: tLList446370796tllist @ A @ B,A1: A] :
% 2.85/1.56 ( ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ A22 ) )
% 2.85/1.56 => ( member @ A @ X3 @ ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1 @ A22 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_30_tllist_Oset__intros_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,A1: A,A22: tLList446370796tllist @ A @ B] : ( member @ A @ A1 @ ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1 @ A22 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_31_tllist_Oset__induct_I2_J,axiom,
% 2.85/1.56 ! [A: $tType,Aa: $tType,X3: A,A2: tLList446370796tllist @ Aa @ A,P: A > ( tLList446370796tllist @ Aa @ A ) > $o] :
% 2.85/1.56 ( ( member @ A @ X3 @ ( tLList457864275tllist @ Aa @ A @ A2 ) )
% 2.85/1.56 => ( ! [Z: A] : ( P @ Z @ ( tLList57907754e_TNil @ A @ Aa @ Z ) )
% 2.85/1.56 => ( ! [Z1: Aa,Z2: tLList446370796tllist @ Aa @ A,Xb: A] :
% 2.85/1.56 ( ( member @ A @ Xb @ ( tLList457864275tllist @ Aa @ A @ Z2 ) )
% 2.85/1.56 => ( ( P @ Xb @ Z2 )
% 2.85/1.56 => ( P @ Xb @ ( tLList1992840728_TCons @ Aa @ A @ Z1 @ Z2 ) ) ) )
% 2.85/1.56 => ( P @ X3 @ A2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_32_tllist_Oset__cases_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,E2: B,A2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( member @ B @ E2 @ ( tLList457864275tllist @ A @ B @ A2 ) )
% 2.85/1.56 => ( ( A2
% 2.85/1.56 != ( tLList57907754e_TNil @ B @ A @ E2 ) )
% 2.85/1.56 => ~ ! [Z1: A,Z2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ Z1 @ Z2 ) )
% 2.85/1.56 => ~ ( member @ B @ E2 @ ( tLList457864275tllist @ A @ B @ Z2 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_33_tllist_Oset__sel_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.85/1.56 => ( member @ A @ ( tLList_Mirabelle_thd @ A @ B @ A2 ) @ ( tLList1719791291e_tset @ A @ B @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_34_tllist_OdiscI_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( Tllist
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.85/1.56 => ~ ( tLList1968894004s_TNil @ A @ B @ Tllist ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_35_tllist_Odisc_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_36_tllist_Oexhaust,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,Y: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ! [X13: B] :
% 2.85/1.56 ( Y
% 2.85/1.56 != ( tLList57907754e_TNil @ B @ A @ X13 ) )
% 2.85/1.56 => ~ ! [X212: A,X222: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( Y
% 2.85/1.56 != ( tLList1992840728_TCons @ A @ B @ X212 @ X222 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_37_tllist_Odistinct_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X1: B,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList57907754e_TNil @ B @ A @ X1 )
% 2.85/1.56 != ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_38_tllist_Osel_I5_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.85/1.56 = X22 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_39_tllist_Osimps_I6_J,axiom,
% 2.85/1.56 ! [C: $tType,B: $tType,A: $tType,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.85/1.56 = ( F2 @ X21 @ X22 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_40_tllist_Oset__intros_I3_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,Aa2: B] : ( member @ B @ Aa2 @ ( tLList457864275tllist @ A @ B @ ( tLList57907754e_TNil @ B @ A @ Aa2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_41_tllist_Oexhaust__sel,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( Tllist
% 2.85/1.56 != ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 2.85/1.56 => ( Tllist
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_42_tllist_Osplit__sel__asm,axiom,
% 2.85/1.56 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( P @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 2.85/1.56 = ( ~ ( ( ( Tllist
% 2.85/1.56 = ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 2.85/1.56 & ~ ( P @ ( F1 @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) ) )
% 2.85/1.56 | ( ( Tllist
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) )
% 2.85/1.56 & ~ ( P @ ( F2 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_43_tllist_Orel__coinduct,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,P: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o,X3: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,R2: B > D > $o,R1: A > C > $o] :
% 2.85/1.56 ( ( P @ X3 @ Y )
% 2.85/1.56 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ( ( P @ Tllist4 @ Tllist5 )
% 2.85/1.56 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 = ( tLList1968894004s_TNil @ C @ D @ Tllist5 ) )
% 2.85/1.56 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 => ( ( tLList1968894004s_TNil @ C @ D @ Tllist5 )
% 2.85/1.56 => ( R2 @ ( tLList2110128105rminal @ A @ B @ Tllist4 ) @ ( tLList2110128105rminal @ C @ D @ Tllist5 ) ) ) )
% 2.85/1.56 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.85/1.56 => ( ~ ( tLList1968894004s_TNil @ C @ D @ Tllist5 )
% 2.85/1.56 => ( ( R1 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_thd @ C @ D @ Tllist5 ) )
% 2.85/1.56 & ( P @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ C @ D @ Tllist5 ) ) ) ) ) ) )
% 2.85/1.56 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X3 @ Y ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_44_mem__Collect__eq,axiom,
% 2.85/1.56 ! [A: $tType,A2: A,P: A > $o] :
% 2.85/1.56 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.85/1.56 = ( P @ A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_45_Collect__mem__eq,axiom,
% 2.85/1.56 ! [A: $tType,A3: set @ A] :
% 2.85/1.56 ( ( collect @ A
% 2.85/1.56 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 2.85/1.56 = A3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_46_Collect__cong,axiom,
% 2.85/1.56 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.85/1.56 ( ! [X4: A] :
% 2.85/1.56 ( ( P @ X4 )
% 2.85/1.56 = ( Q @ X4 ) )
% 2.85/1.56 => ( ( collect @ A @ P )
% 2.85/1.56 = ( collect @ A @ Q ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_47_ext,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.85/1.56 ( ! [X4: A] :
% 2.85/1.56 ( ( F @ X4 )
% 2.85/1.56 = ( G @ X4 ) )
% 2.85/1.56 => ( F = G ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_48_tllist_Orel__sel,axiom,
% 2.85/1.56 ! [B: $tType,D: $tType,C: $tType,A: $tType] :
% 2.85/1.56 ( ( tLList1380991092t_all2 @ A @ C @ B @ D )
% 2.85/1.56 = ( ^ [R12: A > C > $o,R22: B > D > $o,A4: tLList446370796tllist @ A @ B,B2: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ( ( ( tLList1968894004s_TNil @ A @ B @ A4 )
% 2.85/1.56 = ( tLList1968894004s_TNil @ C @ D @ B2 ) )
% 2.85/1.56 & ( ( tLList1968894004s_TNil @ A @ B @ A4 )
% 2.85/1.56 => ( ( tLList1968894004s_TNil @ C @ D @ B2 )
% 2.85/1.56 => ( R22 @ ( tLList2110128105rminal @ A @ B @ A4 ) @ ( tLList2110128105rminal @ C @ D @ B2 ) ) ) )
% 2.85/1.56 & ( ~ ( tLList1968894004s_TNil @ A @ B @ A4 )
% 2.85/1.56 => ( ~ ( tLList1968894004s_TNil @ C @ D @ B2 )
% 2.85/1.56 => ( ( R12 @ ( tLList_Mirabelle_thd @ A @ B @ A4 ) @ ( tLList_Mirabelle_thd @ C @ D @ B2 ) )
% 2.85/1.56 & ( tLList1380991092t_all2 @ A @ C @ B @ D @ R12 @ R22 @ ( tLList_Mirabelle_ttl @ A @ B @ A4 ) @ ( tLList_Mirabelle_ttl @ C @ D @ B2 ) ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_49_tllist_Opred__cong,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,P1: A > $o,P1a: A > $o,P2: B > $o,P2a: B > $o] :
% 2.85/1.56 ( ( X3 = Ya )
% 2.85/1.56 => ( ! [Z1: A] :
% 2.85/1.56 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 2.85/1.56 => ( ( P1 @ Z1 )
% 2.85/1.56 = ( P1a @ Z1 ) ) )
% 2.85/1.56 => ( ! [Z2: B] :
% 2.85/1.56 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 2.85/1.56 => ( ( P2 @ Z2 )
% 2.85/1.56 = ( P2a @ Z2 ) ) )
% 2.85/1.56 => ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ X3 )
% 2.85/1.56 = ( tLList11265572tllist @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_50_tllist_Opred__mono__strong,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,X3: tLList446370796tllist @ A @ B,P1a: A > $o,P2a: B > $o] :
% 2.85/1.56 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ X3 )
% 2.85/1.56 => ( ! [Z1: A] :
% 2.85/1.56 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 2.85/1.56 => ( ( P1 @ Z1 )
% 2.85/1.56 => ( P1a @ Z1 ) ) )
% 2.85/1.56 => ( ! [Z2: B] :
% 2.85/1.56 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 2.85/1.56 => ( ( P2 @ Z2 )
% 2.85/1.56 => ( P2a @ Z2 ) ) )
% 2.85/1.56 => ( tLList11265572tllist @ A @ B @ P1a @ P2a @ X3 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_51_tllist_Ocorec__code,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,E: $tType] :
% 2.85/1.56 ( ( tLList1614408749tllist @ E @ B @ A )
% 2.85/1.56 = ( ^ [P3: E > $o,G1: E > B,G21: E > A,Q22: E > $o,G221: E > ( tLList446370796tllist @ A @ B ),G222: E > E,A4: E] : ( if @ ( tLList446370796tllist @ A @ B ) @ ( P3 @ A4 ) @ ( tLList57907754e_TNil @ B @ A @ ( G1 @ A4 ) ) @ ( tLList1992840728_TCons @ A @ B @ ( G21 @ A4 ) @ ( if @ ( tLList446370796tllist @ A @ B ) @ ( Q22 @ A4 ) @ ( G221 @ A4 ) @ ( tLList1614408749tllist @ E @ B @ A @ P3 @ G1 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_52_tllist_Osimps_I21_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.85/1.56 = ( insert @ A @ X21 @ ( tLList1719791291e_tset @ A @ B @ X22 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_53_tllist_Omap__cong,axiom,
% 2.85/1.56 ! [D: $tType,C: $tType,B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,F1: A > C,G12: A > C,F2: B > D,G2: B > D] :
% 2.85/1.56 ( ( X3 = Ya )
% 2.85/1.56 => ( ! [Z1: A] :
% 2.85/1.56 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 2.85/1.56 => ( ( F1 @ Z1 )
% 2.85/1.56 = ( G12 @ Z1 ) ) )
% 2.85/1.56 => ( ! [Z2: B] :
% 2.85/1.56 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 2.85/1.56 => ( ( F2 @ Z2 )
% 2.85/1.56 = ( G2 @ Z2 ) ) )
% 2.85/1.56 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X3 )
% 2.85/1.56 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G12 @ G2 @ Ya ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_54_tllist_Omap__cong0,axiom,
% 2.85/1.56 ! [D: $tType,C: $tType,B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,F1: A > C,G12: A > C,F2: B > D,G2: B > D] :
% 2.85/1.56 ( ! [Z1: A] :
% 2.85/1.56 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 2.85/1.56 => ( ( F1 @ Z1 )
% 2.85/1.56 = ( G12 @ Z1 ) ) )
% 2.85/1.56 => ( ! [Z2: B] :
% 2.85/1.56 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 2.85/1.56 => ( ( F2 @ Z2 )
% 2.85/1.56 = ( G2 @ Z2 ) ) )
% 2.85/1.56 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X3 )
% 2.85/1.56 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G12 @ G2 @ X3 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_55_tllist_Oinj__map__strong,axiom,
% 2.85/1.56 ! [C: $tType,D: $tType,B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,Xa2: tLList446370796tllist @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
% 2.85/1.56 ( ! [Z1: A,Z1a: A] :
% 2.85/1.56 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 2.85/1.56 => ( ( member @ A @ Z1a @ ( tLList1719791291e_tset @ A @ B @ Xa2 ) )
% 2.85/1.56 => ( ( ( F1 @ Z1 )
% 2.85/1.56 = ( F1a @ Z1a ) )
% 2.85/1.56 => ( Z1 = Z1a ) ) ) )
% 2.85/1.56 => ( ! [Z2: B,Z2a: B] :
% 2.85/1.56 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 2.85/1.56 => ( ( member @ B @ Z2a @ ( tLList457864275tllist @ A @ B @ Xa2 ) )
% 2.85/1.56 => ( ( ( F2 @ Z2 )
% 2.85/1.56 = ( F2a @ Z2a ) )
% 2.85/1.56 => ( Z2 = Z2a ) ) ) )
% 2.85/1.56 => ( ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X3 )
% 2.85/1.56 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1a @ F2a @ Xa2 ) )
% 2.85/1.56 => ( X3 = Xa2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_56_tllist_Omap__sel_I2_J,axiom,
% 2.85/1.56 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 2.85/1.56 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.85/1.56 => ( ( tLList_Mirabelle_thd @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 2.85/1.56 = ( F1 @ ( tLList_Mirabelle_thd @ A @ B @ A2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_57_tllist_Orel__inject_I2_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X21: A,X22: tLList446370796tllist @ A @ B,Y21: C,Y22: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) )
% 2.85/1.56 = ( ( R1 @ X21 @ Y21 )
% 2.85/1.56 & ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_58_tllist_Omap__disc__iff,axiom,
% 2.85/1.56 ! [C: $tType,D: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,A2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList1968894004s_TNil @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 2.85/1.56 = ( tLList1968894004s_TNil @ A @ B @ A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_59_tllist_Orel__inject_I1_J,axiom,
% 2.85/1.56 ! [C: $tType,A: $tType,B: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,X1: B,Y1: D] :
% 2.85/1.56 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList57907754e_TNil @ D @ C @ Y1 ) )
% 2.85/1.56 = ( R2 @ X1 @ Y1 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_60_tllist_Ocorec__disc__iff_I2_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E,A2: E] :
% 2.85/1.56 ( ( ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) )
