%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT224^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 08:45:12 AM UTC 2026
% Result : Theorem 3.00s 1.67s
% Output : Refutation 3.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT224^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:10:56 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.32/0.46 ---- Original DTF file ---
% 0.32/0.46 thf(spec,logic,$$dhol).
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 % File : DAT224^1 : TPTP v9.2.1. Released v7.0.0.
% 0.32/0.46 % Domain : Data Structures
% 0.32/0.46 % Problem : Terminated lazy lists 605
% 0.32/0.46 % Version : [Bla16] axioms : Especial.
% 0.32/0.46 % English :
% 0.32/0.46
% 0.32/0.46 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.32/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.32/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.32/0.46 % Source : [Bla16]
% 0.32/0.46 % Names : tllist__605.p [Bla16]
% 0.32/0.46
% 0.32/0.46 % Status : Theorem
% 0.32/0.46 % Rating : 0.67 v8.2.0, 0.33 v8.1.0, 0.75 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.32/0.46 % Syntax : Number of formulae : 321 ( 165 unt; 67 typ; 0 def)
% 0.32/0.46 % Number of atoms : 630 ( 341 equ; 0 cnn)
% 0.32/0.46 % Maximal formula atoms : 10 ( 2 avg)
% 0.32/0.46 % Number of connectives : 5065 ( 105 ~; 10 |; 74 &;4611 @)
% 0.32/0.46 % ( 0 <=>; 265 =>; 0 <=; 0 <~>)
% 0.32/0.46 % Maximal formula depth : 29 ( 9 avg)
% 0.32/0.46 % Number of types : 8 ( 7 usr)
% 0.32/0.46 % Number of type conns : 493 ( 493 >; 0 *; 0 +; 0 <<)
% 0.32/0.46 % Number of symbols : 63 ( 60 usr; 5 con; 0-10 aty)
% 0.32/0.46 % Number of variables : 1536 ( 164 ^;1273 !; 17 ?;1536 :)
% 0.32/0.46 % ( 82 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.46 % SPC : TH1_THM_EQU_NAR
% 0.32/0.46
% 0.32/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.32/0.46 % 2016-07-13 14:52:57.049
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 %----Could-be-implicit typings (11)
% 0.32/0.46 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist,type,
% 0.32/0.46 tLList446370796tllist: $tType > $tType > $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_t_Coinductive__List_Ollist,type,
% 0.32/0.46 coinductive_llist: $tType > $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_t_Product__Type_Ounit,type,
% 0.32/0.46 product_unit: $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_t_Set_Oset,type,
% 0.32/0.46 set: $tType > $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_t_itself,type,
% 0.32/0.46 itself: $tType > $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_tf_f,type,
% 0.32/0.46 f: $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_tf_e,type,
% 0.32/0.46 e: $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_tf_d,type,
% 0.32/0.46 d: $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_tf_c,type,
% 0.32/0.46 c: $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_tf_b,type,
% 0.32/0.46 b: $tType ).
% 0.32/0.46
% 0.32/0.46 thf(ty_tf_a,type,
% 0.32/0.46 a: $tType ).
% 0.32/0.46
% 0.32/0.46 %----Explicit typings (56)
% 0.32/0.46 thf(sy_c_Coinductive__List_Oiterates,type,
% 0.32/0.46 coinductive_iterates:
% 0.32/0.46 !>[A: $tType] : ( ( A > A ) > A > ( coinductive_llist @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Olappend,type,
% 0.32/0.46 coinductive_lappend:
% 0.32/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Olconcat,type,
% 0.32/0.46 coinductive_lconcat:
% 0.32/0.46 !>[A: $tType] : ( ( coinductive_llist @ ( coinductive_llist @ A ) ) > ( coinductive_llist @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Olfilter,type,
% 0.32/0.46 coinductive_lfilter:
% 0.32/0.46 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.32/0.46 coinductive_lfinite:
% 0.32/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.32/0.46 coinductive_LCons:
% 0.32/0.46 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.32/0.46 coinductive_LNil:
% 0.32/0.46 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Ollist_Ocase__llist,type,
% 0.32/0.46 coindu1381640503_llist:
% 0.32/0.46 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Ollist_Olhd,type,
% 0.32/0.46 coinductive_lhd:
% 0.32/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 0.32/0.46 coinductive_lnull:
% 0.32/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 0.32/0.46 coinductive_lset:
% 0.32/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Coinductive__List_Ollist_Oltl,type,
% 0.32/0.46 coinductive_ltl:
% 0.32/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Fun_Oid,type,
% 0.32/0.46 id:
% 0.32/0.46 !>[A: $tType] : ( A > A ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 0.32/0.46 default_default:
% 0.32/0.46 !>[A: $tType] : A ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_HOL_Oundefined,type,
% 0.32/0.46 undefined:
% 0.32/0.46 !>[A: $tType] : A ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_If,type,
% 0.32/0.46 if:
% 0.32/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.32/0.46 sup_sup:
% 0.32/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.32/0.46 bot_bot:
% 0.32/0.46 !>[A: $tType] : A ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.32/0.46 ord_less_eq:
% 0.32/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Product__Type_OUnity,type,
% 0.32/0.46 product_Unity: product_unit ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 0.32/0.46 product_rec_unit:
% 0.32/0.46 !>[T: $tType] : ( T > product_unit > T ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Product__Type_Ounit_Ocase__unit,type,
% 0.32/0.46 product_case_unit:
% 0.32/0.46 !>[A: $tType] : ( A > product_unit > A ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Pure_Otype,type,
% 0.32/0.46 type:
% 0.32/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Set_OCollect,type,
% 0.32/0.46 collect:
% 0.32/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_Set_Oinsert,type,
% 0.32/0.46 insert:
% 0.32/0.46 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Olappendt,type,
% 0.32/0.46 tLList98099029ppendt:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( coinductive_llist @ A ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ollist__of__tllist,type,
% 0.32/0.46 tLList798109904tllist:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( coinductive_llist @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otappend,type,
% 0.32/0.46 tLList192138471append:
% 0.32/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( B > ( tLList446370796tllist @ A @ C ) ) > ( tLList446370796tllist @ A @ C ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otcast,type,
% 0.32/0.46 tLList222516140_tcast:
% 0.32/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ C ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otconcat,type,
% 0.32/0.46 tLList365522113concat:
% 0.32/0.46 !>[B: $tType,A: $tType] : ( B > ( tLList446370796tllist @ ( coinductive_llist @ A ) @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otconcat_H,type,
% 0.32/0.46 tLList1329345514concat:
% 0.32/0.46 !>[B: $tType,A: $tType] : ( ( product_unit > B ) > ( tLList446370796tllist @ ( coinductive_llist @ A ) @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Oterminal0,type,
% 0.32/0.46 tLList1825092077minal0:
% 0.32/0.46 !>[A: $tType] : A ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otfilter,type,
% 0.32/0.46 tLList1813626245filter:
% 0.32/0.46 !>[B: $tType,A: $tType] : ( B > ( A > $o ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otfilter_H,type,
% 0.32/0.46 tLList1122525870filter:
% 0.32/0.46 !>[B: $tType,A: $tType] : ( ( product_unit > B ) > ( A > $o ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTCons,type,
% 0.32/0.46 tLList1992840728_TCons:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( A > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTNil,type,
% 0.32/0.46 tLList57907754e_TNil:
% 0.32/0.46 !>[B: $tType,A: $tType] : ( B > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocase__tllist,type,
% 0.32/0.46 tLList200813139tllist:
% 0.32/0.46 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > ( tLList446370796tllist @ A @ B ) > C ) > ( tLList446370796tllist @ A @ B ) > C ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocorec__tllist,type,
% 0.32/0.46 tLList1614408749tllist:
% 0.32/0.46 !>[E: $tType,B: $tType,A: $tType] : ( ( E > $o ) > ( E > B ) > ( E > A ) > ( E > $o ) > ( E > ( tLList446370796tllist @ A @ B ) ) > ( E > E ) > E > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ois__TNil,type,
% 0.32/0.46 tLList1968894004s_TNil:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > $o ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Opred__tllist,type,
% 0.32/0.46 tLList11265572tllist:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( tLList446370796tllist @ A @ B ) > $o ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oset2__tllist,type,
% 0.32/0.46 tLList457864275tllist:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( set @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oterminal,type,
% 0.32/0.46 tLList2110128105rminal:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > B ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Othd,type,
% 0.32/0.46 tLList_Mirabelle_thd:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > A ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otllist__all2,type,
% 0.32/0.46 tLList1380991092t_all2:
% 0.32/0.46 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otmap,type,
% 0.32/0.46 tLList1669959861e_tmap:
% 0.32/0.46 !>[A: $tType,Aa: $tType,B: $tType,Ba: $tType] : ( ( A > Aa ) > ( B > Ba ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ Aa @ Ba ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otset,type,
% 0.32/0.46 tLList1719791291e_tset:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( set @ A ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ottl,type,
% 0.32/0.46 tLList_Mirabelle_ttl:
% 0.32/0.46 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist__of__llist,type,
% 0.32/0.46 tLList1672613558_llist:
% 0.32/0.46 !>[B: $tType,A: $tType] : ( B > ( coinductive_llist @ A ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ounfold__tllist,type,
% 0.32/0.46 tLList636831159tllist:
% 0.32/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > $o ) > ( A > B ) > ( A > C ) > ( A > A ) > A > ( tLList446370796tllist @ C @ B ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_c_member,type,
% 0.32/0.46 member:
% 0.32/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.32/0.46
% 0.32/0.46 thf(sy_v_P,type,
% 0.32/0.46 p: a > b > $o ).
% 0.32/0.46
% 0.32/0.46 thf(sy_v_Q,type,
% 0.32/0.46 q: c > d > $o ).
% 0.32/0.46
% 0.32/0.46 thf(sy_v_f,type,
% 0.32/0.46 f2: e > a ).
% 0.32/0.46
% 0.32/0.46 thf(sy_v_g,type,
% 0.32/0.46 g: f > c ).
% 0.32/0.46
% 0.32/0.46 thf(sy_v_xs,type,
% 0.32/0.46 xs: tLList446370796tllist @ e @ f ).
% 0.32/0.46
% 0.32/0.46 thf(sy_v_ys,type,
% 0.32/0.46 ys: tLList446370796tllist @ b @ d ).