% 2.85/1.56 = ( ~ ( P4 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_61_tllist_Ocorec__disc__iff_I1_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E,A2: E] :
% 2.85/1.56 ( ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.85/1.56 = ( P4 @ A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_62_tllist_Opred__inject_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,A2: A,Aa2: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ ( tLList1992840728_TCons @ A @ B @ A2 @ Aa2 ) )
% 2.85/1.56 = ( ( P1 @ A2 )
% 2.85/1.56 & ( tLList11265572tllist @ A @ B @ P1 @ P2 @ Aa2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_63_tllist_Opred__inject_I1_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,P1: A > $o,P2: B > $o,A2: B] :
% 2.85/1.56 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ ( tLList57907754e_TNil @ B @ A @ A2 ) )
% 2.85/1.56 = ( P2 @ A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_64_tllist_Orel__refl,axiom,
% 2.85/1.56 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X3: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ( ! [X4: C] : ( R1a @ X4 @ X4 )
% 2.85/1.56 => ( ! [X4: D] : ( R2a @ X4 @ X4 )
% 2.85/1.56 => ( tLList1380991092t_all2 @ C @ C @ D @ D @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_65_tllist_Orel__eq,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType] :
% 2.85/1.56 ( ( tLList1380991092t_all2 @ A @ A @ B @ B
% 2.85/1.56 @ ^ [Y2: A,Z3: A] : ( Y2 = Z3 )
% 2.85/1.56 @ ^ [Y2: B,Z3: B] : ( Y2 = Z3 ) )
% 2.85/1.56 = ( ^ [Y2: tLList446370796tllist @ A @ B,Z3: tLList446370796tllist @ A @ B] : ( Y2 = Z3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_66_tllist_Orel__intros_I2_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,X21: A,Y21: C,R2: B > D > $o,X22: tLList446370796tllist @ A @ B,Y22: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ( ( R1 @ X21 @ Y21 )
% 2.85/1.56 => ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 )
% 2.85/1.56 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_67_tllist_Orel__intros_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,C: $tType,D: $tType,R2: B > D > $o,X1: B,Y1: D,R1: A > C > $o] :
% 2.85/1.56 ( ( R2 @ X1 @ Y1 )
% 2.85/1.56 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList57907754e_TNil @ D @ C @ Y1 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_68_tllist_Omap__id,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,T: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList1669959861e_tmap @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) @ T )
% 2.85/1.56 = T ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_69_tllist_Omap__id0,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType] :
% 2.85/1.56 ( ( tLList1669959861e_tmap @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 2.85/1.56 = ( id @ ( tLList446370796tllist @ A @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_70_tllist_Osimps_I15_J,axiom,
% 2.85/1.56 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.85/1.56 = ( tLList1992840728_TCons @ C @ D @ ( F1 @ X21 ) @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X22 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_71_tllist_Osimps_I14_J,axiom,
% 2.85/1.56 ! [A: $tType,C: $tType,D: $tType,B: $tType,F1: A > C,F2: B > D,X1: B] :
% 2.85/1.56 ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.85/1.56 = ( tLList57907754e_TNil @ D @ C @ ( F2 @ X1 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_72_tllist_Ocorec__disc_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.85/1.56 ( ~ ( P4 @ A2 )
% 2.85/1.56 => ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_73_tllist_Ocorec__disc_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.85/1.56 ( ( P4 @ A2 )
% 2.85/1.56 => ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_74_tllist_Ocorec_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.85/1.56 ( ~ ( P4 @ A2 )
% 2.85/1.56 => ( ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ ( G212 @ A2 ) @ ( if @ ( tLList446370796tllist @ A @ B ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_75_tllist_Ocorec_I1_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.85/1.56 ( ( P4 @ A2 )
% 2.85/1.56 => ( ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.85/1.56 = ( tLList57907754e_TNil @ B @ A @ ( G12 @ A2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_76_tllist_Ocorec__sel_I3_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,Q222: E > $o,G12: E > B,G212: E > A,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.85/1.56 ( ~ ( P4 @ A2 )
% 2.85/1.56 => ( ( ( Q222 @ A2 )
% 2.85/1.56 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.85/1.56 = ( G2212 @ A2 ) ) )
% 2.85/1.56 & ( ~ ( Q222 @ A2 )
% 2.85/1.56 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.85/1.56 = ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_77_tllist_Ocorec__sel_I1_J,axiom,
% 2.85/1.56 ! [Aa: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > A,G212: E > Aa,Q222: E > $o,G2212: E > ( tLList446370796tllist @ Aa @ A ),G2222: E > E] :
% 2.85/1.56 ( ( P4 @ A2 )
% 2.85/1.56 => ( ( tLList2110128105rminal @ Aa @ A @ ( tLList1614408749tllist @ E @ A @ Aa @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.85/1.56 = ( G12 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_78_tllist_Ocorec__sel_I2_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G12: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.85/1.56 ( ~ ( P4 @ A2 )
% 2.85/1.56 => ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G12 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.85/1.56 = ( G212 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_79_tllist_Orel__distinct_I2_J,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,Y21: A,Y22: tLList446370796tllist @ A @ B,X1: D] :
% 2.85/1.56 ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ Y21 @ Y22 ) @ ( tLList57907754e_TNil @ D @ C @ X1 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_80_tllist_Orel__distinct_I1_J,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X1: B,Y21: C,Y22: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_81_tllist_Orel__cases,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,A2: tLList446370796tllist @ A @ B,B3: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ A2 @ B3 )
% 2.85/1.56 => ( ! [X4: B] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( tLList57907754e_TNil @ B @ A @ X4 ) )
% 2.85/1.56 => ! [Y3: D] :
% 2.85/1.56 ( ( B3
% 2.85/1.56 = ( tLList57907754e_TNil @ D @ C @ Y3 ) )
% 2.85/1.56 => ~ ( R2 @ X4 @ Y3 ) ) )
% 2.85/1.56 => ~ ! [X1a: A,X23: tLList446370796tllist @ A @ B] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( tLList1992840728_TCons @ A @ B @ X1a @ X23 ) )
% 2.85/1.56 => ! [Y1a: C,Y23: tLList446370796tllist @ C @ D] :
% 2.85/1.56 ( ( B3
% 2.85/1.56 = ( tLList1992840728_TCons @ C @ D @ Y1a @ Y23 ) )
% 2.85/1.56 => ( ( R1 @ X1a @ Y1a )
% 2.85/1.56 => ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X23 @ Y23 ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_82_tllist_Orel__refl__strong,axiom,
% 2.85/1.56 ! [B: $tType,A: $tType,X3: tLList446370796tllist @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 2.85/1.56 ( ! [Z1: A] :
% 2.85/1.56 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 2.85/1.56 => ( R1a @ Z1 @ Z1 ) )
% 2.85/1.56 => ( ! [Z2: B] :
% 2.85/1.56 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 2.85/1.56 => ( R2a @ Z2 @ Z2 ) )
% 2.85/1.56 => ( tLList1380991092t_all2 @ A @ A @ B @ B @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_83_tllist_Orel__mono__strong,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X3: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 2.85/1.56 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X3 @ Y )
% 2.85/1.56 => ( ! [Z1: A,Y12: C] :
% 2.85/1.56 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ X3 ) )
% 2.85/1.56 => ( ( member @ C @ Y12 @ ( tLList1719791291e_tset @ C @ D @ Y ) )
% 2.85/1.56 => ( ( R1 @ Z1 @ Y12 )
% 2.85/1.56 => ( R1a @ Z1 @ Y12 ) ) ) )
% 2.85/1.56 => ( ! [Z2: B,Y23: D] :
% 2.85/1.56 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ X3 ) )
% 2.85/1.56 => ( ( member @ D @ Y23 @ ( tLList457864275tllist @ C @ D @ Y ) )
% 2.85/1.56 => ( ( R2 @ Z2 @ Y23 )
% 2.85/1.56 => ( R2a @ Z2 @ Y23 ) ) ) )
% 2.85/1.56 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a @ X3 @ Y ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_84_tllist_Orel__cong,axiom,
% 2.85/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,X3: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,Xa2: tLList446370796tllist @ C @ D,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
% 2.85/1.56 ( ( X3 = Ya )
% 2.85/1.56 => ( ( Y = Xa2 )
% 2.85/1.56 => ( ! [Z1: A,Y12: C] :
% 2.85/1.56 ( ( member @ A @ Z1 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 2.85/1.56 => ( ( member @ C @ Y12 @ ( tLList1719791291e_tset @ C @ D @ Xa2 ) )
% 2.85/1.56 => ( ( R1 @ Z1 @ Y12 )
% 2.85/1.56 = ( R1a @ Z1 @ Y12 ) ) ) )
% 2.85/1.56 => ( ! [Z2: B,Y23: D] :
% 2.85/1.56 ( ( member @ B @ Z2 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 2.85/1.56 => ( ( member @ D @ Y23 @ ( tLList457864275tllist @ C @ D @ Xa2 ) )
% 2.85/1.56 => ( ( R2 @ Z2 @ Y23 )
% 2.85/1.56 = ( R2a @ Z2 @ Y23 ) ) ) )
% 2.85/1.56 => ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X3 @ Y )
% 2.85/1.56 = ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa2 ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_85_tllist_Omap__sel_I3_J,axiom,
% 2.85/1.56 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 2.85/1.56 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.85/1.56 => ( ( tLList_Mirabelle_ttl @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 2.85/1.56 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_86_tllist_Omap__sel_I1_J,axiom,
% 2.85/1.57 ! [C: $tType,D: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 2.85/1.57 ( ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.85/1.57 => ( ( tLList2110128105rminal @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 2.85/1.57 = ( F2 @ ( tLList2110128105rminal @ A @ B @ A2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_87_insert__absorb2,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A] :
% 2.85/1.57 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A3 ) )
% 2.85/1.57 = ( insert @ A @ X3 @ A3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_88_insert__iff,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 2.85/1.57 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 2.85/1.57 = ( ( A2 = B3 )
% 2.85/1.57 | ( member @ A @ A2 @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_89_insertCI,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 2.85/1.57 ( ( ~ ( member @ A @ A2 @ B4 )
% 2.85/1.57 => ( A2 = B3 ) )
% 2.85/1.57 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_90_tllist_Osimps_I22_J,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType,X1: B] :
% 2.85/1.57 ( ( tLList457864275tllist @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.85/1.57 = ( insert @ B @ X1 @ ( bot_bot @ ( set @ B ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_91_tllist_Opred__set,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( tLList11265572tllist @ A @ B )
% 2.85/1.57 = ( ^ [P12: A > $o,P22: B > $o,X2: tLList446370796tllist @ A @ B] :
% 2.85/1.57 ( ! [Y4: A] :
% 2.85/1.57 ( ( member @ A @ Y4 @ ( tLList1719791291e_tset @ A @ B @ X2 ) )
% 2.85/1.57 => ( P12 @ Y4 ) )
% 2.85/1.57 & ! [Y4: B] :
% 2.85/1.57 ( ( member @ B @ Y4 @ ( tLList457864275tllist @ A @ B @ X2 ) )
% 2.85/1.57 => ( P22 @ Y4 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_92_mk__disjoint__insert,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A] :
% 2.85/1.57 ( ( member @ A @ A2 @ A3 )
% 2.85/1.57 => ? [B5: set @ A] :
% 2.85/1.57 ( ( A3
% 2.85/1.57 = ( insert @ A @ A2 @ B5 ) )
% 2.85/1.57 & ~ ( member @ A @ A2 @ B5 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_93_insert__commute,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,Y: A,A3: set @ A] :
% 2.85/1.57 ( ( insert @ A @ X3 @ ( insert @ A @ Y @ A3 ) )
% 2.85/1.57 = ( insert @ A @ Y @ ( insert @ A @ X3 @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_94_empty__iff,axiom,
% 2.85/1.57 ! [A: $tType,C2: A] :
% 2.85/1.57 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_95_all__not__in__conv,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( ! [X2: A] :
% 2.85/1.57 ~ ( member @ A @ X2 @ A3 ) )
% 2.85/1.57 = ( A3
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_96_Collect__empty__eq,axiom,
% 2.85/1.57 ! [A: $tType,P: A > $o] :
% 2.85/1.57 ( ( ( collect @ A @ P )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( ! [X2: A] :
% 2.85/1.57 ~ ( P @ X2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_97_empty__Collect__eq,axiom,
% 2.85/1.57 ! [A: $tType,P: A > $o] :
% 2.85/1.57 ( ( ( bot_bot @ ( set @ A ) )
% 2.85/1.57 = ( collect @ A @ P ) )
% 2.85/1.57 = ( ! [X2: A] :
% 2.85/1.57 ~ ( P @ X2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_98_singletonI,axiom,
% 2.85/1.57 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_99_ball__empty,axiom,
% 2.85/1.57 ! [A: $tType,P: A > $o,X: A] :