% 0.32/0.46
% 0.32/0.46 %----Relevant facts (250)
% 0.32/0.46 thf(fact_0_tllist_Orel__map_I2_J,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,E: $tType,F: $tType,D: $tType,C: $tType,S1a: A > E > $o,S2a: B > F > $o,X: tLList446370796tllist @ A @ B,G1: C > E,G2: D > F,Y: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ A @ E @ B @ F @ S1a @ S2a @ X @ ( tLList1669959861e_tmap @ C @ E @ D @ F @ G1 @ G2 @ Y ) )
% 0.32/0.46 = ( tLList1380991092t_all2 @ A @ C @ B @ D
% 0.32/0.46 @ ^ [X2: A,Y2: C] : ( S1a @ X2 @ ( G1 @ Y2 ) )
% 0.32/0.46 @ ^ [X2: B,Y2: D] : ( S2a @ X2 @ ( G2 @ Y2 ) )
% 0.32/0.46 @ X
% 0.32/0.46 @ Y ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.rel_map(2)
% 0.32/0.46 thf(fact_1_tllist_Orel__map_I1_J,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,E: $tType,F: $tType,D: $tType,C: $tType,S1b: E > C > $o,S2b: F > D > $o,I1: A > E,I2: B > F,X: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ E @ C @ F @ D @ S1b @ S2b @ ( tLList1669959861e_tmap @ A @ E @ B @ F @ I1 @ I2 @ X ) @ Y )
% 0.32/0.46 = ( tLList1380991092t_all2 @ A @ C @ B @ D
% 0.32/0.46 @ ^ [X2: A] : ( S1b @ ( I1 @ X2 ) )
% 0.32/0.46 @ ^ [X2: B] : ( S2b @ ( I2 @ X2 ) )
% 0.32/0.46 @ X
% 0.32/0.46 @ Y ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.rel_map(1)
% 0.32/0.46 thf(fact_2_tllist_Orel__eq,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ A @ A @ B @ B
% 0.32/0.46 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.32/0.46 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) )
% 0.32/0.46 = ( ^ [Y3: tLList446370796tllist @ A @ B,Z: tLList446370796tllist @ A @ B] : ( Y3 = Z ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.rel_eq
% 0.32/0.46 thf(fact_3_tllist_Orel__refl,axiom,
% 0.32/0.46 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ! [X3: C] : ( R1a @ X3 @ X3 )
% 0.32/0.46 => ( ! [X3: D] : ( R2a @ X3 @ X3 )
% 0.32/0.46 => ( tLList1380991092t_all2 @ C @ C @ D @ D @ R1a @ R2a @ X @ X ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.rel_refl
% 0.32/0.46 thf(fact_4_tllist_Omap__ident,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,T2: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( tLList1669959861e_tmap @ A @ A @ B @ B
% 0.32/0.46 @ ^ [X2: A] : X2
% 0.32/0.46 @ ^ [X2: B] : X2
% 0.32/0.46 @ T2 )
% 0.32/0.46 = T2 ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.map_ident
% 0.32/0.46 thf(fact_5_tllist_Omap__cong__pred,axiom,
% 0.32/0.46 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 0.32/0.46 ( ( X = Ya )
% 0.32/0.46 => ( ( tLList11265572tllist @ A @ B
% 0.32/0.46 @ ^ [Z1: A] :
% 0.32/0.46 ( ( F1 @ Z1 )
% 0.32/0.46 = ( G1 @ Z1 ) )
% 0.32/0.46 @ ^ [Z2: B] :
% 0.32/0.46 ( ( F2 @ Z2 )
% 0.32/0.46 = ( G2 @ Z2 ) )
% 0.32/0.46 @ Ya )
% 0.32/0.46 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X )
% 0.32/0.46 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.map_cong_pred
% 0.32/0.46 thf(fact_6_ttl__tmap,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,D: $tType,C: $tType,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs ) )
% 0.32/0.46 = ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ ( tLList_Mirabelle_ttl @ C @ D @ Xs ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % ttl_tmap
% 0.32/0.46 thf(fact_7_tllist__all2__TCons,axiom,
% 0.32/0.46 ! [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] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) )
% 0.32/0.46 = ( ( R1 @ X21 @ Y21 )
% 0.32/0.46 & ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist_all2_TCons
% 0.32/0.46 thf(fact_8_tllist__all2__TNil,axiom,
% 0.32/0.46 ! [C: $tType,A: $tType,B: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,X1: B,Y1: D] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList57907754e_TNil @ D @ C @ Y1 ) )
% 0.32/0.46 = ( R2 @ X1 @ Y1 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist_all2_TNil
% 0.32/0.46 thf(fact_9_tllist_Omap__disc__iff,axiom,
% 0.32/0.46 ! [C: $tType,D: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,A2: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( tLList1968894004s_TNil @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 0.32/0.46 = ( tLList1968894004s_TNil @ A @ B @ A2 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.map_disc_iff
% 0.32/0.46 thf(fact_10_tllist_Osimps_I15_J,axiom,
% 0.32/0.46 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.32/0.46 = ( tLList1992840728_TCons @ C @ D @ ( F1 @ X21 ) @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X22 ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.simps(15)
% 0.32/0.46 thf(fact_11_TCons__eq__tmap__conv,axiom,
% 0.32/0.46 ! [D: $tType,B: $tType,A: $tType,C: $tType,Y: A,Ys: tLList446370796tllist @ A @ B,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( ( tLList1992840728_TCons @ A @ B @ Y @ Ys )
% 0.32/0.46 = ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs ) )
% 0.32/0.46 = ( ? [Z3: C,Zs: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( Xs
% 0.32/0.46 = ( tLList1992840728_TCons @ C @ D @ Z3 @ Zs ) )
% 0.32/0.46 & ( ( F3 @ Z3 )
% 0.32/0.46 = Y )
% 0.32/0.46 & ( ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Zs )
% 0.32/0.46 = Ys ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % TCons_eq_tmap_conv
% 0.32/0.46 thf(fact_12_tmap__eq__TCons__conv,axiom,
% 0.32/0.46 ! [D: $tType,B: $tType,A: $tType,C: $tType,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D,Y: A,Ys: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs )
% 0.32/0.46 = ( tLList1992840728_TCons @ A @ B @ Y @ Ys ) )
% 0.32/0.46 = ( ? [Z3: C,Zs: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( Xs
% 0.32/0.46 = ( tLList1992840728_TCons @ C @ D @ Z3 @ Zs ) )
% 0.32/0.46 & ( ( F3 @ Z3 )
% 0.32/0.46 = Y )
% 0.32/0.46 & ( ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Zs )
% 0.32/0.46 = Ys ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tmap_eq_TCons_conv
% 0.32/0.46 thf(fact_13_tllist_Osimps_I14_J,axiom,
% 0.32/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,F1: A > C,F2: B > D,X1: B] :
% 0.32/0.46 ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.32/0.46 = ( tLList57907754e_TNil @ D @ C @ ( F2 @ X1 ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.simps(14)
% 0.32/0.46 thf(fact_14_TNil__eq__tmap__conv,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: B,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( ( tLList57907754e_TNil @ B @ A @ Y )
% 0.32/0.46 = ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs ) )
% 0.32/0.46 = ( ? [Y4: D] :
% 0.32/0.46 ( ( Xs
% 0.32/0.46 = ( tLList57907754e_TNil @ D @ C @ Y4 ) )
% 0.32/0.46 & ( ( G @ Y4 )
% 0.32/0.46 = Y ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % TNil_eq_tmap_conv
% 0.32/0.46 thf(fact_15_tmap__eq__TNil__conv,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D,Y: B] :
% 0.32/0.46 ( ( ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs )
% 0.32/0.46 = ( tLList57907754e_TNil @ B @ A @ Y ) )
% 0.32/0.46 = ( ? [Y4: D] :
% 0.32/0.46 ( ( Xs
% 0.32/0.46 = ( tLList57907754e_TNil @ D @ C @ Y4 ) )
% 0.32/0.46 & ( ( G @ Y4 )
% 0.32/0.46 = Y ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tmap_eq_TNil_conv
% 0.32/0.46 thf(fact_16_tllist_Orel__intros_I2_J,axiom,
% 0.32/0.46 ! [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] :
% 0.32/0.46 ( ( R1 @ X21 @ Y21 )
% 0.32/0.46 => ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 )
% 0.32/0.46 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.rel_intros(2)
% 0.32/0.46 thf(fact_17_tllist_Oinject_I1_J,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,X1: B,Y1: B] :
% 0.32/0.46 ( ( ( tLList57907754e_TNil @ B @ A @ X1 )
% 0.32/0.46 = ( tLList57907754e_TNil @ B @ A @ Y1 ) )
% 0.32/0.46 = ( X1 = Y1 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.inject(1)
% 0.32/0.46 thf(fact_18_tllist_Oinject_I2_J,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B,Y21: A,Y22: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( ( tLList1992840728_TCons @ A @ B @ X21 @ X22 )
% 0.32/0.46 = ( tLList1992840728_TCons @ A @ B @ Y21 @ Y22 ) )
% 0.32/0.46 = ( ( X21 = Y21 )
% 0.32/0.46 & ( X22 = Y22 ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.inject(2)
% 0.32/0.46 thf(fact_19_tllist_Opred__inject_I1_J,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,P1: A > $o,P2: B > $o,A2: B] :
% 0.32/0.46 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ ( tLList57907754e_TNil @ B @ A @ A2 ) )
% 0.32/0.46 = ( P2 @ A2 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.pred_inject(1)
% 0.32/0.46 thf(fact_20_tllist_Opred__inject_I2_J,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,A2: A,Aa2: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ ( tLList1992840728_TCons @ A @ B @ A2 @ Aa2 ) )
% 0.32/0.46 = ( ( P1 @ A2 )
% 0.32/0.46 & ( tLList11265572tllist @ A @ B @ P1 @ P2 @ Aa2 ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.pred_inject(2)
% 0.32/0.46 thf(fact_21_tllist_Osel_I5_J,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.32/0.46 = X22 ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.sel(5)
% 0.32/0.46 thf(fact_22_tllist_Osel_I4_J,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,X1: B] :
% 0.32/0.46 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.32/0.46 = ( tLList57907754e_TNil @ B @ A @ X1 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.sel(4)
% 0.32/0.46 thf(fact_23_tllist_Odisc_I2_J,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.disc(2)
% 0.32/0.46 thf(fact_24_tllist_Odisc_I1_J,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,X1: B] : ( tLList1968894004s_TNil @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.disc(1)
% 0.32/0.46 thf(fact_25_tllist_OdiscI_I2_J,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( Tllist
% 0.32/0.46 = ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.32/0.46 => ~ ( tLList1968894004s_TNil @ A @ B @ Tllist ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.discI(2)
% 0.32/0.46 thf(fact_26_tllist_OdiscI_I1_J,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,X1: B] :
% 0.32/0.46 ( ( Tllist
% 0.32/0.46 = ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.32/0.46 => ( tLList1968894004s_TNil @ A @ B @ Tllist ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.discI(1)
% 0.32/0.46 thf(fact_27_tllist_Odistinct_I1_J,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,X1: B,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( tLList57907754e_TNil @ B @ A @ X1 )
% 0.32/0.46 != ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.distinct(1)
% 0.32/0.46 thf(fact_28_is__TNil__ttl,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.46 => ( tLList1968894004s_TNil @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % is_TNil_ttl
% 0.32/0.46 thf(fact_29_tllist_Oexhaust,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,Y: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ! [X12: B] :
% 0.32/0.46 ( Y
% 0.32/0.46 != ( tLList57907754e_TNil @ B @ A @ X12 ) )
% 0.32/0.46 => ~ ! [X212: A,X222: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( Y
% 0.32/0.46 != ( tLList1992840728_TCons @ A @ B @ X212 @ X222 ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.exhaust
% 0.32/0.46 thf(fact_30_is__TNil__def,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType] :
% 0.32/0.46 ( ( tLList1968894004s_TNil @ A @ B )
% 0.32/0.46 = ( ^ [Tllist2: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ? [X13: B] :
% 0.32/0.46 ( Tllist2
% 0.32/0.46 = ( tLList57907754e_TNil @ B @ A @ X13 ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % is_TNil_def
% 0.32/0.46 thf(fact_31_tllist__all2__cases,axiom,
% 0.32/0.46 ! [A: $tType,C: $tType,D: $tType,B: $tType,P: A > B > $o,Q: C > D > $o,Xs: tLList446370796tllist @ A @ C,Ys: tLList446370796tllist @ B @ D] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Xs @ Ys )
% 0.32/0.46 => ( ! [B2: C] :
% 0.32/0.46 ( ( Xs
% 0.32/0.46 = ( tLList57907754e_TNil @ C @ A @ B2 ) )
% 0.32/0.46 => ! [B3: D] :
% 0.32/0.46 ( ( Ys
% 0.32/0.46 = ( tLList57907754e_TNil @ D @ B @ B3 ) )
% 0.32/0.46 => ~ ( Q @ B2 @ B3 ) ) )
% 0.32/0.46 => ~ ! [X3: A,Xs2: tLList446370796tllist @ A @ C] :
% 0.32/0.46 ( ( Xs
% 0.32/0.46 = ( tLList1992840728_TCons @ A @ C @ X3 @ Xs2 ) )
% 0.32/0.46 => ! [Y5: B,Ys2: tLList446370796tllist @ B @ D] :
% 0.32/0.46 ( ( Ys
% 0.32/0.46 = ( tLList1992840728_TCons @ B @ D @ Y5 @ Ys2 ) )
% 0.32/0.46 => ( ( P @ X3 @ Y5 )
% 0.32/0.46 => ~ ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist_all2_cases
% 0.32/0.46 thf(fact_32_tllist_Orel__cases,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,A2: tLList446370796tllist @ A @ B,B4: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ A2 @ B4 )
% 0.32/0.46 => ( ! [X3: B] :
% 0.32/0.46 ( ( A2
% 0.32/0.46 = ( tLList57907754e_TNil @ B @ A @ X3 ) )
% 0.32/0.46 => ! [Y5: D] :
% 0.32/0.46 ( ( B4
% 0.32/0.46 = ( tLList57907754e_TNil @ D @ C @ Y5 ) )
% 0.32/0.46 => ~ ( R2 @ X3 @ Y5 ) ) )
% 0.32/0.46 => ~ ! [X1a: A,X23: tLList446370796tllist @ A @ B] :
% 0.32/0.46 ( ( A2
% 0.32/0.46 = ( tLList1992840728_TCons @ A @ B @ X1a @ X23 ) )
% 0.32/0.46 => ! [Y1a: C,Y23: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ( ( B4
% 0.32/0.46 = ( tLList1992840728_TCons @ C @ D @ Y1a @ Y23 ) )
% 0.32/0.46 => ( ( R1 @ X1a @ Y1a )
% 0.32/0.46 => ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X23 @ Y23 ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.rel_cases
% 0.32/0.46 thf(fact_33_tllist_Orel__distinct_I1_J,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X1: B,Y21: C,Y22: tLList446370796tllist @ C @ D] :
% 0.32/0.46 ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.rel_distinct(1)
% 0.32/0.46 thf(fact_34_tllist_Orel__distinct_I2_J,axiom,
% 0.32/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,Y21: A,Y22: tLList446370796tllist @ A @ B,X1: D] :
% 0.32/0.46 ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ Y21 @ Y22 ) @ ( tLList57907754e_TNil @ D @ C @ X1 ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.rel_distinct(2)
% 0.32/0.46 thf(fact_35_tllist_Omap__sel_I3_J,axiom,
% 0.32/0.46 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 0.32/0.46 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.32/0.46 => ( ( tLList_Mirabelle_ttl @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 0.32/0.46 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.map_sel(3)
% 0.32/0.46 thf(fact_36_tllist_Opred__True,axiom,
% 0.32/0.46 ! [B: $tType,A: $tType] :
% 0.32/0.46 ( ( tLList11265572tllist @ A @ B
% 0.32/0.46 @ ^ [Uu: A] : $true
% 0.32/0.46 @ ^ [Uu: B] : $true )
% 0.32/0.46 = ( ^ [Uu: tLList446370796tllist @ A @ B] : $true ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist.pred_True
% 0.32/0.46 thf(fact_37_tllist__all2__TNil2,axiom,
% 0.32/0.46 ! [B: $tType,D: $tType,A: $tType,C: $tType,P: A > B > $o,Q: C > D > $o,Ts: tLList446370796tllist @ A @ C,B5: D] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Ts @ ( tLList57907754e_TNil @ D @ B @ B5 ) )
% 0.32/0.46 = ( ? [B6: C] :
% 0.32/0.46 ( ( Ts
% 0.32/0.46 = ( tLList57907754e_TNil @ C @ A @ B6 ) )
% 0.32/0.46 & ( Q @ B6 @ B5 ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 % tllist_all2_TNil2
% 0.32/0.46 thf(fact_38_tllist__all2__TNil1,axiom,
% 0.32/0.46 ! [A: $tType,C: $tType,B: $tType,D: $tType,P: A > B > $o,Q: C > D > $o,B4: C,Ts: tLList446370796tllist @ B @ D] :
% 0.32/0.46 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ ( tLList57907754e_TNil @ C @ A @ B4 ) @ Ts )
% 0.32/0.47 = ( ? [B7: D] :
% 0.32/0.47 ( ( Ts
% 0.32/0.47 = ( tLList57907754e_TNil @ D @ B @ B7 ) )
% 0.32/0.47 & ( Q @ B4 @ B7 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_all2_TNil1
% 0.32/0.47 thf(fact_39_tllist_Orel__intros_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,C: $tType,D: $tType,R2: B > D > $o,X1: B,Y1: D,R1: A > C > $o] :
% 0.32/0.47 ( ( R2 @ X1 @ Y1 )
% 0.32/0.47 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList57907754e_TNil @ D @ C @ Y1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.rel_intros(1)
% 0.32/0.47 thf(fact_40_tllist__all2__TCons2,axiom,
% 0.32/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,P: A > B > $o,Q: C > D > $o,Ts2: tLList446370796tllist @ A @ C,X: B,Ts: tLList446370796tllist @ B @ D] :
% 0.32/0.47 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Ts2 @ ( tLList1992840728_TCons @ B @ D @ X @ Ts ) )
% 0.32/0.47 = ( ? [X4: A,Ts3: tLList446370796tllist @ A @ C] :
% 0.32/0.47 ( ( Ts2
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ C @ X4 @ Ts3 ) )
% 0.32/0.47 & ( P @ X4 @ X )
% 0.32/0.47 & ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Ts3 @ Ts ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_all2_TCons2
% 0.32/0.47 thf(fact_41_tllist__all2__TCons1,axiom,
% 0.32/0.47 ! [D: $tType,A: $tType,C: $tType,B: $tType,P: A > B > $o,Q: C > D > $o,X: A,Ts: tLList446370796tllist @ A @ C,Ts2: tLList446370796tllist @ B @ D] :
% 0.32/0.47 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ ( tLList1992840728_TCons @ A @ C @ X @ Ts ) @ Ts2 )
% 0.32/0.47 = ( ? [X4: B,Ts3: tLList446370796tllist @ B @ D] :
% 0.32/0.47 ( ( Ts2
% 0.32/0.47 = ( tLList1992840728_TCons @ B @ D @ X4 @ Ts3 ) )
% 0.32/0.47 & ( P @ X @ X4 )
% 0.32/0.47 & ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Ts @ Ts3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_all2_TCons1
% 0.32/0.47 thf(fact_42_tllist_Ocollapse_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.32/0.47 => ( ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) )
% 0.32/0.47 = Tllist ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.collapse(2)
% 0.32/0.47 thf(fact_43_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.32/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.32/0.47 = ( P @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_44_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A: $tType,A3: set @ A] :
% 0.32/0.47 ( ( collect @ A
% 0.32/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.32/0.47 = A3 ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_45_Collect__cong,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.47 ( ! [X3: A] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 = ( Q @ X3 ) )
% 0.32/0.47 => ( ( collect @ A @ P )
% 0.32/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_cong
% 0.32/0.47 thf(fact_46_ext,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,F3: A > B,G: A > B] :
% 0.32/0.47 ( ! [X3: A] :
% 0.32/0.47 ( ( F3 @ X3 )
% 0.32/0.47 = ( G @ X3 ) )
% 0.32/0.47 => ( F3 = G ) ) ).
% 0.32/0.47
% 0.32/0.47 % ext
% 0.32/0.47 thf(fact_47_tconcat__TNil,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,B4: B,B5: B] :
% 0.32/0.47 ( ( tLList365522113concat @ B @ A @ B4 @ ( tLList57907754e_TNil @ B @ ( coinductive_llist @ A ) @ B5 ) )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ B5 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tconcat_TNil
% 0.32/0.47 thf(fact_48_ttl__def,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList_Mirabelle_ttl @ A @ B )
% 0.32/0.47 = ( tLList200813139tllist @ B @ ( tLList446370796tllist @ A @ B ) @ A @ ( tLList57907754e_TNil @ B @ A )
% 0.32/0.47 @ ^ [X213: A,X223: tLList446370796tllist @ A @ B] : X223 ) ) ).
% 0.32/0.47
% 0.32/0.47 % ttl_def
% 0.32/0.47 thf(fact_49_tllist_Omap__sel_I2_J,axiom,
% 0.32/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.32/0.47 => ( ( tLList_Mirabelle_thd @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 0.32/0.47 = ( F1 @ ( tLList_Mirabelle_thd @ A @ B @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.map_sel(2)
% 0.32/0.47 thf(fact_50_tmap__is__TNil,axiom,
% 0.32/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B,F3: A > C,G: B > D] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F3 @ G @ Xs )
% 0.32/0.47 = ( tLList57907754e_TNil @ D @ C @ ( G @ ( tLList2110128105rminal @ A @ B @ Xs ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tmap_is_TNil
% 0.32/0.47 thf(fact_51_ttl__unfold__tllist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,C: $tType,IS_TNIL: C > $o,A2: C,TNIL: C > B,THD: C > A,TTL: C > C] :
% 0.32/0.47 ( ( ( IS_TNIL @ A2 )
% 0.32/0.47 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ A2 ) )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ ( TNIL @ A2 ) ) ) )
% 0.32/0.47 & ( ~ ( IS_TNIL @ A2 )
% 0.32/0.47 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ A2 ) )
% 0.32/0.47 = ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ ( TTL @ A2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ttl_unfold_tllist
% 0.32/0.47 thf(fact_52_tllist_Ocorec__code,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,E: $tType] :
% 0.32/0.47 ( ( tLList1614408749tllist @ E @ B @ A )
% 0.32/0.47 = ( ^ [P3: E > $o,G12: 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 @ ( G12 @ A4 ) ) @ ( tLList1992840728_TCons @ A @ B @ ( G21 @ A4 ) @ ( if @ ( tLList446370796tllist @ A @ B ) @ ( Q22 @ A4 ) @ ( G221 @ A4 ) @ ( tLList1614408749tllist @ E @ B @ A @ P3 @ G12 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec_code
% 0.32/0.47 thf(fact_53_unfold__tllist_Ocode,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList636831159tllist @ A @ B @ C )
% 0.32/0.47 = ( ^ [P3: A > $o,G12: A > B,G21: A > C,G22: A > A,A4: A] : ( if @ ( tLList446370796tllist @ C @ B ) @ ( P3 @ A4 ) @ ( tLList57907754e_TNil @ B @ C @ ( G12 @ A4 ) ) @ ( tLList1992840728_TCons @ C @ B @ ( G21 @ A4 ) @ ( tLList636831159tllist @ A @ B @ C @ P3 @ G12 @ G21 @ G22 @ ( G22 @ A4 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.code
% 0.32/0.47 thf(fact_54_tconcat_H__code_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,B4: product_unit > B,B5: B] :
% 0.32/0.47 ( ( tLList1329345514concat @ B @ A @ B4 @ ( tLList57907754e_TNil @ B @ ( coinductive_llist @ A ) @ B5 ) )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ B5 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tconcat'_code(1)
% 0.32/0.47 thf(fact_55_tllist_Ocollapse_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.32/0.47 => ( ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) )
% 0.32/0.47 = Tllist ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.collapse(1)
% 0.32/0.47 thf(fact_56_terminal__TCons,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,X: B,Xs: tLList446370796tllist @ B @ A] :
% 0.32/0.47 ( ( tLList2110128105rminal @ B @ A @ ( tLList1992840728_TCons @ B @ A @ X @ Xs ) )
% 0.32/0.47 = ( tLList2110128105rminal @ B @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_TCons
% 0.32/0.47 thf(fact_57_terminal__ttl,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,Xs: tLList446370796tllist @ B @ A] :
% 0.32/0.47 ( ( tLList2110128105rminal @ B @ A @ ( tLList_Mirabelle_ttl @ B @ A @ Xs ) )
% 0.32/0.47 = ( tLList2110128105rminal @ B @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_ttl
% 0.32/0.47 thf(fact_58_unfold__tllist_Odisc__iff_I1_J,axiom,
% 0.32/0.47 ! [C: $tType,B: $tType,A: $tType,P4: A > $o,G1: A > B,G212: A > C,G223: A > A,A2: A] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) )
% 0.32/0.47 = ( P4 @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.disc_iff(1)
% 0.32/0.47 thf(fact_59_unfold__tllist_Odisc__iff_I2_J,axiom,
% 0.32/0.47 ! [C: $tType,B: $tType,A: $tType,P4: A > $o,G1: A > B,G212: A > C,G223: A > A,A2: A] :
% 0.32/0.47 ( ( ~ ( tLList1968894004s_TNil @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) ) )
% 0.32/0.47 = ( ~ ( P4 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.disc_iff(2)
% 0.32/0.47 thf(fact_60_tllist_Ocorec__disc__iff_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E,A2: E] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.32/0.47 = ( P4 @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec_disc_iff(1)
% 0.32/0.47 thf(fact_61_tllist_Ocorec__disc__iff_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E,A2: E] :
% 0.32/0.47 ( ( ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) )
% 0.32/0.47 = ( ~ ( P4 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec_disc_iff(2)
% 0.32/0.47 thf(fact_62_unfold__tllist__eq__TNil,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,C: $tType,IS_TNIL: C > $o,TNIL: C > B,THD: C > A,TTL: C > C,A2: C,B4: B] :
% 0.32/0.47 ( ( ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ A2 )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 0.32/0.47 = ( ( IS_TNIL @ A2 )
% 0.32/0.47 & ( B4