% 2.85/1.57 ( ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 => ( P @ X ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_100_singleton__inject,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,B3: A] :
% 2.85/1.57 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.57 => ( A2 = B3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_101_insert__not__empty,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A] :
% 2.85/1.57 ( ( insert @ A @ A2 @ A3 )
% 2.85/1.57 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_102_doubleton__eq__iff,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,B3: A,C2: A,D2: A] :
% 2.85/1.57 ( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.57 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.85/1.57 = ( ( ( A2 = C2 )
% 2.85/1.57 & ( B3 = D2 ) )
% 2.85/1.57 | ( ( A2 = D2 )
% 2.85/1.57 & ( B3 = C2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_103_singleton__iff,axiom,
% 2.85/1.57 ! [A: $tType,B3: A,A2: A] :
% 2.85/1.57 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.57 = ( B3 = A2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_104_singletonD,axiom,
% 2.85/1.57 ! [A: $tType,B3: A,A2: A] :
% 2.85/1.57 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.57 => ( B3 = A2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_105_emptyE,axiom,
% 2.85/1.57 ! [A: $tType,A2: A] :
% 2.85/1.57 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_106_Ball__def,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ball @ A )
% 2.85/1.57 = ( ^ [A5: set @ A,P5: A > $o] :
% 2.85/1.57 ! [X2: A] :
% 2.85/1.57 ( ( member @ A @ X2 @ A5 )
% 2.85/1.57 => ( P5 @ X2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_107_equals0D,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,A2: A] :
% 2.85/1.57 ( ( A3
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_108_equals0I,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ! [Y3: A] :
% 2.85/1.57 ~ ( member @ A @ Y3 @ A3 )
% 2.85/1.57 => ( A3
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_109_ex__in__conv,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 2.85/1.57 = ( A3
% 2.85/1.57 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_110_tllist_Osimps_I20_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,X1: B] :
% 2.85/1.57 ( ( tLList1719791291e_tset @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_111_insertE,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 2.85/1.57 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 2.85/1.57 => ( ( A2 != B3 )
% 2.85/1.57 => ( member @ A @ A2 @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_112_insertI1,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,B4: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_113_insertI2,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 2.85/1.57 ( ( member @ A @ A2 @ B4 )
% 2.85/1.57 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_114_Set_Oset__insert,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A] :
% 2.85/1.57 ( ( member @ A @ X3 @ A3 )
% 2.85/1.57 => ~ ! [B5: set @ A] :
% 2.85/1.57 ( ( A3
% 2.85/1.57 = ( insert @ A @ X3 @ B5 ) )
% 2.85/1.57 => ( member @ A @ X3 @ B5 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_115_insert__ident,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ~ ( member @ A @ X3 @ A3 )
% 2.85/1.57 => ( ~ ( member @ A @ X3 @ B4 )
% 2.85/1.57 => ( ( ( insert @ A @ X3 @ A3 )
% 2.85/1.57 = ( insert @ A @ X3 @ B4 ) )
% 2.85/1.57 = ( A3 = B4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_116_insert__absorb,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A] :
% 2.85/1.57 ( ( member @ A @ A2 @ A3 )
% 2.85/1.57 => ( ( insert @ A @ A2 @ A3 )
% 2.85/1.57 = A3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_117_insert__eq__iff,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A,B3: A,B4: set @ A] :
% 2.85/1.57 ( ~ ( member @ A @ A2 @ A3 )
% 2.85/1.57 => ( ~ ( member @ A @ B3 @ B4 )
% 2.85/1.57 => ( ( ( insert @ A @ A2 @ A3 )
% 2.85/1.57 = ( insert @ A @ B3 @ B4 ) )
% 2.85/1.57 = ( ( ( A2 = B3 )
% 2.85/1.57 => ( A3 = B4 ) )
% 2.85/1.57 & ( ( A2 != B3 )
% 2.85/1.57 => ? [C3: set @ A] :
% 2.85/1.57 ( ( A3
% 2.85/1.57 = ( insert @ A @ B3 @ C3 ) )
% 2.85/1.57 & ~ ( member @ A @ B3 @ C3 )
% 2.85/1.57 & ( B4
% 2.85/1.57 = ( insert @ A @ A2 @ C3 ) )
% 2.85/1.57 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_118_the__elem__eq,axiom,
% 2.85/1.57 ! [A: $tType,X3: A] :
% 2.85/1.57 ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.57 = X3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_119_bot__apply,axiom,
% 2.85/1.57 ! [C: $tType,D: $tType] :
% 2.85/1.57 ( ( bot @ C @ ( type2 @ C ) )
% 2.85/1.57 => ( ( bot_bot @ ( D > C ) )
% 2.85/1.57 = ( ^ [X2: D] : ( bot_bot @ C ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_120_is__singletonI,axiom,
% 2.85/1.57 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_121_override__on__emptyset,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.85/1.57 ( ( override_on @ A @ B @ F @ G @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = F ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_122_Set_Ois__empty__def,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( is_empty @ A )
% 2.85/1.57 = ( ^ [A5: set @ A] :
% 2.85/1.57 ( A5
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_123_override__on__apply__notin,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,A2: A,A3: set @ A,F: A > B,G: A > B] :
% 2.85/1.57 ( ~ ( member @ A @ A2 @ A3 )
% 2.85/1.57 => ( ( override_on @ A @ B @ F @ G @ A3 @ A2 )
% 2.85/1.57 = ( F @ A2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_124_override__on__apply__in,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,A2: A,A3: set @ A,F: A > B,G: A > B] :
% 2.85/1.57 ( ( member @ A @ A2 @ A3 )
% 2.85/1.57 => ( ( override_on @ A @ B @ F @ G @ A3 @ A2 )
% 2.85/1.57 = ( G @ A2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_125_bot__set__def,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( bot_bot @ ( set @ A ) )
% 2.85/1.57 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_126_override__on__def,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( override_on @ A @ B )
% 2.85/1.57 = ( ^ [F3: A > B,G3: A > B,A5: set @ A,A4: A] : ( if @ B @ ( member @ A @ A4 @ A5 ) @ ( G3 @ A4 ) @ ( F3 @ A4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_127_is__singleton__the__elem,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( is_singleton @ A )
% 2.85/1.57 = ( ^ [A5: set @ A] :
% 2.85/1.57 ( A5
% 2.85/1.57 = ( insert @ A @ ( the_elem @ A @ A5 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_128_is__singletonI_H,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( A3
% 2.85/1.57 != ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 => ( ! [X4: A,Y3: A] :
% 2.85/1.57 ( ( member @ A @ X4 @ A3 )
% 2.85/1.57 => ( ( member @ A @ Y3 @ A3 )
% 2.85/1.57 => ( X4 = Y3 ) ) )
% 2.85/1.57 => ( is_singleton @ A @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_129_bot__fun__def,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( bot @ B @ ( type2 @ B ) )
% 2.85/1.57 => ( ( bot_bot @ ( A > B ) )
% 2.85/1.57 = ( ^ [X2: A] : ( bot_bot @ B ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_130_is__singletonE,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( is_singleton @ A @ A3 )
% 2.85/1.57 => ~ ! [X4: A] :
% 2.85/1.57 ( A3
% 2.85/1.57 != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_131_is__singleton__def,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( is_singleton @ A )
% 2.85/1.57 = ( ^ [A5: set @ A] :
% 2.85/1.57 ? [X2: A] :
% 2.85/1.57 ( A5
% 2.85/1.57 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_132_pairwise__singleton,axiom,
% 2.85/1.57 ! [A: $tType,P: A > A > $o,A3: A] : ( pairwise @ A @ P @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_133_ball__reg,axiom,
% 2.85/1.57 ! [A: $tType,R: set @ A,P: A > $o,Q: A > $o] :
% 2.85/1.57 ( ! [X4: A] :
% 2.85/1.57 ( ( member @ A @ X4 @ R )
% 2.85/1.57 => ( ( P @ X4 )
% 2.85/1.57 => ( Q @ X4 ) ) )
% 2.85/1.57 => ( ! [X4: A] :
% 2.85/1.57 ( ( member @ A @ X4 @ R )
% 2.85/1.57 => ( P @ X4 ) )
% 2.85/1.57 => ! [X: A] :
% 2.85/1.57 ( ( member @ A @ X @ R )
% 2.85/1.57 => ( Q @ X ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_134_bot__empty__eq,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( bot_bot @ ( A > $o ) )
% 2.85/1.57 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_135_Collect__empty__eq__bot,axiom,
% 2.85/1.57 ! [A: $tType,P: A > $o] :
% 2.85/1.57 ( ( ( collect @ A @ P )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( P
% 2.85/1.57 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_136_pairwise__def,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( pairwise @ A )
% 2.85/1.57 = ( ^ [R3: A > A > $o,S: set @ A] :
% 2.85/1.57 ! [X2: A] :
% 2.85/1.57 ( ( member @ A @ X2 @ S )
% 2.85/1.57 => ! [Y4: A] :
% 2.85/1.57 ( ( member @ A @ Y4 @ S )
% 2.85/1.57 => ( ( X2 != Y4 )
% 2.85/1.57 => ( R3 @ X2 @ Y4 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_137_pairwise__empty,axiom,
% 2.85/1.57 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_138_pairwise__insert,axiom,
% 2.85/1.57 ! [A: $tType,R4: A > A > $o,X3: A,S2: set @ A] :
% 2.85/1.57 ( ( pairwise @ A @ R4 @ ( insert @ A @ X3 @ S2 ) )
% 2.85/1.57 = ( ! [Y4: A] :
% 2.85/1.57 ( ( ( member @ A @ Y4 @ S2 )
% 2.85/1.57 & ( Y4 != X3 ) )
% 2.85/1.57 => ( ( R4 @ X3 @ Y4 )
% 2.85/1.57 & ( R4 @ Y4 @ X3 ) ) )
% 2.85/1.57 & ( pairwise @ A @ R4 @ S2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_139_in__inv__imagep,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( inv_imagep @ A @ B )
% 2.85/1.57 = ( ^ [R5: A > A > $o,F3: B > A,X2: B,Y4: B] : ( R5 @ ( F3 @ X2 ) @ ( F3 @ Y4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_140_id__fcomp,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,G: A > B] :
% 2.85/1.57 ( ( fcomp @ A @ A @ B @ ( id @ A ) @ G )
% 2.85/1.57 = G ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_141_fcomp__id,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,F: A > B] :
% 2.85/1.57 ( ( fcomp @ A @ B @ B @ F @ ( id @ B ) )
% 2.85/1.57 = F ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_142_singleton__insert__inj__eq_H,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A,B3: A] :
% 2.85/1.57 ( ( ( insert @ A @ A2 @ A3 )
% 2.85/1.57 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.57 = ( ( A2 = B3 )
% 2.85/1.57 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_143_order__refl,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( preorder @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_144_subsetI,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ! [X4: A] :
% 2.85/1.57 ( ( member @ A @ X4 @ A3 )
% 2.85/1.57 => ( member @ A @ X4 @ B4 ) )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_145_subset__antisym,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 2.85/1.57 => ( A3 = B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_146_fcomp__apply,axiom,
% 2.85/1.57 ! [A: $tType,C: $tType,B: $tType] :
% 2.85/1.57 ( ( fcomp @ B @ C @ A )
% 2.85/1.57 = ( ^ [F3: B > C,G3: C > A,X2: B] : ( G3 @ ( F3 @ X2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_147_subset__empty,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( A3
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_148_empty__subsetI,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_149_insert__subset,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A3 ) @ B4 )
% 2.85/1.57 = ( ( member @ A @ X3 @ B4 )
% 2.85/1.57 & ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_150_singleton__insert__inj__eq,axiom,
% 2.85/1.57 ! [A: $tType,B3: A,A2: A,A3: set @ A] :
% 2.85/1.57 ( ( ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( insert @ A @ A2 @ A3 ) )
% 2.85/1.57 = ( ( A2 = B3 )
% 2.85/1.57 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_151_bot_Oextremum,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_152_bot_Oextremum__unique,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [A2: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.85/1.57 = ( A2
% 2.85/1.57 = ( bot_bot @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_153_bot_Oextremum__uniqueI,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [A2: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.85/1.57 => ( A2
% 2.85/1.57 = ( bot_bot @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_154_set__mp,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A,X3: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ( member @ A @ X3 @ A3 )
% 2.85/1.57 => ( member @ A @ X3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_155_in__mono,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A,X3: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ( member @ A @ X3 @ A3 )
% 2.85/1.57 => ( member @ A @ X3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_156_subsetD,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A,C2: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ( member @ A @ C2 @ A3 )
% 2.85/1.57 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_157_subsetCE,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A,C2: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ( member @ A @ C2 @ A3 )
% 2.85/1.57 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_158_equalityE,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( A3 = B4 )
% 2.85/1.57 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_159_subset__eq,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) )
% 2.85/1.57 = ( ^ [A5: set @ A,B6: set @ A] :
% 2.85/1.57 ! [X2: A] :
% 2.85/1.57 ( ( member @ A @ X2 @ A5 )
% 2.85/1.57 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_160_equalityD1,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( A3 = B4 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_161_equalityD2,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( A3 = B4 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_162_set__rev__mp,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( member @ A @ X3 @ A3 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( member @ A @ X3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_163_subset__iff,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) )
% 2.85/1.57 = ( ^ [A5: set @ A,B6: set @ A] :
% 2.85/1.57 ! [T2: A] :
% 2.85/1.57 ( ( member @ A @ T2 @ A5 )
% 2.85/1.57 => ( member @ A @ T2 @ B6 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_164_rev__subsetD,axiom,
% 2.85/1.57 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( member @ A @ C2 @ A3 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_165_subset__refl,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_166_Collect__mono,axiom,
% 2.85/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.85/1.57 ( ! [X4: A] :
% 2.85/1.57 ( ( P @ X4 )
% 2.85/1.57 => ( Q @ X4 ) )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_167_subset__trans,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A,C4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_168_set__eq__subset,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ^ [Y2: set @ A,Z3: set @ A] : ( Y2 = Z3 ) )
% 2.85/1.57 = ( ^ [A5: set @ A,B6: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 2.85/1.57 & ( ord_less_eq @ ( set @ A ) @ B6 @ A5 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_169_contra__subsetD,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A,C2: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ~ ( member @ A @ C2 @ B4 )
% 2.85/1.57 => ~ ( member @ A @ C2 @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_170_Collect__mono__iff,axiom,
% 2.85/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.85/1.57 = ( ! [X2: A] :
% 2.85/1.57 ( ( P @ X2 )
% 2.85/1.57 => ( Q @ X2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_171_fcomp__def,axiom,
% 2.85/1.57 ! [C: $tType,B: $tType,A: $tType] :
% 2.85/1.57 ( ( fcomp @ A @ B @ C )
% 2.85/1.57 = ( ^ [F3: A > B,G3: B > C,X2: A] : ( G3 @ ( F3 @ X2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_172_fcomp__assoc,axiom,
% 2.85/1.57 ! [A: $tType,D: $tType,B: $tType,C: $tType,F: A > D,G: D > C,H: C > B] :
% 2.85/1.57 ( ( fcomp @ A @ C @ B @ ( fcomp @ A @ D @ C @ F @ G ) @ H )
% 2.85/1.57 = ( fcomp @ A @ D @ B @ F @ ( fcomp @ D @ C @ B @ G @ H ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_173_subset__insertI2,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A,B3: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_174_subset__insertI,axiom,
% 2.85/1.57 ! [A: $tType,B4: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B4 @ ( insert @ A @ A2 @ B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_175_subset__insert,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ~ ( member @ A @ X3 @ A3 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ B4 ) )
% 2.85/1.57 = ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_176_Set_Oinsert__mono,axiom,
% 2.85/1.57 ! [A: $tType,C4: set @ A,D3: set @ A,A2: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C4 ) @ ( insert @ A @ A2 @ D3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_177_le__funD,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( ord @ B @ ( type2 @ B ) )
% 2.85/1.57 => ! [F: A > B,G: A > B,X3: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.85/1.57 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_178_le__funE,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( ord @ B @ ( type2 @ B ) )
% 2.85/1.57 => ! [F: A > B,G: A > B,X3: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.85/1.57 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_179_le__funI,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( ord @ B @ ( type2 @ B ) )
% 2.85/1.57 => ! [F: A > B,G: A > B] :
% 2.85/1.57 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 2.85/1.57 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_180_le__fun__def,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( ord @ B @ ( type2 @ B ) )
% 2.85/1.57 => ( ( ord_less_eq @ ( A > B ) )
% 2.85/1.57 = ( ^ [F3: A > B,G3: A > B] :
% 2.85/1.57 ! [X2: A] : ( ord_less_eq @ B @ ( F3 @ X2 ) @ ( G3 @ X2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_181_order__subst1,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType] :
% 2.85/1.57 ( ( ( order @ B @ ( type2 @ B ) )
% 2.85/1.57 & ( order @ A @ ( type2 @ A ) ) )
% 2.85/1.57 => ! [A2: A,F: B > A,B3: B,C2: B] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 2.85/1.57 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 2.85/1.57 => ( ! [X4: B,Y3: B] :
% 2.85/1.57 ( ( ord_less_eq @ B @ X4 @ Y3 )
% 2.85/1.57 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.85/1.57 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_182_order__subst2,axiom,
% 2.85/1.57 ! [A: $tType,C: $tType] :
% 2.85/1.57 ( ( ( order @ C @ ( type2 @ C ) )
% 2.85/1.57 & ( order @ A @ ( type2 @ A ) ) )
% 2.85/1.57 => ! [A2: A,B3: A,F: A > C,C2: C] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.85/1.57 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C2 )
% 2.85/1.57 => ( ! [X4: A,Y3: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.85/1.57 => ( ord_less_eq @ C @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.85/1.57 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_183_ord__eq__le__subst,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType] :
% 2.85/1.57 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.85/1.57 & ( ord @ A @ ( type2 @ A ) ) )
% 2.85/1.57 => ! [A2: A,F: B > A,B3: B,C2: B] :
% 2.85/1.57 ( ( A2
% 2.85/1.57 = ( F @ B3 ) )
% 2.85/1.57 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 2.85/1.57 => ( ! [X4: B,Y3: B] :
% 2.85/1.57 ( ( ord_less_eq @ B @ X4 @ Y3 )
% 2.85/1.57 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.85/1.57 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_184_ord__le__eq__subst,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType] :
% 2.85/1.57 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.85/1.57 & ( ord @ A @ ( type2 @ A ) ) )
% 2.85/1.57 => ! [A2: A,B3: A,F: A > B,C2: B] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.85/1.57 => ( ( ( F @ B3 )
% 2.85/1.57 = C2 )
% 2.85/1.57 => ( ! [X4: A,Y3: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.85/1.57 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.85/1.57 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_185_eq__iff,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.85/1.57 => ( ( ^ [Y2: A,Z3: A] : ( Y2 = Z3 ) )
% 2.85/1.57 = ( ^ [X2: A,Y4: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 2.85/1.57 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_186_antisym,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [X3: A,Y: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.85/1.57 => ( ( ord_less_eq @ A @ Y @ X3 )
% 2.85/1.57 => ( X3 = Y ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_187_linear,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [X3: A,Y: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.85/1.57 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_188_eq__refl,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( preorder @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [X3: A,Y: A] :
% 2.85/1.57 ( ( X3 = Y )
% 2.85/1.57 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_189_le__cases,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [X3: A,Y: A] :
% 2.85/1.57 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 2.85/1.57 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_190_order_Otrans,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [A2: A,B3: A,C2: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.85/1.57 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 2.85/1.57 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_191_le__cases3,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [X3: A,Y: A,Z4: A] :
% 2.85/1.57 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 2.85/1.57 => ~ ( ord_less_eq @ A @ Y @ Z4 ) )
% 2.85/1.57 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 2.85/1.57 => ~ ( ord_less_eq @ A @ X3 @ Z4 ) )
% 2.85/1.57 => ( ( ( ord_less_eq @ A @ X3 @ Z4 )
% 2.85/1.57 => ~ ( ord_less_eq @ A @ Z4 @ Y ) )
% 2.85/1.57 => ( ( ( ord_less_eq @ A @ Z4 @ Y )
% 2.85/1.57 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 2.85/1.57 => ( ( ( ord_less_eq @ A @ Y @ Z4 )
% 2.85/1.57 => ~ ( ord_less_eq @ A @ Z4 @ X3 ) )
% 2.85/1.57 => ~ ( ( ord_less_eq @ A @ Z4 @ X3 )
% 2.85/1.57 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_192_antisym__conv,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [Y: A,X3: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ Y @ X3 )
% 2.85/1.57 => ( ( ord_less_eq @ A @ X3 @ Y )
% 2.85/1.57 = ( X3 = Y ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_193_ord__eq__le__trans,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ord @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [A2: A,B3: A,C2: A] :
% 2.85/1.57 ( ( A2 = B3 )
% 2.85/1.57 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 2.85/1.57 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_194_ord__le__eq__trans,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ord @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [A2: A,B3: A,C2: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.85/1.57 => ( ( B3 = C2 )
% 2.85/1.57 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_195_order__class_Oorder_Oantisym,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [A2: A,B3: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.85/1.57 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.85/1.57 => ( A2 = B3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_196_order__trans,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( preorder @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [X3: A,Y: A,Z4: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.85/1.57 => ( ( ord_less_eq @ A @ Y @ Z4 )
% 2.85/1.57 => ( ord_less_eq @ A @ X3 @ Z4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_197_dual__order_Orefl,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_198_linorder__wlog,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [P: A > A > $o,A2: A,B3: A] :
% 2.85/1.57 ( ! [A6: A,B7: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ A6 @ B7 )
% 2.85/1.57 => ( P @ A6 @ B7 ) )
% 2.85/1.57 => ( ! [A6: A,B7: A] :
% 2.85/1.57 ( ( P @ B7 @ A6 )
% 2.85/1.57 => ( P @ A6 @ B7 ) )
% 2.85/1.57 => ( P @ A2 @ B3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_199_dual__order_Otrans,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [B3: A,A2: A,C2: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.85/1.57 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 2.85/1.57 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_200_dual__order_Oantisym,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.85/1.57 => ! [B3: A,A2: A] :
% 2.85/1.57 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.85/1.57 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.85/1.57 => ( A2 = B3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_201_pairwise__subset,axiom,
% 2.85/1.57 ! [A: $tType,P: A > A > $o,S3: set @ A,T3: set @ A] :
% 2.85/1.57 ( ( pairwise @ A @ P @ S3 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ T3 @ S3 )
% 2.85/1.57 => ( pairwise @ A @ P @ T3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_202_subset__singletonD,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,X3: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.57 => ( ( A3
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 | ( A3
% 2.85/1.57 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_203_subset__singleton__iff,axiom,
% 2.85/1.57 ! [A: $tType,X5: set @ A,A2: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ X5 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.57 = ( ( X5
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 | ( X5
% 2.85/1.57 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_204_Ball__Collect,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ball @ A )
% 2.85/1.57 = ( ^ [A5: set @ A,P5: A > $o] : ( ord_less_eq @ ( set @ A ) @ A5 @ ( collect @ A @ P5 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_205_insert__subsetI,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A,X5: set @ A] :
% 2.85/1.57 ( ( member @ A @ X3 @ A3 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ X5 @ A3 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X5 ) @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_206_subset__emptyI,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ! [X4: A] :