% 0.32/0.47 = ( TNIL @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist_eq_TNil
% 0.32/0.47 thf(fact_63_TNil__eq__unfold__tllist,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,C: $tType,B4: B,IS_TNIL: C > $o,TNIL: C > B,THD: C > A,TTL: C > C,A2: C] :
% 0.32/0.47 ( ( ( tLList57907754e_TNil @ B @ A @ B4 )
% 0.32/0.47 = ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ A2 ) )
% 0.32/0.47 = ( ( IS_TNIL @ A2 )
% 0.32/0.47 & ( B4
% 0.32/0.47 = ( TNIL @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % TNil_eq_unfold_tllist
% 0.32/0.47 thf(fact_64_unfold__tllist_Osimps_I3_J,axiom,
% 0.32/0.47 ! [C: $tType,B: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 0.32/0.47 ( ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList2110128105rminal @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) )
% 0.32/0.47 = ( G1 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.simps(3)
% 0.32/0.47 thf(fact_65_unfold__tllist_Osimps_I4_J,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 0.32/0.47 ( ~ ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList_Mirabelle_thd @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) )
% 0.32/0.47 = ( G212 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.simps(4)
% 0.32/0.47 thf(fact_66_tllist_Ocorec__sel_I1_J,axiom,
% 0.32/0.47 ! [Aa: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > A,G212: E > Aa,Q222: E > $o,G2212: E > ( tLList446370796tllist @ Aa @ A ),G2222: E > E] :
% 0.32/0.47 ( ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList2110128105rminal @ Aa @ A @ ( tLList1614408749tllist @ E @ A @ Aa @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.32/0.47 = ( G1 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec_sel(1)
% 0.32/0.47 thf(fact_67_tllist_Ocorec__sel_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.32/0.47 ( ~ ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.32/0.47 = ( G212 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec_sel(2)
% 0.32/0.47 thf(fact_68_tconcat__code,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList365522113concat @ A @ B )
% 0.32/0.47 = ( ^ [B6: A] :
% 0.32/0.47 ( tLList1329345514concat @ A @ B
% 0.32/0.47 @ ^ [Uu: product_unit] : B6 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tconcat_code
% 0.32/0.47 thf(fact_69_tllist_Ocase__eq__if,axiom,
% 0.32/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.32/0.47 ( ( tLList200813139tllist @ B @ C @ A )
% 0.32/0.47 = ( ^ [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 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.case_eq_if
% 0.32/0.47 thf(fact_70_tllist_Ocase__distrib,axiom,
% 0.32/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( H @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 0.32/0.47 = ( tLList200813139tllist @ B @ D @ A
% 0.32/0.47 @ ^ [X2: B] : ( H @ ( F1 @ X2 ) )
% 0.32/0.47 @ ^ [X13: A,X24: tLList446370796tllist @ A @ B] : ( H @ ( F2 @ X13 @ X24 ) )
% 0.32/0.47 @ Tllist ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.case_distrib
% 0.32/0.47 thf(fact_71_tllist_Ocoinduct__strong,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,R: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) > $o,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( R @ Tllist @ Tllist3 )
% 0.32/0.47 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( R @ Tllist4 @ Tllist5 )
% 0.32/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 = ( tLList1968894004s_TNil @ A @ B @ Tllist5 ) )
% 0.32/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ Tllist4 )
% 0.32/0.47 = ( tLList2110128105rminal @ A @ B @ Tllist5 ) ) ) )
% 0.32/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 0.32/0.47 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist4 )
% 0.32/0.47 = ( tLList_Mirabelle_thd @ A @ B @ Tllist5 ) )
% 0.32/0.47 & ( ( R @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) )
% 0.32/0.47 | ( ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 )
% 0.32/0.47 = ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( Tllist = Tllist3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.coinduct_strong
% 0.32/0.47 thf(fact_72_tllist_Ocoinduct,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,R: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) > $o,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( R @ Tllist @ Tllist3 )
% 0.32/0.47 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( R @ Tllist4 @ Tllist5 )
% 0.32/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 = ( tLList1968894004s_TNil @ A @ B @ Tllist5 ) )
% 0.32/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ Tllist4 )
% 0.32/0.47 = ( tLList2110128105rminal @ A @ B @ Tllist5 ) ) ) )
% 0.32/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 0.32/0.47 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist4 )
% 0.32/0.47 = ( tLList_Mirabelle_thd @ A @ B @ Tllist5 ) )
% 0.32/0.47 & ( R @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) ) ) ) ) ) )
% 0.32/0.47 => ( Tllist = Tllist3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.coinduct
% 0.32/0.47 thf(fact_73_tllist_Oexpand,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.32/0.47 = ( tLList1968894004s_TNil @ A @ B @ Tllist3 ) )
% 0.32/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.32/0.47 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist3 )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ Tllist )
% 0.32/0.47 = ( tLList2110128105rminal @ A @ B @ Tllist3 ) ) ) )
% 0.32/0.47 => ( ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 0.32/0.47 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist3 )
% 0.32/0.47 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist )
% 0.32/0.47 = ( tLList_Mirabelle_thd @ A @ B @ Tllist3 ) )
% 0.32/0.47 & ( ( tLList_Mirabelle_ttl @ A @ B @ Tllist )
% 0.32/0.47 = ( tLList_Mirabelle_ttl @ A @ B @ Tllist3 ) ) ) ) )
% 0.32/0.47 => ( Tllist = Tllist3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.expand
% 0.32/0.47 thf(fact_74_tllist_Osplit__sel__asm,axiom,
% 0.32/0.47 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( P @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 0.32/0.47 = ( ~ ( ( ( Tllist
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 0.32/0.47 & ~ ( P @ ( F1 @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) ) )
% 0.32/0.47 | ( ( Tllist
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) )
% 0.32/0.47 & ~ ( P @ ( F2 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.split_sel_asm
% 0.32/0.47 thf(fact_75_tllist_Osplit__sel,axiom,
% 0.32/0.47 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( P @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 0.32/0.47 = ( ( ( Tllist
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 0.32/0.47 => ( P @ ( F1 @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) ) )
% 0.32/0.47 & ( ( Tllist
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) )
% 0.32/0.47 => ( P @ ( F2 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.split_sel
% 0.32/0.47 thf(fact_76_terminal__TNil,axiom,
% 0.32/0.47 ! [Aa: $tType,A: $tType,X1: A] :
% 0.32/0.47 ( ( tLList2110128105rminal @ Aa @ A @ ( tLList57907754e_TNil @ A @ Aa @ X1 ) )
% 0.32/0.47 = X1 ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_TNil
% 0.32/0.47 thf(fact_77_tllist_Osel_I3_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.32/0.47 = X21 ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.sel(3)
% 0.32/0.47 thf(fact_78_unfold__tllist_Odisc_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 0.32/0.47 ( ( P4 @ A2 )
% 0.32/0.47 => ( tLList1968894004s_TNil @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.disc(1)
% 0.32/0.47 thf(fact_79_unfold__tllist_Odisc_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 0.32/0.47 ( ~ ( P4 @ A2 )
% 0.32/0.47 => ~ ( tLList1968894004s_TNil @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.disc(2)
% 0.32/0.47 thf(fact_80_tllist_Ocorec__disc_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.32/0.47 ( ( P4 @ A2 )
% 0.32/0.47 => ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec_disc(1)
% 0.32/0.47 thf(fact_81_tllist_Ocorec__disc_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.32/0.47 ( ~ ( P4 @ A2 )
% 0.32/0.47 => ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec_disc(2)
% 0.32/0.47 thf(fact_82_tllist__all2__coinduct,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,X5: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o,Xs: tLList446370796tllist @ A @ B,Ys: tLList446370796tllist @ C @ D,R: B > D > $o,P: A > C > $o] :
% 0.32/0.47 ( ( X5 @ Xs @ Ys )
% 0.32/0.47 => ( ! [Xs3: tLList446370796tllist @ A @ B,Ys3: tLList446370796tllist @ C @ D] :
% 0.32/0.47 ( ( X5 @ Xs3 @ Ys3 )
% 0.32/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 0.32/0.47 = ( tLList1968894004s_TNil @ C @ D @ Ys3 ) )
% 0.32/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 0.32/0.47 => ( ( tLList1968894004s_TNil @ C @ D @ Ys3 )
% 0.32/0.47 => ( R @ ( tLList2110128105rminal @ A @ B @ Xs3 ) @ ( tLList2110128105rminal @ C @ D @ Ys3 ) ) ) )
% 0.32/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 0.32/0.47 => ( ~ ( tLList1968894004s_TNil @ C @ D @ Ys3 )
% 0.32/0.47 => ( ( P @ ( tLList_Mirabelle_thd @ A @ B @ Xs3 ) @ ( tLList_Mirabelle_thd @ C @ D @ Ys3 ) )
% 0.32/0.47 & ( ( X5 @ ( tLList_Mirabelle_ttl @ A @ B @ Xs3 ) @ ( tLList_Mirabelle_ttl @ C @ D @ Ys3 ) )
% 0.32/0.47 | ( tLList1380991092t_all2 @ A @ C @ B @ D @ P @ R @ ( tLList_Mirabelle_ttl @ A @ B @ Xs3 ) @ ( tLList_Mirabelle_ttl @ C @ D @ Ys3 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ P @ R @ Xs @ Ys ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_all2_coinduct
% 0.32/0.47 thf(fact_83_tllist_Orel__coinduct,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,P: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o,X: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,R2: B > D > $o,R1: A > C > $o] :
% 0.32/0.47 ( ( P @ X @ Y )
% 0.32/0.47 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ C @ D] :
% 0.32/0.47 ( ( P @ Tllist4 @ Tllist5 )
% 0.32/0.47 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 = ( tLList1968894004s_TNil @ C @ D @ Tllist5 ) )
% 0.32/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 => ( ( tLList1968894004s_TNil @ C @ D @ Tllist5 )
% 0.32/0.47 => ( R2 @ ( tLList2110128105rminal @ A @ B @ Tllist4 ) @ ( tLList2110128105rminal @ C @ D @ Tllist5 ) ) ) )
% 0.32/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 0.32/0.47 => ( ~ ( tLList1968894004s_TNil @ C @ D @ Tllist5 )
% 0.32/0.47 => ( ( R1 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_thd @ C @ D @ Tllist5 ) )
% 0.32/0.47 & ( P @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ C @ D @ Tllist5 ) ) ) ) ) ) )
% 0.32/0.47 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X @ Y ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.rel_coinduct
% 0.32/0.47 thf(fact_84_tllist_Orel__sel,axiom,
% 0.32/0.47 ! [B: $tType,D: $tType,C: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList1380991092t_all2 @ A @ C @ B @ D )
% 0.32/0.47 = ( ^ [R12: A > C > $o,R22: B > D > $o,A4: tLList446370796tllist @ A @ B,B6: tLList446370796tllist @ C @ D] :
% 0.32/0.47 ( ( ( tLList1968894004s_TNil @ A @ B @ A4 )
% 0.32/0.47 = ( tLList1968894004s_TNil @ C @ D @ B6 ) )
% 0.32/0.47 & ( ( tLList1968894004s_TNil @ A @ B @ A4 )
% 0.32/0.47 => ( ( tLList1968894004s_TNil @ C @ D @ B6 )
% 0.32/0.47 => ( R22 @ ( tLList2110128105rminal @ A @ B @ A4 ) @ ( tLList2110128105rminal @ C @ D @ B6 ) ) ) )
% 0.32/0.47 & ( ~ ( tLList1968894004s_TNil @ A @ B @ A4 )
% 0.32/0.47 => ( ~ ( tLList1968894004s_TNil @ C @ D @ B6 )
% 0.32/0.47 => ( ( R12 @ ( tLList_Mirabelle_thd @ A @ B @ A4 ) @ ( tLList_Mirabelle_thd @ C @ D @ B6 ) )
% 0.32/0.47 & ( tLList1380991092t_all2 @ A @ C @ B @ D @ R12 @ R22 @ ( tLList_Mirabelle_ttl @ A @ B @ A4 ) @ ( tLList_Mirabelle_ttl @ C @ D @ B6 ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.rel_sel
% 0.32/0.47 thf(fact_85_tllist_Oexhaust__sel,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( Tllist
% 0.32/0.47 != ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 0.32/0.47 => ( Tllist