% 2.85/1.57 ~ ( member @ A @ X4 @ A3 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_207_subset__Compl__singleton,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B3: A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.85/1.57 = ( ~ ( member @ A @ B3 @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_208_Compl__eq__Compl__iff,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ( uminus_uminus @ ( set @ A ) @ A3 )
% 2.85/1.57 = ( uminus_uminus @ ( set @ A ) @ B4 ) )
% 2.85/1.57 = ( A3 = B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_209_Compl__iff,axiom,
% 2.85/1.57 ! [A: $tType,C2: A,A3: set @ A] :
% 2.85/1.57 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 2.85/1.57 = ( ~ ( member @ A @ C2 @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_210_ComplI,axiom,
% 2.85/1.57 ! [A: $tType,C2: A,A3: set @ A] :
% 2.85/1.57 ( ~ ( member @ A @ C2 @ A3 )
% 2.85/1.57 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_211_Compl__anti__mono,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B4 ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_212_Compl__subset__Compl__iff,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) @ ( uminus_uminus @ ( set @ A ) @ B4 ) )
% 2.85/1.57 = ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_213_tllist_Orel__mono,axiom,
% 2.85/1.57 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
% 2.85/1.57 ( ( ord_less_eq @ ( A > C > $o ) @ R1 @ R1a )
% 2.85/1.57 => ( ( ord_less_eq @ ( B > D > $o ) @ R2 @ R2a )
% 2.85/1.57 => ( ord_less_eq @ ( ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o ) @ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 ) @ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_214_double__complement,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 2.85/1.57 = A3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_215_ComplD,axiom,
% 2.85/1.57 ! [A: $tType,C2: A,A3: set @ A] :
% 2.85/1.57 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 2.85/1.57 => ~ ( member @ A @ C2 @ A3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_216_subset__Compl__self__eq,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 2.85/1.57 = ( A3
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_217_Compl__insert,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A] :
% 2.85/1.57 ( ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ X3 @ A3 ) )
% 2.85/1.57 = ( minus_minus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_218_disjoint__eq__subset__Compl,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( ord_less_eq @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_219_IntI,axiom,
% 2.85/1.57 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( member @ A @ C2 @ A3 )
% 2.85/1.57 => ( ( member @ A @ C2 @ B4 )
% 2.85/1.57 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_220_Int__iff,axiom,
% 2.85/1.57 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 2.85/1.57 = ( ( member @ A @ C2 @ A3 )
% 2.85/1.57 & ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_221_DiffI,axiom,
% 2.85/1.57 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( member @ A @ C2 @ A3 )
% 2.85/1.57 => ( ~ ( member @ A @ C2 @ B4 )
% 2.85/1.57 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_222_Diff__iff,axiom,
% 2.85/1.57 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) )
% 2.85/1.57 = ( ( member @ A @ C2 @ A3 )
% 2.85/1.57 & ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_223_Diff__idemp,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) @ B4 )
% 2.85/1.57 = ( minus_minus @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_224_predicate2I,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 2.85/1.57 ( ! [X4: A,Y3: B] :
% 2.85/1.57 ( ( P @ X4 @ Y3 )
% 2.85/1.57 => ( Q @ X4 @ Y3 ) )
% 2.85/1.57 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_225_Int__subset__iff,axiom,
% 2.85/1.57 ! [A: $tType,C4: set @ A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 2.85/1.57 = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A3 )
% 2.85/1.57 & ( ord_less_eq @ ( set @ A ) @ C4 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_226_Diff__empty,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( minus_minus @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = A3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_227_empty__Diff,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_228_Diff__cancel,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( minus_minus @ ( set @ A ) @ A3 @ A3 )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_229_Int__insert__right__if1,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( member @ A @ A2 @ A3 )
% 2.85/1.57 => ( ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B4 ) )
% 2.85/1.57 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_230_Int__insert__right__if0,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ~ ( member @ A @ A2 @ A3 )
% 2.85/1.57 => ( ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B4 ) )
% 2.85/1.57 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_231_insert__inter__insert,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A3 ) @ ( insert @ A @ A2 @ B4 ) )
% 2.85/1.57 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_232_Int__insert__left__if1,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,C4: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( member @ A @ A2 @ C4 )
% 2.85/1.57 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B4 ) @ C4 )
% 2.85/1.57 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ B4 @ C4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_233_Int__insert__left__if0,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,C4: set @ A,B4: set @ A] :
% 2.85/1.57 ( ~ ( member @ A @ A2 @ C4 )
% 2.85/1.57 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B4 ) @ C4 )
% 2.85/1.57 = ( inf_inf @ ( set @ A ) @ B4 @ C4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_234_insert__Diff1,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,B4: set @ A,A3: set @ A] :
% 2.85/1.57 ( ( member @ A @ X3 @ B4 )
% 2.85/1.57 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A3 ) @ B4 )
% 2.85/1.57 = ( minus_minus @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_235_Diff__insert0,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ~ ( member @ A @ X3 @ A3 )
% 2.85/1.57 => ( ( minus_minus @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ B4 ) )
% 2.85/1.57 = ( minus_minus @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_236_insert__disjoint_I1_J,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A3 ) @ B4 )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( ~ ( member @ A @ A2 @ B4 )
% 2.85/1.57 & ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_237_insert__disjoint_I2_J,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ( bot_bot @ ( set @ A ) )
% 2.85/1.57 = ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A3 ) @ B4 ) )
% 2.85/1.57 = ( ~ ( member @ A @ A2 @ B4 )
% 2.85/1.57 & ( ( bot_bot @ ( set @ A ) )
% 2.85/1.57 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_238_disjoint__insert_I1_J,axiom,
% 2.85/1.57 ! [A: $tType,B4: set @ A,A2: A,A3: set @ A] :
% 2.85/1.57 ( ( ( inf_inf @ ( set @ A ) @ B4 @ ( insert @ A @ A2 @ A3 ) )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( ~ ( member @ A @ A2 @ B4 )
% 2.85/1.57 & ( ( inf_inf @ ( set @ A ) @ B4 @ A3 )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_239_disjoint__insert_I2_J,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B3: A,B4: set @ A] :
% 2.85/1.57 ( ( ( bot_bot @ ( set @ A ) )
% 2.85/1.57 = ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ B3 @ B4 ) ) )
% 2.85/1.57 = ( ~ ( member @ A @ B3 @ A3 )
% 2.85/1.57 & ( ( bot_bot @ ( set @ A ) )
% 2.85/1.57 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_240_Diff__eq__empty__iff,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ( minus_minus @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.57 = ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_241_insert__Diff__single,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,A3: set @ A] :
% 2.85/1.57 ( ( insert @ A @ A2 @ ( minus_minus @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.85/1.57 = ( insert @ A @ A2 @ A3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_242_Diff__disjoint,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( inf_inf @ ( set @ A ) @ A3 @ ( minus_minus @ ( set @ A ) @ B4 @ A3 ) )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_243_Compl__disjoint,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( inf_inf @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_244_Compl__disjoint2,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( inf_inf @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) @ A3 )
% 2.85/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_245_Diff__Compl,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( minus_minus @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ B4 ) )
% 2.85/1.57 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_246_Int__mono,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,C4: set @ A,B4: set @ A,D3: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ D3 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ ( inf_inf @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_247_Diff__mono,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,C4: set @ A,D3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ D3 @ B4 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) @ ( minus_minus @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_248_Int__lower1,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ A3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_249_Int__lower2,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ B4 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_250_Diff__subset,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ B4 ) @ A3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_251_Int__absorb1,axiom,
% 2.85/1.57 ! [A: $tType,B4: set @ A,A3: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 2.85/1.57 => ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 = B4 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_252_Int__absorb2,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 = A3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_253_double__diff,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A,B4: set @ A,C4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 2.85/1.57 => ( ( minus_minus @ ( set @ A ) @ B4 @ ( minus_minus @ ( set @ A ) @ C4 @ A3 ) )
% 2.85/1.57 = A3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_254_Int__greatest,axiom,
% 2.85/1.57 ! [A: $tType,C4: set @ A,A3: set @ A,B4: set @ A] :
% 2.85/1.57 ( ( ord_less_eq @ ( set @ A ) @ C4 @ A3 )
% 2.85/1.57 => ( ( ord_less_eq @ ( set @ A ) @ C4 @ B4 )
% 2.85/1.57 => ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.85/1.57 ! [A7: $tType,A8: $tType] :
% 2.85/1.57 ( ( order_bot @ A8 @ ( type2 @ A8 ) )
% 2.85/1.57 => ( order_bot @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.85/1.57 ! [A7: $tType,A8: $tType] :
% 2.85/1.57 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 2.85/1.57 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.85/1.57 ! [A7: $tType,A8: $tType] :
% 2.85/1.57 ( ( order @ A8 @ ( type2 @ A8 ) )
% 2.85/1.57 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_fun___Orderings_Oord,axiom,
% 2.85/1.57 ! [A7: $tType,A8: $tType] :
% 2.85/1.57 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 2.85/1.57 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_fun___Orderings_Obot,axiom,
% 2.85/1.57 ! [A7: $tType,A8: $tType] :
% 2.85/1.57 ( ( bot @ A8 @ ( type2 @ A8 ) )
% 2.85/1.57 => ( bot @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_Set_Oset___Orderings_Oorder__bot_1,axiom,
% 2.85/1.57 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 2.85/1.57 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 2.85/1.57 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_Set_Oset___Orderings_Oord_4,axiom,
% 2.85/1.57 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_Set_Oset___Orderings_Obot_5,axiom,
% 2.85/1.57 ! [A7: $tType] : ( bot @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_HOL_Obool___Orderings_Oorder__bot_6,axiom,
% 2.85/1.57 order_bot @ $o @ ( type2 @ $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 2.85/1.57 preorder @ $o @ ( type2 @ $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.85/1.57 linorder @ $o @ ( type2 @ $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_HOL_Obool___Orderings_Oorder_8,axiom,
% 2.85/1.57 order @ $o @ ( type2 @ $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_HOL_Obool___Orderings_Oord_9,axiom,
% 2.85/1.57 ord @ $o @ ( type2 @ $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(tcon_HOL_Obool___Orderings_Obot_10,axiom,
% 2.85/1.57 bot @ $o @ ( type2 @ $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(help_If_3_1_T,axiom,
% 2.85/1.57 ! [P: $o] :
% 2.85/1.57 ( ( P = $true )
% 2.85/1.57 | ( P = $false ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(help_If_2_1_T,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,Y: A] :
% 2.85/1.57 ( ( if @ A @ $false @ X3 @ Y )
% 2.85/1.57 = Y ) ).
% 2.85/1.57
% 2.85/1.57 thf(help_If_1_1_T,axiom,
% 2.85/1.57 ! [A: $tType,X3: A,Y: A] :
% 2.85/1.57 ( ( if @ A @ $true @ X3 @ Y )
% 2.85/1.57 = X3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(conj_0,hypothesis,
% 2.85/1.57 ( x
% 2.85/1.57 = ( tLList57907754e_TNil @ b @ a @ x1 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(conj_1,conjecture,
% 2.85/1.57 ( ( ( tLList1968894004s_TNil @ a @ b @ x )
% 2.85/1.57 => ( ( tLList200813139tllist @ b @ b @ a @ ( id @ b ) @ ( undefined @ ( a > ( tLList446370796tllist @ a @ b ) > b ) ) @ x )
% 2.85/1.57 = ( tLList2110128105rminal @ a @ b @ x ) ) )
% 2.85/1.57 & ( ~ ( tLList1968894004s_TNil @ a @ b @ x )
% 2.85/1.57 => ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ a @ b ) > b ) @ ( tLList_Mirabelle_ttl @ a @ b @ x ) )
% 2.85/1.57 = ( tLList2110128105rminal @ a @ b @ x ) ) ) ) ).
% 2.85/1.57 ------------------------
% 2.85/1.59 % (19276)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18945 for (2999ds/2Mi)
% 2.85/1.59 % (19274)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_18945 for (2999ds/4Mi)
% 2.85/1.59 % (19277)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_18945 for (2999ds/2Mi)
% 2.85/1.59 % (19276)Instruction limit reached!
% 2.85/1.59 % (19276)------------------------------
% 2.85/1.59 % (19276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.59 % (19276)Termination reason: Unknown
% 2.85/1.59 % (19276)Termination phase: shuffling
% 2.85/1.59
% 2.85/1.59 % (19276)Memory used [KB]: 1407
% 2.85/1.59 % (19276)Time elapsed: 0.003 s
% 2.85/1.59 % (19276)Instructions burned: 3 (million)
% 2.85/1.59 % (19276)------------------------------
% 2.85/1.59 % (19276)------------------------------
% 2.85/1.59 % (19277)Instruction limit reached!
% 2.85/1.59 % (19277)------------------------------
% 2.85/1.59 % (19277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.59 % (19277)Termination reason: Unknown
% 2.85/1.59 % (19277)Termination phase: shuffling
% 2.85/1.59
% 2.85/1.59 % (19277)Memory used [KB]: 1407
% 2.85/1.59 % (19277)Time elapsed: 0.002 s
% 2.85/1.59 % (19277)Instructions burned: 3 (million)
% 2.85/1.59 % (19277)------------------------------
% 2.85/1.59 % (19277)------------------------------
% 2.85/1.59 % (19274)Instruction limit reached!
% 2.85/1.59 % (19274)------------------------------
% 2.85/1.59 % (19274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.59 % (19274)Termination reason: Unknown
% 2.85/1.59 % (19274)Termination phase: shuffling
% 2.85/1.59
% 2.85/1.59 % (19274)Memory used [KB]: 1407
% 2.85/1.59 % (19274)Time elapsed: 0.003 s
% 2.85/1.59 % (19274)Instructions burned: 6 (million)
% 2.85/1.59 % (19274)------------------------------
% 2.85/1.59 % (19274)------------------------------
% 2.85/1.60 % (19273)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18945 for (2999ds/183Mi)
% 2.95/1.60 % (19275)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_18945 for (2999ds/27Mi)
% 2.95/1.60 % (19279)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18945 for (2999ds/18Mi)
% 2.95/1.60 % (19278)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_18945 for (2999ds/275Mi)
% 2.95/1.60 % (19280)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18945 for (2999ds/3Mi)
% 2.95/1.60 % (19281)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_18945 for (2999ds/37Mi)
% 2.95/1.60 % (19282)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_18945 for (2999ds/15Mi)
% 2.95/1.60 % (19280)Instruction limit reached!
% 2.95/1.60 % (19280)------------------------------
% 2.95/1.60 % (19280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (19280)Termination reason: Unknown
% 2.95/1.60 % (19280)Termination phase: shuffling
% 2.95/1.60
% 2.95/1.60 % (19280)Memory used [KB]: 1407
% 2.95/1.60 % (19280)Time elapsed: 0.003 s
% 2.95/1.60 % (19280)Instructions burned: 5 (million)
% 2.95/1.60 % (19280)------------------------------
% 2.95/1.60 % (19280)------------------------------
% 2.95/1.61 % (19282)Instruction limit reached!
% 2.95/1.61 % (19282)------------------------------
% 2.95/1.61 % (19282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19282)Termination reason: Unknown
% 2.95/1.61 % (19282)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19282)Memory used [KB]: 1791
% 2.95/1.61 % (19282)Time elapsed: 0.007 s
% 2.95/1.61 % (19282)Instructions burned: 17 (million)
% 2.95/1.61 % (19282)------------------------------
% 2.95/1.61 % (19282)------------------------------
% 2.95/1.61 % (19279)Instruction limit reached!
% 2.95/1.61 % (19279)------------------------------
% 2.95/1.61 % (19279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19279)Termination reason: Unknown
% 2.95/1.61 % (19279)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19279)Memory used [KB]: 1791
% 2.95/1.61 % (19279)Time elapsed: 0.014 s
% 2.95/1.61 % (19279)Instructions burned: 19 (million)
% 2.95/1.61 % (19279)------------------------------
% 2.95/1.61 % (19279)------------------------------
% 2.95/1.61 % (19283)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_18945 for (2999ds/3Mi)
% 2.95/1.61 % (19283)Instruction limit reached!
% 2.95/1.61 % (19283)------------------------------
% 2.95/1.61 % (19283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19283)Termination reason: Unknown
% 2.95/1.61 % (19283)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19283)Memory used [KB]: 1407
% 2.95/1.61 % (19283)Time elapsed: 0.002 s
% 2.95/1.61 % (19283)Instructions burned: 3 (million)
% 2.95/1.61 % (19283)------------------------------
% 2.95/1.61 % (19283)------------------------------
% 2.95/1.61 % (19281)Instruction limit reached!
% 2.95/1.61 % (19281)------------------------------
% 2.95/1.61 % (19281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19281)Termination reason: Unknown
% 2.95/1.61 % (19281)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19281)Memory used [KB]: 2174
% 2.95/1.61 % (19281)Time elapsed: 0.013 s
% 2.95/1.61 % (19281)Instructions burned: 40 (million)
% 2.95/1.61 % (19281)------------------------------
% 2.95/1.61 % (19281)------------------------------
% 2.95/1.61 % (19275)Instruction limit reached!
% 2.95/1.61 % (19275)------------------------------
% 2.95/1.61 % (19275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19275)Termination reason: Unknown
% 2.95/1.61 % (19275)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19275)Memory used [KB]: 1918
% 2.95/1.61 % (19275)Time elapsed: 0.019 s
% 2.95/1.61 % (19275)Instructions burned: 27 (million)
% 2.95/1.61 % (19275)------------------------------
% 2.95/1.61 % (19275)------------------------------
% 2.95/1.62 % (19284)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_18945 for (2999ds/1041Mi)
% 2.95/1.62 % (19286)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18945 for (2999ds/16Mi)
% 2.95/1.62 % (19287)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_18945 for (2999ds/3Mi)
% 2.95/1.62 % (19287)Instruction limit reached!
% 2.95/1.62 % (19287)------------------------------
% 2.95/1.62 % (19287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (19287)Termination reason: Unknown
% 2.95/1.62 % (19287)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (19287)Memory used [KB]: 1407
% 2.95/1.62 % (19287)Time elapsed: 0.003 s
% 2.95/1.62 % (19287)Instructions burned: 4 (million)
% 2.95/1.62 % (19287)------------------------------
% 2.95/1.62 % (19287)------------------------------
% 2.95/1.63 % (19285)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18945 for (2999ds/7Mi)
% 2.95/1.63 % (19286)Instruction limit reached!
% 2.95/1.63 % (19286)------------------------------
% 2.95/1.63 % (19286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (19286)Termination reason: Unknown
% 2.95/1.63 % (19286)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (19286)Memory used [KB]: 1791
% 2.95/1.63 % (19286)Time elapsed: 0.007 s
% 2.95/1.63 % (19286)Instructions burned: 18 (million)
% 2.95/1.63 % (19286)------------------------------
% 2.95/1.63 % (19286)------------------------------
% 2.95/1.63 % (19285)Instruction limit reached!
% 2.95/1.63 % (19285)------------------------------
% 2.95/1.63 % (19285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (19285)Termination reason: Unknown
% 2.95/1.63 % (19285)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (19285)Memory used [KB]: 1535
% 2.95/1.63 % (19285)Time elapsed: 0.006 s
% 2.95/1.63 % (19285)Instructions burned: 7 (million)
% 2.95/1.63 % (19285)------------------------------
% 2.95/1.63 % (19285)------------------------------
% 2.95/1.63 % (19288)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_18945 for (2999ds/3Mi)
% 2.95/1.63 % (19288)Instruction limit reached!
% 2.95/1.63 % (19288)------------------------------
% 2.95/1.63 % (19288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (19288)Termination reason: Unknown
% 2.95/1.63 % (19288)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (19288)Memory used [KB]: 1407
% 2.95/1.63 % (19288)Time elapsed: 0.004 s
% 2.95/1.63 % (19288)Instructions burned: 3 (million)
% 2.95/1.63 % (19288)------------------------------
% 2.95/1.63 % (19288)------------------------------
% 2.95/1.63 % (19289)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18945 for (2999ds/7Mi)
% 2.95/1.64 % (19290)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18945 for (2999ds/3Mi)
% 2.95/1.64 % (19289)Instruction limit reached!
% 2.95/1.64 % (19289)------------------------------
% 2.95/1.64 % (19289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (19289)Termination reason: Unknown
% 2.95/1.64 % (19289)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (19289)Memory used [KB]: 1535
% 2.95/1.64 % (19289)Time elapsed: 0.004 s
% 2.95/1.64 % (19289)Instructions burned: 9 (million)
% 2.95/1.64 % (19289)------------------------------
% 2.95/1.64 % (19289)------------------------------
% 2.95/1.64 % (19290)Instruction limit reached!
% 2.95/1.64 % (19290)------------------------------
% 2.95/1.64 % (19290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (19290)Termination reason: Unknown
% 2.95/1.64 % (19290)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (19290)Memory used [KB]: 1407
% 2.95/1.64 % (19290)Time elapsed: 0.002 s
% 2.95/1.64 % (19290)Instructions burned: 3 (million)
% 2.95/1.64 % (19290)------------------------------
% 2.95/1.64 % (19290)------------------------------
% 2.95/1.64 % (19278)First to succeed.
% 2.95/1.64 % (19278)Refutation found. Thanks to Tanya!
% 2.95/1.64 % SZS status Theorem for DTF2THF_18945
% 2.95/1.64 % SZS output start Proof for DTF2THF_18945
% 2.95/1.64 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.95/1.64 thf(type_def_7, type, set: ($tType) > $tType).
% 2.95/1.64 thf(type_def_8, type, tLList446370796tllist: ($tType * $tType) > $tType).
% 2.95/1.64 thf(type_def_9, type, a: $tType).
% 2.95/1.64 thf(type_def_10, type, b: $tType).
% 2.95/1.64 thf(func_def_0, type, tLList446370796tllist: ($tType * $tType) > $tType).
% 2.95/1.64 thf(func_def_1, type, set: ($tType) > $tType).
% 2.95/1.64 thf(func_def_2, type, itself: ($tType) > $tType).
% 2.95/1.64 thf(func_def_3, type, b: $tType).
% 2.95/1.64 thf(func_def_4, type, a: $tType).
% 2.95/1.64 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.95/1.64 thf(func_def_6, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.95/1.64 thf(func_def_7, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.95/1.64 thf(func_def_8, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.95/1.64 thf(func_def_9, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.95/1.64 thf(func_def_10, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.95/1.64 thf(func_def_11, type, order_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.95/1.64 thf(func_def_12, type, fcomp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X1 > X2) > X0 > X2)).
% 2.95/1.64 thf(func_def_13, type, id: !>[X0: $tType]:(X0 > X0)).
% 2.95/1.64 thf(func_def_14, type, override_on: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > set @ X0 > X0 > X1)).
% 2.95/1.64 thf(func_def_15, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.95/1.64 thf(func_def_16, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 2.95/1.64 thf(func_def_17, type, undefined: !>[X0: $tType]:(X0)).