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.exhaust_sel
% 0.32/0.47 thf(fact_86_unfold__tllist_Octr_I1_J,axiom,
% 0.32/0.47 ! [C: $tType,B: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 0.32/0.47 ( ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ C @ ( G1 @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.ctr(1)
% 0.32/0.47 thf(fact_87_tllist_Osimps_I5_J,axiom,
% 0.32/0.47 ! [A: $tType,C: $tType,B: $tType,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,X1: B] :
% 0.32/0.47 ( ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.32/0.47 = ( F1 @ X1 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.simps(5)
% 0.32/0.47 thf(fact_88_tllist_Ocorec_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.32/0.47 ( ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ ( G1 @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec(1)
% 0.32/0.47 thf(fact_89_unfold__tllist_Octr_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 0.32/0.47 ( ~ ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 )
% 0.32/0.47 = ( tLList1992840728_TCons @ C @ B @ ( G212 @ A2 ) @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.ctr(2)
% 0.32/0.47 thf(fact_90_tllist_Osimps_I6_J,axiom,
% 0.32/0.47 ! [C: $tType,B: $tType,A: $tType,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.32/0.47 = ( F2 @ X21 @ X22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.simps(6)
% 0.32/0.47 thf(fact_91_tllist_Ocorec_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.32/0.47 ( ~ ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ ( G212 @ A2 ) @ ( if @ ( tLList446370796tllist @ A @ B ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec(2)
% 0.32/0.47 thf(fact_92_unfold__tllist_Osimps_I5_J,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 0.32/0.47 ( ~ ( P4 @ A2 )
% 0.32/0.47 => ( ( tLList_Mirabelle_ttl @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) )
% 0.32/0.47 = ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unfold_tllist.simps(5)
% 0.32/0.47 thf(fact_93_tllist_Ocorec__sel_I3_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,Q222: E > $o,G1: E > B,G212: E > A,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 0.32/0.47 ( ~ ( P4 @ A2 )
% 0.32/0.47 => ( ( ( Q222 @ A2 )
% 0.32/0.47 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.32/0.47 = ( G2212 @ A2 ) ) )
% 0.32/0.47 & ( ~ ( Q222 @ A2 )
% 0.32/0.47 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.32/0.47 = ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.corec_sel(3)
% 0.32/0.47 thf(fact_94_tllist_Omap__sel_I1_J,axiom,
% 0.32/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.32/0.47 => ( ( tLList2110128105rminal @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 0.32/0.47 = ( F2 @ ( tLList2110128105rminal @ A @ B @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.map_sel(1)
% 0.32/0.47 thf(fact_95_terminal__def,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList2110128105rminal @ A @ B )
% 0.32/0.47 = ( tLList200813139tllist @ B @ B @ A
% 0.32/0.47 @ ^ [X13: B] : X13
% 0.32/0.47 @ ^ [X_dummy: A] : ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ A @ B ) > B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_def
% 0.32/0.47 thf(fact_96_tllist_Osel_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,Aa: $tType,X21: Aa,X22: tLList446370796tllist @ Aa @ A] :
% 0.32/0.47 ( ( tLList2110128105rminal @ Aa @ A @ ( tLList1992840728_TCons @ Aa @ A @ X21 @ X22 ) )
% 0.32/0.47 = ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ Aa @ A ) > A ) @ X22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.sel(2)
% 0.32/0.47 thf(fact_97_terminal0__terminal,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ A @ B ) > B ) )
% 0.32/0.47 = ( tLList2110128105rminal @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal0_terminal
% 0.32/0.47 thf(fact_98_set2__tllist__induct,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,X: A,Xs: tLList446370796tllist @ B @ A,P: A > ( tLList446370796tllist @ B @ A ) > $o] :
% 0.32/0.47 ( ( member @ A @ X @ ( tLList457864275tllist @ B @ A @ Xs ) )
% 0.32/0.47 => ( ! [Xs3: tLList446370796tllist @ B @ A] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ B @ A @ Xs3 )
% 0.32/0.47 => ( P @ ( tLList2110128105rminal @ B @ A @ Xs3 ) @ Xs3 ) )
% 0.32/0.47 => ( ! [Xs3: tLList446370796tllist @ B @ A,Y5: A] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ B @ A @ Xs3 )
% 0.32/0.47 => ( ( member @ A @ Y5 @ ( tLList457864275tllist @ B @ A @ ( tLList_Mirabelle_ttl @ B @ A @ Xs3 ) ) )
% 0.32/0.47 => ( ( P @ Y5 @ ( tLList_Mirabelle_ttl @ B @ A @ Xs3 ) )
% 0.32/0.47 => ( P @ Y5 @ Xs3 ) ) ) )
% 0.32/0.47 => ( P @ X @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % set2_tllist_induct
% 0.32/0.47 thf(fact_99_tllist__set__induct,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X: A,Xs: tLList446370796tllist @ A @ B,P: A > ( tLList446370796tllist @ A @ B ) > $o] :
% 0.32/0.47 ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ Xs ) )
% 0.32/0.47 => ( ! [Xs3: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 0.32/0.47 => ( P @ ( tLList_Mirabelle_thd @ A @ B @ Xs3 ) @ Xs3 ) )
% 0.32/0.47 => ( ! [Xs3: tLList446370796tllist @ A @ B,Y5: A] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 0.32/0.47 => ( ( member @ A @ Y5 @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs3 ) ) )
% 0.32/0.47 => ( ( P @ Y5 @ ( tLList_Mirabelle_ttl @ A @ B @ Xs3 ) )
% 0.32/0.47 => ( P @ Y5 @ Xs3 ) ) ) )
% 0.32/0.47 => ( P @ X @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_set_induct
% 0.32/0.47 thf(fact_100_tconcat__TCons,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,A2: coinductive_llist @ A,Tr: tLList446370796tllist @ ( coinductive_llist @ A ) @ B] :
% 0.32/0.47 ( ( tLList365522113concat @ B @ A @ B4 @ ( tLList1992840728_TCons @ ( coinductive_llist @ A ) @ B @ A2 @ Tr ) )
% 0.32/0.47 = ( tLList98099029ppendt @ A @ B @ A2 @ ( tLList365522113concat @ B @ A @ B4 @ Tr ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tconcat_TCons
% 0.32/0.47 thf(fact_101_tconcat_H__def,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType] :
% 0.32/0.47 ( ( tLList1329345514concat @ B @ A )
% 0.32/0.47 = ( ^ [B6: product_unit > B] : ( tLList365522113concat @ B @ A @ ( B6 @ product_Unity ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tconcat'_def
% 0.32/0.47 thf(fact_102_tllist_Orel__cong,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,X: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,Xa: tLList446370796tllist @ C @ D,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
% 0.32/0.47 ( ( X = Ya )
% 0.32/0.47 => ( ( Y = Xa )
% 0.32/0.47 => ( ! [Z12: A,Y12: C] :
% 0.32/0.47 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 0.32/0.47 => ( ( member @ C @ Y12 @ ( tLList1719791291e_tset @ C @ D @ Xa ) )
% 0.32/0.47 => ( ( R1 @ Z12 @ Y12 )
% 0.32/0.47 = ( R1a @ Z12 @ Y12 ) ) ) )
% 0.32/0.47 => ( ! [Z22: B,Y23: D] :
% 0.32/0.47 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 0.32/0.47 => ( ( member @ D @ Y23 @ ( tLList457864275tllist @ C @ D @ Xa ) )
% 0.32/0.47 => ( ( R2 @ Z22 @ Y23 )
% 0.32/0.47 = ( R2a @ Z22 @ Y23 ) ) ) )
% 0.32/0.47 => ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X @ Y )
% 0.32/0.47 = ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.rel_cong
% 0.32/0.47 thf(fact_103_tllist_Orel__mono__strong,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 0.32/0.47 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X @ Y )
% 0.32/0.47 => ( ! [Z12: A,Y12: C] :
% 0.32/0.47 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 0.32/0.47 => ( ( member @ C @ Y12 @ ( tLList1719791291e_tset @ C @ D @ Y ) )
% 0.32/0.47 => ( ( R1 @ Z12 @ Y12 )
% 0.32/0.47 => ( R1a @ Z12 @ Y12 ) ) ) )
% 0.32/0.47 => ( ! [Z22: B,Y23: D] :
% 0.32/0.47 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 0.32/0.47 => ( ( member @ D @ Y23 @ ( tLList457864275tllist @ C @ D @ Y ) )
% 0.32/0.47 => ( ( R2 @ Z22 @ Y23 )
% 0.32/0.47 => ( R2a @ Z22 @ Y23 ) ) ) )
% 0.32/0.47 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a @ X @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.rel_mono_strong
% 0.32/0.47 thf(fact_104_tllist_Orel__refl__strong,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 0.32/0.47 ( ! [Z12: A] :
% 0.32/0.47 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 0.32/0.47 => ( R1a @ Z12 @ Z12 ) )
% 0.32/0.47 => ( ! [Z22: B] :
% 0.32/0.47 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 0.32/0.47 => ( R2a @ Z22 @ Z22 ) )
% 0.32/0.47 => ( tLList1380991092t_all2 @ A @ A @ B @ B @ R1a @ R2a @ X @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.rel_refl_strong
% 0.32/0.47 thf(fact_105_tllist_Omap__cong,axiom,
% 0.32/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 0.32/0.47 ( ( X = Ya )
% 0.32/0.47 => ( ! [Z12: A] :
% 0.32/0.47 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 0.32/0.47 => ( ( F1 @ Z12 )
% 0.32/0.47 = ( G1 @ Z12 ) ) )
% 0.32/0.47 => ( ! [Z22: B] :
% 0.32/0.47 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 0.32/0.47 => ( ( F2 @ Z22 )
% 0.32/0.47 = ( G2 @ Z22 ) ) )
% 0.32/0.47 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X )
% 0.32/0.47 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.map_cong
% 0.32/0.47 thf(fact_106_tllist_Omap__cong0,axiom,
% 0.32/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 0.32/0.47 ( ! [Z12: A] :
% 0.32/0.47 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 0.32/0.47 => ( ( F1 @ Z12 )
% 0.32/0.47 = ( G1 @ Z12 ) ) )
% 0.32/0.47 => ( ! [Z22: B] :
% 0.32/0.47 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 0.32/0.47 => ( ( F2 @ Z22 )
% 0.32/0.47 = ( G2 @ Z22 ) ) )
% 0.32/0.47 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X )
% 0.32/0.47 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G1 @ G2 @ X ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.map_cong0
% 0.32/0.47 thf(fact_107_tllist_Oinj__map__strong,axiom,
% 0.32/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,Xa: tLList446370796tllist @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
% 0.32/0.47 ( ! [Z12: A,Z1a: A] :
% 0.32/0.47 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 0.32/0.47 => ( ( member @ A @ Z1a @ ( tLList1719791291e_tset @ A @ B @ Xa ) )
% 0.32/0.47 => ( ( ( F1 @ Z12 )
% 0.32/0.47 = ( F1a @ Z1a ) )
% 0.32/0.47 => ( Z12 = Z1a ) ) ) )
% 0.32/0.47 => ( ! [Z22: B,Z2a: B] :
% 0.32/0.47 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 0.32/0.47 => ( ( member @ B @ Z2a @ ( tLList457864275tllist @ A @ B @ Xa ) )
% 0.32/0.47 => ( ( ( F2 @ Z22 )
% 0.32/0.47 = ( F2a @ Z2a ) )
% 0.32/0.47 => ( Z22 = Z2a ) ) ) )
% 0.32/0.47 => ( ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X )
% 0.32/0.47 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1a @ F2a @ Xa ) )
% 0.32/0.47 => ( X = Xa ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.inj_map_strong
% 0.32/0.47 thf(fact_108_tllist_Opred__mono__strong,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,X: tLList446370796tllist @ A @ B,P1a: A > $o,P2a: B > $o] :
% 0.32/0.47 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ X )
% 0.32/0.47 => ( ! [Z12: A] :
% 0.32/0.47 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 0.32/0.47 => ( ( P1 @ Z12 )
% 0.32/0.47 => ( P1a @ Z12 ) ) )
% 0.32/0.47 => ( ! [Z22: B] :
% 0.32/0.47 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 0.32/0.47 => ( ( P2 @ Z22 )
% 0.32/0.47 => ( P2a @ Z22 ) ) )
% 0.32/0.47 => ( tLList11265572tllist @ A @ B @ P1a @ P2a @ X ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.pred_mono_strong
% 0.32/0.47 thf(fact_109_tllist_Opred__cong,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,P1: A > $o,P1a: A > $o,P2: B > $o,P2a: B > $o] :
% 0.32/0.47 ( ( X = Ya )
% 0.32/0.47 => ( ! [Z12: A] :
% 0.32/0.47 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 0.32/0.47 => ( ( P1 @ Z12 )
% 0.32/0.47 = ( P1a @ Z12 ) ) )
% 0.32/0.47 => ( ! [Z22: B] :
% 0.32/0.47 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 0.32/0.47 => ( ( P2 @ Z22 )
% 0.32/0.47 = ( P2a @ Z22 ) ) )
% 0.32/0.47 => ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ X )
% 0.32/0.47 = ( tLList11265572tllist @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.pred_cong
% 0.32/0.47 thf(fact_110_tllist_Oset__cases_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,E2: A,A2: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( member @ A @ E2 @ ( tLList1719791291e_tset @ A @ B @ A2 ) )
% 0.32/0.47 => ( ! [Z22: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( A2
% 0.32/0.47 != ( tLList1992840728_TCons @ A @ B @ E2 @ Z22 ) )
% 0.32/0.47 => ~ ! [Z12: A,Z22: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ Z12 @ Z22 ) )
% 0.32/0.47 => ~ ( member @ A @ E2 @ ( tLList1719791291e_tset @ A @ B @ Z22 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_cases(1)
% 0.32/0.47 thf(fact_111_tllist_Oset__induct_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X: A,A2: tLList446370796tllist @ A @ B,P: A > ( tLList446370796tllist @ A @ B ) > $o] :
% 0.32/0.47 ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ A2 ) )
% 0.32/0.47 => ( ! [Z12: A,Z22: tLList446370796tllist @ A @ B] : ( P @ Z12 @ ( tLList1992840728_TCons @ A @ B @ Z12 @ Z22 ) )
% 0.32/0.47 => ( ! [Z12: A,Z22: tLList446370796tllist @ A @ B,Xa2: A] :
% 0.32/0.47 ( ( member @ A @ Xa2 @ ( tLList1719791291e_tset @ A @ B @ Z22 ) )
% 0.32/0.47 => ( ( P @ Xa2 @ Z22 )
% 0.32/0.47 => ( P @ Xa2 @ ( tLList1992840728_TCons @ A @ B @ Z12 @ Z22 ) ) ) )
% 0.32/0.47 => ( P @ X @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_induct(1)
% 0.32/0.47 thf(fact_112_tllist_Oset__intros_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X: A,A22: tLList446370796tllist @ A @ B,A1: A] :
% 0.32/0.47 ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ A22 ) )
% 0.32/0.47 => ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1 @ A22 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_intros(2)
% 0.32/0.47 thf(fact_113_tllist_Oset__intros_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,A1: A,A22: tLList446370796tllist @ A @ B] : ( member @ A @ A1 @ ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1 @ A22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_intros(1)
% 0.32/0.47 thf(fact_114_in__tset__ttlD,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X: A,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs ) ) )
% 0.32/0.47 => ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_tset_ttlD
% 0.32/0.47 thf(fact_115_tllist_Oset__intros_I3_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,Aa2: B] : ( member @ B @ Aa2 @ ( tLList457864275tllist @ A @ B @ ( tLList57907754e_TNil @ B @ A @ Aa2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_intros(3)
% 0.32/0.47 thf(fact_116_tllist_Osimps_I23_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList457864275tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.32/0.47 = ( tLList457864275tllist @ A @ B @ X22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.simps(23)
% 0.32/0.47 thf(fact_117_tllist_Oset__intros_I4_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xc: B,A2a: tLList446370796tllist @ A @ B,A1a: A] :
% 0.32/0.47 ( ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ A2a ) )
% 0.32/0.47 => ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1a @ A2a ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_intros(4)
% 0.32/0.47 thf(fact_118_tllist_Odisc__eq__case_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist ) )
% 0.32/0.47 = ( tLList200813139tllist @ B @ $o @ A
% 0.32/0.47 @ ^ [Uu: B] : $false
% 0.32/0.47 @ ^ [Uu: A,Uv: tLList446370796tllist @ A @ B] : $true
% 0.32/0.47 @ Tllist ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.disc_eq_case(2)
% 0.32/0.47 thf(fact_119_tllist_Odisc__eq__case_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B )
% 0.32/0.47 = ( tLList200813139tllist @ B @ $o @ A
% 0.32/0.47 @ ^ [Uu: B] : $true
% 0.32/0.47 @ ^ [Uu: A,Uv: tLList446370796tllist @ A @ B] : $false ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.disc_eq_case(1)
% 0.32/0.47 thf(fact_120_tllist_Oset__sel_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,X: A] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.32/0.47 => ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) )
% 0.32/0.47 => ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_sel(2)
% 0.32/0.47 thf(fact_121_tllist_Oset__sel_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.32/0.47 => ( member @ A @ ( tLList_Mirabelle_thd @ A @ B @ A2 ) @ ( tLList1719791291e_tset @ A @ B @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_sel(1)
% 0.32/0.47 thf(fact_122_tllist_Oset__sel_I3_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.32/0.47 => ( member @ B @ ( tLList2110128105rminal @ A @ B @ A2 ) @ ( tLList457864275tllist @ A @ B @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_sel(3)
% 0.32/0.47 thf(fact_123_tllist_Oset__cases_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,E2: B,A2: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( member @ B @ E2 @ ( tLList457864275tllist @ A @ B @ A2 ) )
% 0.32/0.47 => ( ( A2
% 0.32/0.47 != ( tLList57907754e_TNil @ B @ A @ E2 ) )
% 0.32/0.47 => ~ ! [Z12: A,Z22: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ Z12 @ Z22 ) )
% 0.32/0.47 => ~ ( member @ B @ E2 @ ( tLList457864275tllist @ A @ B @ Z22 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_cases(2)
% 0.32/0.47 thf(fact_124_tllist_Oset__induct_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,Aa: $tType,X: A,A2: tLList446370796tllist @ Aa @ A,P: A > ( tLList446370796tllist @ Aa @ A ) > $o] :
% 0.32/0.47 ( ( member @ A @ X @ ( tLList457864275tllist @ Aa @ A @ A2 ) )
% 0.32/0.47 => ( ! [Z4: A] : ( P @ Z4 @ ( tLList57907754e_TNil @ A @ Aa @ Z4 ) )
% 0.32/0.47 => ( ! [Z12: Aa,Z22: tLList446370796tllist @ Aa @ A,Xb: A] :
% 0.32/0.47 ( ( member @ A @ Xb @ ( tLList457864275tllist @ Aa @ A @ Z22 ) )
% 0.32/0.47 => ( ( P @ Xb @ Z22 )
% 0.32/0.47 => ( P @ Xb @ ( tLList1992840728_TCons @ Aa @ A @ Z12 @ Z22 ) ) ) )
% 0.32/0.47 => ( P @ X @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_induct(2)
% 0.32/0.47 thf(fact_125_tllist_Oset__sel_I4_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,Xc: B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 0.32/0.47 => ( ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) )
% 0.32/0.47 => ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.set_sel(4)
% 0.32/0.47 thf(fact_126_tconcat_H__code_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,B4: product_unit > B,A2: coinductive_llist @ C,Tr: tLList446370796tllist @ ( coinductive_llist @ C ) @ B] :
% 0.32/0.47 ( ( tLList1329345514concat @ B @ C @ B4 @ ( tLList1992840728_TCons @ ( coinductive_llist @ C ) @ B @ A2 @ Tr ) )
% 0.32/0.47 = ( tLList98099029ppendt @ C @ B @ A2 @ ( tLList1329345514concat @ B @ C @ B4 @ Tr ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tconcat'_code(2)
% 0.32/0.47 thf(fact_127_unit__abs__eta__conv,axiom,
% 0.32/0.47 ! [A: $tType,F3: product_unit > A] :
% 0.32/0.47 ( ( ^ [U: product_unit] : ( F3 @ product_Unity ) )
% 0.32/0.47 = F3 ) ).
% 0.32/0.47
% 0.32/0.47 % unit_abs_eta_conv
% 0.32/0.47 thf(fact_128_is__TNil__tfilter,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Y: B,P: A > $o,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ ( tLList1813626245filter @ B @ A @ Y @ P @ Xs ) )
% 0.32/0.47 = ( ! [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ ( tLList1719791291e_tset @ A @ B @ Xs ) )
% 0.32/0.47 => ~ ( P @ X2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % is_TNil_tfilter
% 0.32/0.47 thf(fact_129_old_Ounit_Oexhaust,axiom,
% 0.32/0.47 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 0.32/0.47
% 0.32/0.47 % old.unit.exhaust
% 0.32/0.47 thf(fact_130_old_Ounit_Oinducts,axiom,
% 0.32/0.47 ! [P: product_unit > $o,Unit: product_unit] :
% 0.32/0.47 ( ( P @ product_Unity )
% 0.32/0.47 => ( P @ Unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.unit.inducts
% 0.32/0.47 thf(fact_131_unit__all__impI,axiom,
% 0.32/0.47 ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.32/0.47 ( ( ( P @ product_Unity )
% 0.32/0.47 => ( Q @ product_Unity ) )
% 0.32/0.47 => ! [X6: product_unit] :
% 0.32/0.47 ( ( P @ X6 )
% 0.32/0.47 => ( Q @ X6 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % unit_all_impI
% 0.32/0.47 thf(fact_132_tfilter__TNil,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,B5: B,P: A > $o,B4: B] :
% 0.32/0.47 ( ( tLList1813626245filter @ B @ A @ B5 @ P @ ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ B4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfilter_TNil
% 0.32/0.47 thf(fact_133_tfilter__TCons,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,P: A > $o,A2: A,B4: B,Tr: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( ( P @ A2 )
% 0.32/0.47 => ( ( tLList1813626245filter @ B @ A @ B4 @ P @ ( tLList1992840728_TCons @ A @ B @ A2 @ Tr ) )
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ A2 @ ( tLList1813626245filter @ B @ A @ B4 @ P @ Tr ) ) ) )
% 0.32/0.47 & ( ~ ( P @ A2 )
% 0.32/0.47 => ( ( tLList1813626245filter @ B @ A @ B4 @ P @ ( tLList1992840728_TCons @ A @ B @ A2 @ Tr ) )
% 0.32/0.47 = ( tLList1813626245filter @ B @ A @ B4 @ P @ Tr ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfilter_TCons
% 0.32/0.47 thf(fact_134_eq__sym__Unity__conv,axiom,
% 0.32/0.47 ! [X: $o] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( product_Unity = product_Unity ) )
% 0.32/0.47 = X ) ).
% 0.32/0.47
% 0.32/0.47 % eq_sym_Unity_conv
% 0.32/0.47 thf(fact_135_old_Ounit_Orec,axiom,
% 0.32/0.47 ! [T: $tType,F1: T] :
% 0.32/0.47 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 0.32/0.47 = F1 ) ).
% 0.32/0.47
% 0.32/0.47 % old.unit.rec
% 0.32/0.47 thf(fact_136_default__unit__def,axiom,
% 0.32/0.47 ( ( default_default @ product_unit )
% 0.32/0.47 = product_Unity ) ).
% 0.32/0.47
% 0.32/0.47 % default_unit_def
% 0.32/0.47 thf(fact_137_tfilter_H__def,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType] :
% 0.32/0.47 ( ( tLList1122525870filter @ B @ A )
% 0.32/0.47 = ( ^ [B6: product_unit > B] : ( tLList1813626245filter @ B @ A @ ( B6 @ product_Unity ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfilter'_def
% 0.32/0.47 thf(fact_138_tfilter__code,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList1813626245filter @ A @ B )
% 0.32/0.47 = ( ^ [B6: A] :
% 0.32/0.47 ( tLList1122525870filter @ A @ B
% 0.32/0.47 @ ^ [Uu: product_unit] : B6 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfilter_code
% 0.32/0.47 thf(fact_139_tfilter_H__code_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,B5: product_unit > B,P: A > $o,B4: B] :
% 0.32/0.47 ( ( tLList1122525870filter @ B @ A @ B5 @ P @ ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ B4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfilter'_code(1)
% 0.32/0.47 thf(fact_140_tfilter_H__code_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,P: A > $o,A2: A,B5: product_unit > B,Tr: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( ( P @ A2 )
% 0.32/0.47 => ( ( tLList1122525870filter @ B @ A @ B5 @ P @ ( tLList1992840728_TCons @ A @ B @ A2 @ Tr ) )
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ A2 @ ( tLList1122525870filter @ B @ A @ B5 @ P @ Tr ) ) ) )
% 0.32/0.47 & ( ~ ( P @ A2 )
% 0.32/0.47 => ( ( tLList1122525870filter @ B @ A @ B5 @ P @ ( tLList1992840728_TCons @ A @ B @ A2 @ Tr ) )
% 0.32/0.47 = ( tLList1122525870filter @ B @ A @ B5 @ P @ Tr ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfilter'_code(2)
% 0.32/0.47 thf(fact_141_tllist_Opred__set,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList11265572tllist @ A @ B )
% 0.32/0.47 = ( ^ [P12: A > $o,P22: B > $o,X2: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ! [Y2: A] :
% 0.32/0.47 ( ( member @ A @ Y2 @ ( tLList1719791291e_tset @ A @ B @ X2 ) )
% 0.32/0.47 => ( P12 @ Y2 ) )
% 0.32/0.47 & ! [Y2: B] :
% 0.32/0.47 ( ( member @ B @ Y2 @ ( tLList457864275tllist @ A @ B @ X2 ) )
% 0.32/0.47 => ( P22 @ Y2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.pred_set
% 0.32/0.47 thf(fact_142_old_Ounit_Ocase,axiom,
% 0.32/0.47 ! [A: $tType,F3: A] :
% 0.32/0.47 ( ( product_case_unit @ A @ F3 @ product_Unity )
% 0.32/0.47 = F3 ) ).