% 2.95/1.64 thf(func_def_18, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.95/1.64 thf(func_def_19, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.95/1.64 thf(func_def_20, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.95/1.64 thf(func_def_21, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.95/1.64 thf(func_def_22, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.95/1.64 thf(func_def_23, type, inv_imagep: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o)).
% 2.95/1.64 thf(func_def_24, type, ball: !>[X0: $tType]:(set @ X0 > (X0 > $o) > $o)).
% 2.95/1.64 thf(func_def_25, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.95/1.64 thf(func_def_26, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.95/1.64 thf(func_def_27, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 2.95/1.64 thf(func_def_28, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 2.95/1.64 thf(func_def_29, type, pairwise: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 2.95/1.64 thf(func_def_30, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 2.95/1.64 thf(func_def_31, type, tLList1825092077minal0: !>[X0: $tType]:(X0)).
% 2.95/1.64 thf(func_def_32, type, tLList1992840728_TCons: !>[X0: $tType, X1: $tType]:(X0 > tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X0 @ X1)).
% 2.95/1.64 thf(func_def_33, type, tLList57907754e_TNil: !>[X0: $tType, X1: $tType]:(X0 > tLList446370796tllist @ X1 @ X0)).
% 2.95/1.64 thf(func_def_34, type, tLList200813139tllist: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > tLList446370796tllist @ X2 @ X0 > X1) > tLList446370796tllist @ X2 @ X0 > X1)).
% 2.95/1.64 thf(func_def_35, type, tLList1614408749tllist: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X2) > (X0 > $o) > (X0 > tLList446370796tllist @ X2 @ X1) > (X0 > X0) > X0 > tLList446370796tllist @ X2 @ X1)).
% 2.95/1.64 thf(func_def_36, type, tLList1968894004s_TNil: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > $o)).
% 2.95/1.64 thf(func_def_37, type, tLList11265572tllist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > tLList446370796tllist @ X0 @ X1 > $o)).
% 2.95/1.64 thf(func_def_38, type, tLList457864275tllist: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > set @ X1)).
% 2.95/1.64 thf(func_def_39, type, tLList2110128105rminal: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > X1)).
% 2.95/1.64 thf(func_def_40, type, tLList_Mirabelle_thd: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > X0)).
% 2.95/1.64 thf(func_def_41, type, tLList1380991092t_all2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > tLList446370796tllist @ X0 @ X2 > tLList446370796tllist @ X1 @ X3 > $o)).
% 2.95/1.64 thf(func_def_42, type, tLList1669959861e_tmap: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > tLList446370796tllist @ X0 @ X2 > tLList446370796tllist @ X1 @ X3)).
% 2.95/1.64 thf(func_def_43, type, tLList1719791291e_tset: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > set @ X0)).
% 2.95/1.64 thf(func_def_44, type, tLList_Mirabelle_ttl: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X0 @ X1)).
% 2.95/1.64 thf(func_def_45, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.95/1.64 thf(func_def_46, type, x: tLList446370796tllist @ a @ b).
% 2.95/1.64 thf(func_def_47, type, x1: b).
% 2.95/1.64 thf(func_def_65, type, sP0: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0 > $o)).
% 2.95/1.64 thf(func_def_66, type, sP1: !>[X0: $tType, X1: $tType, X2: $tType]:(tLList446370796tllist @ X1 @ X2 > tLList446370796tllist @ X1 @ X2 > (X1 > X0) > (X1 > X0) > $o)).
% 2.95/1.64 thf(func_def_67, type, sP2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X3 > X1 > $o) > (tLList446370796tllist @ X3 @ X2 > tLList446370796tllist @ X1 @ X0 > $o) > tLList446370796tllist @ X3 @ X2 > tLList446370796tllist @ X1 @ X0 > $o)).
% 2.95/1.64 thf(func_def_68, type, sP3: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0 > $o) > tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0 > $o)).
% 2.95/1.64 thf(func_def_69, type, sP4: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0 > $o)).
% 2.95/1.64 thf(func_def_70, type, sK5: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0 > $o) > tLList446370796tllist @ X1 @ X0)).
% 2.95/1.64 thf(func_def_71, type, sK6: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0 > $o) > tLList446370796tllist @ X1 @ X0)).
% 2.95/1.64 thf(func_def_72, type, sK7: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > X1)).
% 2.95/1.64 thf(func_def_73, type, sK8: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0)).
% 2.95/1.64 thf(func_def_74, type, sK9: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > X0)).
% 2.95/1.64 thf(func_def_75, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:(tLList446370796tllist @ X1 @ X2 > tLList446370796tllist @ X1 @ X2 > (X1 > X0) > (X1 > X0) > X1)).
% 2.95/1.64 thf(func_def_76, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:(tLList446370796tllist @ X1 @ X2 > tLList446370796tllist @ X1 @ X2 > (X1 > X0) > (X1 > X0) > X1)).
% 2.95/1.64 thf(func_def_77, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0) > (X1 > X0) > tLList446370796tllist @ X2 @ X1 > tLList446370796tllist @ X2 @ X1 > X1)).
% 2.95/1.64 thf(func_def_78, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0) > (X1 > X0) > tLList446370796tllist @ X2 @ X1 > tLList446370796tllist @ X2 @ X1 > X1)).
% 2.95/1.64 thf(func_def_79, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0) > (X2 > X0) > tLList446370796tllist @ X2 @ X1 > X2)).
% 2.95/1.64 thf(func_def_80, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0) > (X1 > X0) > tLList446370796tllist @ X2 @ X1 > X1)).
% 2.95/1.64 thf(func_def_81, type, sK16: !>[X0: $tType]:((X0 > X0) > X0)).
% 2.95/1.64 thf(func_def_82, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X3 > $o) > (X1 > X2 > $o) > (tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X3 @ X2 > $o) > tLList446370796tllist @ X0 @ X1)).
% 2.95/1.64 thf(func_def_83, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X3 > $o) > (X1 > X2 > $o) > (tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X3 @ X2 > $o) > tLList446370796tllist @ X3 @ X2)).
% 2.95/1.64 thf(func_def_84, type, sK19: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X0 @ X1 > X1 > $o) > tLList446370796tllist @ X0 @ X1 > X1)).
% 2.95/1.64 thf(func_def_85, type, sK20: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X0 @ X1 > X1 > $o) > tLList446370796tllist @ X0 @ X1)).
% 2.95/1.64 thf(func_def_86, type, sK21: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X0 @ X1 > X1 > $o) > X1)).
% 2.95/1.64 thf(func_def_87, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0) > (X1 > X0) > tLList446370796tllist @ X2 @ X1 > X1)).
% 2.95/1.64 thf(func_def_88, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0) > (X2 > X0) > tLList446370796tllist @ X2 @ X1 > X2)).
% 2.95/1.64 thf(func_def_89, type, sK24: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.95/1.64 thf(func_def_90, type, sK25: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.95/1.64 thf(func_def_91, type, sK26: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set @ X0 > X0)).
% 2.95/1.64 thf(func_def_92, type, sK27: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0 > $o) > tLList446370796tllist @ X1 @ X0)).
% 2.95/1.64 thf(func_def_93, type, sK28: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0 > $o) > tLList446370796tllist @ X1 @ X0)).
% 2.95/1.64 thf(func_def_94, type, sK29: !>[X0: $tType, X1: $tType]:((X0 > tLList446370796tllist @ X1 @ X0 > $o) > X0)).
% 2.95/1.64 thf(func_def_95, type, sK30: !>[X0: $tType, X1: $tType]:((X0 > tLList446370796tllist @ X1 @ X0 > $o) > X1)).
% 2.95/1.64 thf(func_def_96, type, sK31: !>[X0: $tType, X1: $tType]:((X0 > tLList446370796tllist @ X1 @ X0 > $o) > tLList446370796tllist @ X1 @ X0)).
% 2.95/1.64 thf(func_def_97, type, sK32: !>[X0: $tType, X1: $tType]:((X0 > tLList446370796tllist @ X1 @ X0 > $o) > X0)).
% 2.95/1.64 thf(func_def_98, type, sK33: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > X0 > X1)).
% 2.95/1.64 thf(func_def_99, type, sK34: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > X0 > tLList446370796tllist @ X1 @ X0)).
% 2.95/1.64 thf(func_def_101, type, ph36: !>[X0: $tType]:(X0)).
% 2.95/1.64 thf(f1065,plain,(
% 2.95/1.64 $false),
% 2.95/1.64 inference(subsumption_resolution,[status(thm)],[f1064,f895])).
% 2.95/1.64 thf(f895,plain,(
% 2.95/1.64 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((if @ X0 @ $true @ X1 @ X2) = X1)) )),
% 2.95/1.64 inference(cnf_transformation,[status(thm)],[f512])).
% 2.95/1.64 thf(f512,plain,(
% 2.95/1.64 ! [X0 : $tType,X1 : X0,X2 : X0] : ((if @ X0 @ $true @ X1 @ X2) = X1)),
% 2.95/1.64 inference(fool_elimination,[status(thm)],[f511])).
% 2.95/1.64 thf(f511,plain,(
% 2.95/1.64 ! [X0 : $tType,X1 : X0,X2 : X0] : ((if @ X0 @ $true @ X1 @ X2) = X1)),
% 2.95/1.64 inference(rectify,[status(thm)],[f274])).
% 2.95/1.64 thf(f274,axiom,(
% 2.95/1.64 ! [X0 : $tType,X34 : X0,X17 : X0] : ((if @ X0 @ $true @ X34 @ X17) = X34)),
% 2.95/1.64 file('/export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2THF_18945.p',help_If_1_1_T)).
% 2.95/1.64 thf(f1064,plain,(
% 2.95/1.64 (x1 != (if @ b @ $true @ x1 @ (undefined @ (a > tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_thd @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ (tLList_Mirabelle_ttl @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)))))),
% 2.95/1.64 inference(forward_demodulation,[status(thm)],[f1063,f964])).
% 2.95/1.64 thf(f964,plain,(
% 2.95/1.64 ( ! [X1 : $tType,X0 : $tType,X2 : X1] : (($true = (tLList1968894004s_TNil @ X0 @ X1 @ (tLList57907754e_TNil @ X1 @ X0 @ X2)))) )),
% 2.95/1.64 inference(cnf_transformation,[status(thm)],[f460])).
% 2.95/1.64 thf(f460,plain,(
% 2.95/1.64 ! [X0 : $tType,X1 : $tType,X2 : X1] : ($true = (tLList1968894004s_TNil @ X0 @ X1 @ (tLList57907754e_TNil @ X1 @ X0 @ X2)))),
% 2.95/1.64 inference(fool_elimination,[status(thm)],[f459])).
% 2.95/1.64 thf(f459,plain,(
% 2.95/1.64 ! [X0 : $tType,X1 : $tType,X2 : X1] : (tLList1968894004s_TNil @ X0 @ X1 @ (tLList57907754e_TNil @ X1 @ X0 @ X2))),
% 2.95/1.64 inference(rectify,[status(thm)],[f5])).
% 2.95/1.64 thf(f5,axiom,(
% 2.95/1.64 ! [X0 : $tType,X1 : $tType,X7 : X1] : (tLList1968894004s_TNil @ X0 @ X1 @ (tLList57907754e_TNil @ X1 @ X0 @ X7))),
% 2.95/1.64 file('/export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2THF_18945.p',fact_4_tllist_Odisc_I1_J)).
% 2.95/1.64 thf(f1063,plain,(
% 2.95/1.64 (x1 != (if @ b @ (tLList1968894004s_TNil @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ x1 @ (undefined @ (a > tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_thd @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ (tLList_Mirabelle_ttl @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)))))),
% 2.95/1.64 inference(forward_demodulation,[status(thm)],[f1062,f927])).
% 2.95/1.64 thf(f927,plain,(
% 2.95/1.64 ( ! [X1 : $tType,X0 : $tType,X2 : X1] : (((tLList2110128105rminal @ X0 @ X1 @ (tLList57907754e_TNil @ X1 @ X0 @ X2)) = X2)) )),
% 2.95/1.64 inference(cnf_transformation,[status(thm)],[f743])).