% 0.32/0.47
% 0.32/0.47 % old.unit.case
% 0.32/0.47 thf(fact_143_lappendt__LCons,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X: A,Xs: coinductive_llist @ A,Tr: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList98099029ppendt @ A @ B @ ( coinductive_LCons @ A @ X @ Xs ) @ Tr )
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ X @ ( tLList98099029ppendt @ A @ B @ Xs @ Tr ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lappendt_LCons
% 0.32/0.47 thf(fact_144_terminal__lappendt__lfinite,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Ys: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( coinductive_lfinite @ A @ Xs )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ ( tLList98099029ppendt @ A @ B @ Xs @ Ys ) )
% 0.32/0.47 = ( tLList2110128105rminal @ A @ B @ Ys ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_lappendt_lfinite
% 0.32/0.47 thf(fact_145_unit_Ocase__distrib,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,H: A > B,F3: A,Unit: product_unit] :
% 0.32/0.47 ( ( H @ ( product_case_unit @ A @ F3 @ Unit ) )
% 0.32/0.47 = ( product_case_unit @ B @ ( H @ F3 ) @ Unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % unit.case_distrib
% 0.32/0.47 thf(fact_146_case__unit__Unity,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( product_case_unit @ A )
% 0.32/0.47 = ( ^ [F4: A,U: product_unit] : F4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % case_unit_Unity
% 0.32/0.47 thf(fact_147_tfilter__empty__conv,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,Y: B,P: A > $o,Xs: tLList446370796tllist @ A @ B,Y6: B] :
% 0.32/0.47 ( ( ( tLList1813626245filter @ B @ A @ Y @ P @ Xs )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ Y6 ) )
% 0.32/0.47 = ( ! [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ ( tLList1719791291e_tset @ A @ B @ Xs ) )
% 0.32/0.47 => ~ ( P @ X2 ) )
% 0.32/0.47 & ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ Xs )
% 0.32/0.47 = Y6 ) )
% 0.32/0.47 & ( ~ ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 => ( Y = Y6 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfilter_empty_conv
% 0.32/0.47 thf(fact_148_terminal__tmap,axiom,
% 0.32/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B,F3: A > D,G: B > C] :
% 0.32/0.47 ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 => ( ( tLList2110128105rminal @ D @ C @ ( tLList1669959861e_tmap @ A @ D @ B @ C @ F3 @ G @ Xs ) )
% 0.32/0.47 = ( G @ ( tLList2110128105rminal @ A @ B @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_tmap
% 0.32/0.47 thf(fact_149_tfilter__eq__TConsD,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,A2: B,P: A > $o,Ys: tLList446370796tllist @ A @ B,X: A,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( ( tLList1813626245filter @ B @ A @ A2 @ P @ Ys )
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ X @ Xs ) )
% 0.32/0.47 => ? [Us: coinductive_llist @ A,Vs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( Ys
% 0.32/0.47 = ( tLList98099029ppendt @ A @ B @ Us @ ( tLList1992840728_TCons @ A @ B @ X @ Vs ) ) )
% 0.32/0.47 & ( coinductive_lfinite @ A @ Us )
% 0.32/0.47 & ! [X6: A] :
% 0.32/0.47 ( ( member @ A @ X6 @ ( coinductive_lset @ A @ Us ) )
% 0.32/0.47 => ~ ( P @ X6 ) )
% 0.32/0.47 & ( P @ X )
% 0.32/0.47 & ( Xs
% 0.32/0.47 = ( tLList1813626245filter @ B @ A @ A2 @ P @ Vs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfilter_eq_TConsD
% 0.32/0.47 thf(fact_150_llist__of__tllist__TCons,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xa: A,X: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList798109904tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ Xa @ X ) )
% 0.32/0.47 = ( coinductive_LCons @ A @ Xa @ ( tLList798109904tllist @ A @ B @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist_TCons
% 0.32/0.47 thf(fact_151_lset__llist__of__tllist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( coinductive_lset @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 = ( tLList1719791291e_tset @ A @ B @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % lset_llist_of_tllist
% 0.32/0.47 thf(fact_152_is__TNil__tfinite,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % is_TNil_tfinite
% 0.32/0.47 thf(fact_153_tfinite__induct,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B,P: ( tLList446370796tllist @ A @ B ) > $o] :
% 0.32/0.47 ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 => ( ! [Y5: B] : ( P @ ( tLList57907754e_TNil @ B @ A @ Y5 ) )
% 0.32/0.47 => ( ! [X3: A,Xs3: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs3 ) )
% 0.32/0.47 => ( ( P @ Xs3 )
% 0.32/0.47 => ( P @ ( tLList1992840728_TCons @ A @ B @ X3 @ Xs3 ) ) ) )
% 0.32/0.47 => ( P @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfinite_induct
% 0.32/0.47 thf(fact_154_tset__lappendt__lfinite,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Ys: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( coinductive_lfinite @ A @ Xs )
% 0.32/0.47 => ( ( tLList1719791291e_tset @ A @ B @ ( tLList98099029ppendt @ A @ B @ Xs @ Ys ) )
% 0.32/0.47 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( tLList1719791291e_tset @ A @ B @ Ys ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tset_lappendt_lfinite
% 0.32/0.47 thf(fact_155_tfinite__tappend,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,A: $tType,Xs: tLList446370796tllist @ A @ C,F3: C > ( tLList446370796tllist @ A @ B )] :
% 0.32/0.47 ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ ( tLList192138471append @ A @ C @ B @ Xs @ F3 ) ) )
% 0.32/0.47 = ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ C @ Xs ) )
% 0.32/0.47 & ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ ( F3 @ ( tLList2110128105rminal @ A @ C @ Xs ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tfinite_tappend
% 0.32/0.47 thf(fact_156_terminal__tappend,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,Xs: tLList446370796tllist @ B @ A,F3: A > ( tLList446370796tllist @ B @ A )] :
% 0.32/0.47 ( ( ( coinductive_lfinite @ B @ ( tLList798109904tllist @ B @ A @ Xs ) )
% 0.32/0.47 => ( ( tLList2110128105rminal @ B @ A @ ( tLList192138471append @ B @ A @ A @ Xs @ F3 ) )
% 0.32/0.47 = ( tLList2110128105rminal @ B @ A @ ( F3 @ ( tLList2110128105rminal @ B @ A @ Xs ) ) ) ) )
% 0.32/0.47 & ( ~ ( coinductive_lfinite @ B @ ( tLList798109904tllist @ B @ A @ Xs ) )
% 0.32/0.47 => ( ( tLList2110128105rminal @ B @ A @ ( tLList192138471append @ B @ A @ A @ Xs @ F3 ) )
% 0.32/0.47 = ( tLList2110128105rminal @ B @ A @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_tappend
% 0.32/0.47 thf(fact_157_tappend__TNil2,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList192138471append @ A @ B @ B @ Xs @ ( tLList57907754e_TNil @ B @ A ) )
% 0.32/0.47 = Xs ) ).
% 0.32/0.47
% 0.32/0.47 % tappend_TNil2
% 0.32/0.47 thf(fact_158_tappend__TNil,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,C: $tType,B4: C,F3: C > ( tLList446370796tllist @ A @ B )] :
% 0.32/0.47 ( ( tLList192138471append @ A @ C @ B @ ( tLList57907754e_TNil @ C @ A @ B4 ) @ F3 )
% 0.32/0.47 = ( F3 @ B4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tappend_TNil
% 0.32/0.47 thf(fact_159_tappend__TCons,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,C: $tType,A2: A,Tr: tLList446370796tllist @ A @ C,F3: C > ( tLList446370796tllist @ A @ B )] :
% 0.32/0.47 ( ( tLList192138471append @ A @ C @ B @ ( tLList1992840728_TCons @ A @ C @ A2 @ Tr ) @ F3 )
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ A2 @ ( tLList192138471append @ A @ C @ B @ Tr @ F3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tappend_TCons
% 0.32/0.47 thf(fact_160_tappend__assoc,axiom,
% 0.32/0.47 ! [C: $tType,A: $tType,B: $tType,D: $tType,Xs: tLList446370796tllist @ A @ D,F3: D > ( tLList446370796tllist @ A @ C ),G: C > ( tLList446370796tllist @ A @ B )] :
% 0.32/0.47 ( ( tLList192138471append @ A @ C @ B @ ( tLList192138471append @ A @ D @ C @ Xs @ F3 ) @ G )
% 0.32/0.47 = ( tLList192138471append @ A @ D @ B @ Xs
% 0.32/0.47 @ ^ [B6: D] : ( tLList192138471append @ A @ C @ B @ ( F3 @ B6 ) @ G ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tappend_assoc
% 0.32/0.47 thf(fact_161_tappend__inf,axiom,
% 0.32/0.47 ! [C: $tType,B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B,F3: B > ( tLList446370796tllist @ A @ C )] :
% 0.32/0.47 ( ~ ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 => ( ( tLList192138471append @ A @ B @ C @ Xs @ F3 )
% 0.32/0.47 = ( tLList222516140_tcast @ A @ B @ C @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tappend_inf
% 0.32/0.47 thf(fact_162_Collect__disj__eq,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.47 ( ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 | ( Q @ X2 ) ) )
% 0.32/0.47 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_disj_eq
% 0.32/0.47 thf(fact_163_Un__def,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.32/0.47 = ( ^ [A5: set @ A,B8: set @ A] :
% 0.32/0.47 ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ A5 )
% 0.32/0.47 | ( member @ A @ X2 @ B8 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Un_def
% 0.32/0.47 thf(fact_164_lhd__llist__of__tllist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ( ( coinductive_lhd @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 = ( tLList_Mirabelle_thd @ A @ B @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lhd_llist_of_tllist
% 0.32/0.47 thf(fact_165_terminal__tinfinite,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ Xs )
% 0.32/0.47 = ( undefined @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_tinfinite
% 0.32/0.47 thf(fact_166_llist__of__tllist__inverse,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1672613558_llist @ B @ A @ ( tLList2110128105rminal @ A @ B @ B4 ) @ ( tLList798109904tllist @ A @ B @ B4 ) )
% 0.32/0.47 = B4 ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist_inverse
% 0.32/0.47 thf(fact_167_tllist__of__llist__inject,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,B4: B,Xs: coinductive_llist @ A,C2: B,Ys: coinductive_llist @ A] :
% 0.32/0.47 ( ( ( tLList1672613558_llist @ B @ A @ B4 @ Xs )
% 0.32/0.47 = ( tLList1672613558_llist @ B @ A @ C2 @ Ys ) )
% 0.32/0.47 = ( ( Xs = Ys )
% 0.32/0.47 & ( ( coinductive_lfinite @ A @ Ys )
% 0.32/0.47 => ( B4 = C2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist_inject
% 0.32/0.47 thf(fact_168_tllist__of__llist__inverse,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( tLList798109904tllist @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = Xs ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist_inverse
% 0.32/0.47 thf(fact_169_tllist__of__llist__LCons,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,Xa: A,X: coinductive_llist @ A] :
% 0.32/0.47 ( ( tLList1672613558_llist @ B @ A @ B4 @ ( coinductive_LCons @ A @ Xa @ X ) )
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B @ Xa @ ( tLList1672613558_llist @ B @ A @ B4 @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist_LCons
% 0.32/0.47 thf(fact_170_terminal__tllist__of__llist__lfinite,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ( coinductive_lfinite @ A @ Xs )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = B4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_tllist_of_llist_lfinite
% 0.32/0.47 thf(fact_171_tset__tllist__of__llist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( tLList1719791291e_tset @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = ( coinductive_lset @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % tset_tllist_of_llist
% 0.32/0.47 thf(fact_172_thd__tllist__of__llist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = ( coinductive_lhd @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % thd_tllist_of_llist
% 0.32/0.47 thf(fact_173_terminal__tllist__of__llist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ B,Y: A] :
% 0.32/0.47 ( ( ( coinductive_lfinite @ B @ Xs )
% 0.32/0.47 => ( ( tLList2110128105rminal @ B @ A @ ( tLList1672613558_llist @ A @ B @ Y @ Xs ) )
% 0.32/0.47 = Y ) )
% 0.32/0.47 & ( ~ ( coinductive_lfinite @ B @ Xs )
% 0.32/0.47 => ( ( tLList2110128105rminal @ B @ A @ ( tLList1672613558_llist @ A @ B @ Y @ Xs ) )
% 0.32/0.47 = ( undefined @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_tllist_of_llist
% 0.32/0.47 thf(fact_174_tllist__of__llist__cong,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Xs4: coinductive_llist @ A,B4: B,B5: B] :
% 0.32/0.47 ( ( Xs = Xs4 )
% 0.32/0.47 => ( ( ( coinductive_lfinite @ A @ Xs4 )
% 0.32/0.47 => ( B4 = B5 ) )
% 0.32/0.47 => ( ( tLList1672613558_llist @ B @ A @ B4 @ Xs )
% 0.32/0.47 = ( tLList1672613558_llist @ B @ A @ B5 @ Xs4 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist_cong
% 0.32/0.47 thf(fact_175_llist__of__tllist_Osimps_I3_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ( ( coinductive_lhd @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 = ( tLList200813139tllist @ B @ A @ A
% 0.32/0.47 @ ^ [X2: B] : ( undefined @ A )
% 0.32/0.47 @ ^ [X2: A,Xs5: tLList446370796tllist @ A @ B] : X2
% 0.32/0.47 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.simps(3)
% 0.32/0.47 thf(fact_176_llist__of__tllist_Octr_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ( ( tLList798109904tllist @ A @ B @ Xs )
% 0.32/0.47 = ( coinductive_LCons @ A
% 0.32/0.47 @ ( tLList200813139tllist @ B @ A @ A
% 0.32/0.47 @ ^ [X2: B] : ( undefined @ A )
% 0.32/0.47 @ ^ [X2: A,Xs5: tLList446370796tllist @ A @ B] : X2
% 0.32/0.47 @ Xs )
% 0.32/0.47 @ ( tLList200813139tllist @ B @ ( coinductive_llist @ A ) @ A
% 0.32/0.47 @ ^ [X2: B] : ( undefined @ ( coinductive_llist @ A ) )
% 0.32/0.47 @ ^ [X2: A] : ( tLList798109904tllist @ A @ B )
% 0.32/0.47 @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.ctr(2)
% 0.32/0.47 thf(fact_177_thd__TNil,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B] :
% 0.32/0.47 ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 0.32/0.47 = ( undefined @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % thd_TNil
% 0.32/0.47 thf(fact_178_thd__def,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList_Mirabelle_thd @ A @ B )
% 0.32/0.47 = ( tLList200813139tllist @ B @ A @ A
% 0.32/0.47 @ ^ [X_dummy: B] : ( undefined @ A )
% 0.32/0.47 @ ^ [X213: A,X223: tLList446370796tllist @ A @ B] : X213 ) ) ).