% 2.95/1.64 thf(f743,plain,(
% 2.95/1.64 ! [X0 : $tType,X1 : $tType,X2 : X1] : ((tLList2110128105rminal @ X0 @ X1 @ (tLList57907754e_TNil @ X1 @ X0 @ X2)) = X2)),
% 2.95/1.64 inference(rectify,[status(thm)],[f4])).
% 2.95/1.64 thf(f4,axiom,(
% 2.95/1.64 ! [X5 : $tType,X0 : $tType,X7 : X0] : ((tLList2110128105rminal @ X5 @ X0 @ (tLList57907754e_TNil @ X0 @ X5 @ X7)) = X7)),
% 2.95/1.64 file('/export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2THF_18945.p',fact_3_tllist_Osel_I1_J)).
% 2.95/1.64 thf(f1062,plain,(
% 2.95/1.64 ((if @ b @ (tLList1968894004s_TNil @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ (tLList2110128105rminal @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ (undefined @ (a > tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_thd @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ (tLList_Mirabelle_ttl @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)))) != (tLList2110128105rminal @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)))),
% 2.95/1.64 inference(subsumption_resolution,[status(thm)],[f1061,f964])).
% 2.95/1.64 thf(f1061,plain,(
% 2.95/1.64 ($true != (tLList1968894004s_TNil @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1))) | ((if @ b @ (tLList1968894004s_TNil @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ (tLList2110128105rminal @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ (undefined @ (a > tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_thd @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)) @ (tLList_Mirabelle_ttl @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)))) != (tLList2110128105rminal @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)))),
% 2.95/1.64 inference(beta_eta_normalization,[status(thm)],[f1009])).
% 2.95/1.64 thf(f1009,plain,(
% 2.95/1.64 (((^[Y0 : b > b]: ((^[Y1 : a > tLList446370796tllist @ a @ b > b]: ((^[Y2 : tLList446370796tllist @ a @ b]: (if @ b @ (tLList1968894004s_TNil @ a @ b @ Y2) @ (Y0 @ (tLList2110128105rminal @ a @ b @ Y2)) @ (Y1 @ (tLList_Mirabelle_thd @ a @ b @ Y2) @ (tLList_Mirabelle_ttl @ a @ b @ Y2)))))))) @ (^[Y0 : b]: (Y0)) @ undefined @ (a > tLList446370796tllist @ a @ b > b) @ (tLList57907754e_TNil @ b @ a @ x1)) != (tLList2110128105rminal @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1))) | ($true != (tLList1968894004s_TNil @ a @ b @ (tLList57907754e_TNil @ b @ a @ x1)))),
% 2.95/1.64 inference(definition_unfolding,[status(thm)],[f953,f910,f880,f919,f919,f919])).
% 2.95/1.64 thf(f919,plain,(
% 2.95/1.64 (x = (tLList57907754e_TNil @ b @ a @ x1))),
% 2.95/1.64 inference(cnf_transformation,[status(thm)],[f275])).
% 2.95/1.64 thf(f275,axiom,(
% 2.95/1.64 (x = (tLList57907754e_TNil @ b @ a @ x1))),
% 2.95/1.64 file('/export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2THF_18945.p',conj_0)).
% 2.95/1.64 thf(f880,plain,(
% 2.95/1.64 ( ! [X0 : $tType] : ((id @ X0 = (^[Y0 : X0]: (Y0)))) )),
% 2.95/1.64 inference(cnf_transformation,[status(thm)],[f500])).
% 2.95/1.64 thf(f500,plain,(
% 2.95/1.64 ! [X0 : $tType] : (id @ X0 = (^[Y0 : X0]: (Y0)))),
% 2.95/1.64 inference(fool_elimination,[status(thm)],[f499])).
% 2.95/1.64 thf(f499,plain,(
% 2.95/1.64 ! [X0 : $tType] : ((^[X1 : X0] : (X1)) = id @ X0)),
% 2.95/1.64 inference(rectify,[status(thm)],[f16])).
% 2.95/1.64 thf(f16,axiom,(
% 2.95/1.64 ! [X0 : $tType] : ((^[X22 : X0] : (X22)) = id @ X0)),
% 2.95/1.64 file('/export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2THF_18945.p',fact_15_id__def)).
% 2.95/1.64 thf(f910,plain,(
% 2.95/1.64 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (((^[Y0 : X2 > X1]: ((^[Y1 : X0 > tLList446370796tllist @ X0 @ X2 > X1]: ((^[Y2 : tLList446370796tllist @ X0 @ X2]: (if @ X1 @ (tLList1968894004s_TNil @ X0 @ X2 @ Y2) @ (Y0 @ (tLList2110128105rminal @ X0 @ X2 @ Y2)) @ (Y1 @ (tLList_Mirabelle_thd @ X0 @ X2 @ Y2) @ (tLList_Mirabelle_ttl @ X0 @ X2 @ Y2)))))))) = tLList200813139tllist @ X2 @ X1 @ X0)) )),
% 2.95/1.64 inference(cnf_transformation,[status(thm)],[f558])).
% 2.95/1.64 thf(f558,plain,(
% 2.95/1.64 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((^[Y0 : X2 > X1]: ((^[Y1 : X0 > tLList446370796tllist @ X0 @ X2 > X1]: ((^[Y2 : tLList446370796tllist @ X0 @ X2]: (if @ X1 @ (tLList1968894004s_TNil @ X0 @ X2 @ Y2) @ (Y0 @ (tLList2110128105rminal @ X0 @ X2 @ Y2)) @ (Y1 @ (tLList_Mirabelle_thd @ X0 @ X2 @ Y2) @ (tLList_Mirabelle_ttl @ X0 @ X2 @ Y2)))))))) = tLList200813139tllist @ X2 @ X1 @ X0)),
% 2.95/1.64 inference(fool_elimination,[status(thm)],[f557])).
% 2.95/1.64 thf(f557,plain,(
% 2.95/1.64 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (tLList200813139tllist @ X2 @ X1 @ X0 = (^[X3 : X2 > X1, X4 : X0 > tLList446370796tllist @ X0 @ X2 > X1, X5 : tLList446370796tllist @ X0 @ X2] : (if @ X1 @ (tLList1968894004s_TNil @ X0 @ X2 @ X5) @ (X3 @ (tLList2110128105rminal @ X0 @ X2 @ X5)) @ (X4 @ (tLList_Mirabelle_thd @ X0 @ X2 @ X5) @ (tLList_Mirabelle_ttl @ X0 @ X2 @ X5)))))),
% 2.95/1.64 inference(rectify,[status(thm)],[f12])).
% 2.95/1.64 thf(f12,axiom,(
% 2.95/1.64 ! [X0 : $tType,X2 : $tType,X1 : $tType] : (tLList200813139tllist @ X1 @ X2 @ X0 = (^[X23 : X1 > X2, X24 : X0 > tLList446370796tllist @ X0 @ X1 > X2, X13 : tLList446370796tllist @ X0 @ X1] : (if @ X2 @ (tLList1968894004s_TNil @ X0 @ X1 @ X13) @ (X23 @ (tLList2110128105rminal @ X0 @ X1 @ X13)) @ (X24 @ (tLList_Mirabelle_thd @ X0 @ X1 @ X13) @ (tLList_Mirabelle_ttl @ X0 @ X1 @ X13)))))),
% 2.95/1.64 file('/export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2THF_18945.p',fact_11_tllist_Ocase__eq__if)).
% 2.95/1.64 thf(f953,plain,(
% 2.95/1.64 ((tLList200813139tllist @ b @ b @ a @ id @ b @ undefined @ (a > tLList446370796tllist @ a @ b > b) @ x) != (tLList2110128105rminal @ a @ b @ x)) | ((tLList1968894004s_TNil @ a @ b @ x) != $true)),
% 2.95/1.64 inference(cnf_transformation,[status(thm)],[f776])).
% 2.95/1.64 thf(f776,plain,(
% 2.95/1.64 (((tLList200813139tllist @ b @ b @ a @ id @ b @ undefined @ (a > tLList446370796tllist @ a @ b > b) @ x) != (tLList2110128105rminal @ a @ b @ x)) & ((tLList1968894004s_TNil @ a @ b @ x) = $true)) | (((tLList1968894004s_TNil @ a @ b @ x) != $true) & ((tLList2110128105rminal @ a @ b @ x) != (tLList1825092077minal0 @ (tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_ttl @ a @ b @ x))))),
% 2.95/1.64 inference(ennf_transformation,[status(thm)],[f733])).
% 2.95/1.64 thf(f733,plain,(
% 2.95/1.64 ~((((tLList1968894004s_TNil @ a @ b @ x) != $true) => ((tLList2110128105rminal @ a @ b @ x) = (tLList1825092077minal0 @ (tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_ttl @ a @ b @ x)))) & (((tLList1968894004s_TNil @ a @ b @ x) = $true) => ((tLList200813139tllist @ b @ b @ a @ id @ b @ undefined @ (a > tLList446370796tllist @ a @ b > b) @ x) = (tLList2110128105rminal @ a @ b @ x))))),
% 2.95/1.64 inference(flattening,[status(thm)],[f382])).
% 2.95/1.64 thf(f382,plain,(
% 2.95/1.64 ~((((tLList1968894004s_TNil @ a @ b @ x) = $true) => ((tLList200813139tllist @ b @ b @ a @ id @ b @ undefined @ (a > tLList446370796tllist @ a @ b > b) @ x) = (tLList2110128105rminal @ a @ b @ x))) & (~((tLList1968894004s_TNil @ a @ b @ x) = $true) => ((tLList2110128105rminal @ a @ b @ x) = (tLList1825092077minal0 @ (tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_ttl @ a @ b @ x)))))),
% 2.95/1.64 inference(fool_elimination,[status(thm)],[f381])).
% 2.95/1.64 thf(f381,plain,(
% 2.95/1.64 ~(((tLList1968894004s_TNil @ a @ b @ x) => ((tLList200813139tllist @ b @ b @ a @ id @ b @ undefined @ (a > tLList446370796tllist @ a @ b > b) @ x) = (tLList2110128105rminal @ a @ b @ x))) & (~(tLList1968894004s_TNil @ a @ b @ x) => ((tLList2110128105rminal @ a @ b @ x) = (tLList1825092077minal0 @ (tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_ttl @ a @ b @ x)))))),
% 2.95/1.64 inference(rectify,[status(thm)],[f277])).
% 2.95/1.64 thf(f277,negated_conjecture,(
% 2.95/1.64 ~(((tLList1968894004s_TNil @ a @ b @ x) => ((tLList200813139tllist @ b @ b @ a @ id @ b @ undefined @ (a > tLList446370796tllist @ a @ b > b) @ x) = (tLList2110128105rminal @ a @ b @ x))) & (~(tLList1968894004s_TNil @ a @ b @ x) => ((tLList2110128105rminal @ a @ b @ x) = (tLList1825092077minal0 @ (tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_ttl @ a @ b @ x)))))),
% 2.95/1.64 inference(negated_conjecture,[status(cth)],[f276])).
% 2.95/1.64 thf(f276,conjecture,(
% 2.95/1.64 ((tLList1968894004s_TNil @ a @ b @ x) => ((tLList200813139tllist @ b @ b @ a @ id @ b @ undefined @ (a > tLList446370796tllist @ a @ b > b) @ x) = (tLList2110128105rminal @ a @ b @ x))) & (~(tLList1968894004s_TNil @ a @ b @ x) => ((tLList2110128105rminal @ a @ b @ x) = (tLList1825092077minal0 @ (tLList446370796tllist @ a @ b > b) @ (tLList_Mirabelle_ttl @ a @ b @ x))))),
% 2.95/1.64 file('/export/starexec/sandbox/tmp/tmp.LhLiqwC5rF/DTF2THF_18945.p',conj_1)).
% 2.95/1.64 % SZS output end Proof for DTF2THF_18945
% 2.95/1.64 % (19278)------------------------------
% 2.95/1.64 % (19278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (19278)Termination reason: Refutation
% 2.95/1.64
% 2.95/1.64 % (19278)Memory used [KB]: 6908
% 2.95/1.64 % (19278)Time elapsed: 0.045 s
% 2.95/1.64 % (19278)Instructions burned: 85 (million)
% 2.95/1.64 % (19278)------------------------------
% 2.95/1.64 % (19278)------------------------------
% 2.95/1.64 % (19272)Success in time 0.066 s
%------------------------------------------------------------------------------