% 0.32/0.47
% 0.32/0.47 % thd_def
% 0.32/0.47 thf(fact_179_terminal0_Oraw__induct,axiom,
% 0.32/0.47 ! [C: $tType,D: $tType,P: ( tLList446370796tllist @ C @ D ) > D > $o,Xs: tLList446370796tllist @ C @ D,Y: D] :
% 0.32/0.47 ( ! [Terminal0: ( tLList446370796tllist @ C @ D ) > D] :
% 0.32/0.47 ( ! [X6: tLList446370796tllist @ C @ D] :
% 0.32/0.47 ( ( ( Terminal0 @ X6 )
% 0.32/0.47 != ( undefined @ D ) )
% 0.32/0.47 => ( P @ X6 @ ( Terminal0 @ X6 ) ) )
% 0.32/0.47 => ! [Xs3: tLList446370796tllist @ C @ D,Xsa: D] :
% 0.32/0.47 ( ( ( ( tLList1968894004s_TNil @ C @ D @ Xs3 )
% 0.32/0.47 => ( ( tLList200813139tllist @ D @ D @ C @ ( id @ D ) @ ( undefined @ ( C > ( tLList446370796tllist @ C @ D ) > D ) ) @ Xs3 )
% 0.32/0.47 = Xsa ) )
% 0.32/0.47 & ( ~ ( tLList1968894004s_TNil @ C @ D @ Xs3 )
% 0.32/0.47 => ( ( Terminal0 @ ( tLList_Mirabelle_ttl @ C @ D @ Xs3 ) )
% 0.32/0.47 = Xsa ) ) )
% 0.32/0.47 => ( ( Xsa
% 0.32/0.47 != ( undefined @ D ) )
% 0.32/0.47 => ( P @ Xs3 @ Xsa ) ) ) )
% 0.32/0.47 => ( ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) @ Xs )
% 0.32/0.47 = Y )
% 0.32/0.47 => ( ( Y
% 0.32/0.47 != ( undefined @ D ) )
% 0.32/0.47 => ( P @ Xs @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal0.raw_induct
% 0.32/0.47 thf(fact_180_terminal0_Osimps,axiom,
% 0.32/0.47 ! [D: $tType,C: $tType] :
% 0.32/0.47 ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) )
% 0.32/0.47 = ( ^ [Xs6: tLList446370796tllist @ C @ D] : ( if @ D @ ( tLList1968894004s_TNil @ C @ D @ Xs6 ) @ ( tLList200813139tllist @ D @ D @ C @ ( id @ D ) @ ( undefined @ ( C > ( tLList446370796tllist @ C @ D ) > D ) ) @ Xs6 ) @ ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) @ ( tLList_Mirabelle_ttl @ C @ D @ Xs6 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal0.simps
% 0.32/0.47 thf(fact_181_tllist__of__llist_Ocode,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType] :
% 0.32/0.47 ( ( tLList1672613558_llist @ B @ A )
% 0.32/0.47 = ( ^ [B6: B] :
% 0.32/0.47 ( coindu1381640503_llist @ ( tLList446370796tllist @ A @ B ) @ A @ ( tLList57907754e_TNil @ B @ A @ B6 )
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( tLList1992840728_TCons @ A @ B @ X2 @ ( tLList1672613558_llist @ B @ A @ B6 @ Xs5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.code
% 0.32/0.47 thf(fact_182_tllist_Omap__id,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,T2: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1669959861e_tmap @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) @ T2 )
% 0.32/0.47 = T2 ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.map_id
% 0.32/0.47 thf(fact_183_tllist_Omap__id0,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList1669959861e_tmap @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 0.32/0.47 = ( id @ ( tLList446370796tllist @ A @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.map_id0
% 0.32/0.47 thf(fact_184_lhd__def,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coinductive_lhd @ A )
% 0.32/0.47 = ( coindu1381640503_llist @ A @ A @ ( undefined @ A )
% 0.32/0.47 @ ^ [X213: A,X223: coinductive_llist @ A] : X213 ) ) ).
% 0.32/0.47
% 0.32/0.47 % lhd_def
% 0.32/0.47 thf(fact_185_tllist__of__llist_Octr_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 => ( ( tLList1672613558_llist @ B @ A @ B4 @ Xs )
% 0.32/0.47 = ( tLList1992840728_TCons @ A @ B
% 0.32/0.47 @ ( coindu1381640503_llist @ A @ A @ ( undefined @ A )
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : X2
% 0.32/0.47 @ Xs )
% 0.32/0.47 @ ( coindu1381640503_llist @ ( tLList446370796tllist @ A @ B ) @ A @ ( undefined @ ( tLList446370796tllist @ A @ B ) )
% 0.32/0.47 @ ^ [X2: A] : ( tLList1672613558_llist @ B @ A @ B4 )
% 0.32/0.47 @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.ctr(2)
% 0.32/0.47 thf(fact_186_llist__of__tllist_Osimps_I4_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ( ( coinductive_ltl @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 = ( tLList200813139tllist @ B @ ( coinductive_llist @ A ) @ A
% 0.32/0.47 @ ^ [X2: B] : ( undefined @ ( coinductive_llist @ A ) )
% 0.32/0.47 @ ^ [X2: A] : ( tLList798109904tllist @ A @ B )
% 0.32/0.47 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.simps(4)
% 0.32/0.47 thf(fact_187_tllist__of__llist_Odisc__iff_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) ) )
% 0.32/0.47 = ( ~ ( coinductive_lnull @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.disc_iff(2)
% 0.32/0.47 thf(fact_188_tllist__of__llist_Odisc__iff_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = ( coinductive_lnull @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.disc_iff(1)
% 0.32/0.47 thf(fact_189_llist__of__tllist_Odisc__iff_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( ~ ( coinductive_lnull @ A @ ( tLList798109904tllist @ A @ B @ Xs ) ) )
% 0.32/0.47 = ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.disc_iff(2)
% 0.32/0.47 thf(fact_190_llist__of__tllist_Odisc__iff_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( coinductive_lnull @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 = ( tLList1968894004s_TNil @ A @ B @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.disc_iff(1)
% 0.32/0.47 thf(fact_191_terminal__tllist__of__llist__lnull,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = B4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % terminal_tllist_of_llist_lnull
% 0.32/0.47 thf(fact_192_ttl__tllist__of__llist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = ( tLList1672613558_llist @ B @ A @ B4 @ ( coinductive_ltl @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ttl_tllist_of_llist
% 0.32/0.47 thf(fact_193_ltl__llist__of__tllist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( coinductive_ltl @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 0.32/0.47 = ( tLList798109904tllist @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ltl_llist_of_tllist
% 0.32/0.47 thf(fact_194_llist_Odisc__eq__case_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.32/0.47 ( ( ~ ( coinductive_lnull @ A @ Llist ) )
% 0.32/0.47 = ( coindu1381640503_llist @ $o @ A @ $false
% 0.32/0.47 @ ^ [Uu: A,Uv: coinductive_llist @ A] : $true
% 0.32/0.47 @ Llist ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist.disc_eq_case(2)
% 0.32/0.47 thf(fact_195_llist_Odisc__eq__case_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coinductive_lnull @ A )
% 0.32/0.47 = ( coindu1381640503_llist @ $o @ A @ $true
% 0.32/0.47 @ ^ [Uu: A,Uv: coinductive_llist @ A] : $false ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist.disc_eq_case(1)
% 0.32/0.47 thf(fact_196_tllist__of__llist_Odisc_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 => ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.disc(2)
% 0.32/0.47 thf(fact_197_tllist__of__llist_Odisc_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 => ( tLList1968894004s_TNil @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.disc(1)
% 0.32/0.47 thf(fact_198_llist__of__tllist_Odisc_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ~ ( coinductive_lnull @ A @ ( tLList798109904tllist @ A @ B @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.disc(2)
% 0.32/0.47 thf(fact_199_llist__of__tllist_Odisc_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ( coinductive_lnull @ A @ ( tLList798109904tllist @ A @ B @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.disc(1)
% 0.32/0.47 thf(fact_200_tllist__of__llist_Osimps_I5_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = ( coindu1381640503_llist @ ( tLList446370796tllist @ A @ B ) @ A @ ( undefined @ ( tLList446370796tllist @ A @ B ) )
% 0.32/0.47 @ ^ [X2: A] : ( tLList1672613558_llist @ B @ A @ B4 )
% 0.32/0.47 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.simps(5)
% 0.32/0.47 thf(fact_201_tllist__of__llist_Octr_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 => ( ( tLList1672613558_llist @ B @ A @ B4 @ Xs )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A
% 0.32/0.47 @ ( coindu1381640503_llist @ B @ A @ B4
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( undefined @ B )
% 0.32/0.47 @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.ctr(1)
% 0.32/0.47 thf(fact_202_tllist__of__llist_Osimps_I3_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 => ( ( tLList2110128105rminal @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = ( coindu1381640503_llist @ B @ A @ B4
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( undefined @ B )
% 0.32/0.47 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.simps(3)
% 0.32/0.47 thf(fact_203_tllist__of__llist_Osimps_I4_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 => ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 0.32/0.47 = ( coindu1381640503_llist @ A @ A @ ( undefined @ A )
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : X2
% 0.32/0.47 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist.simps(4)
% 0.32/0.47 thf(fact_204_llist_Ocase__distrib,axiom,
% 0.32/0.47 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: B,F2: A > ( coinductive_llist @ A ) > B,Llist: coinductive_llist @ A] :
% 0.32/0.47 ( ( H @ ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 0.32/0.47 = ( coindu1381640503_llist @ C @ A @ ( H @ F1 )
% 0.32/0.47 @ ^ [X13: A,X24: coinductive_llist @ A] : ( H @ ( F2 @ X13 @ X24 ) )
% 0.32/0.47 @ Llist ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist.case_distrib
% 0.32/0.47 thf(fact_205_lappend_Octr_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.32/0.47 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 | ~ ( coinductive_lnull @ A @ Ys ) )
% 0.32/0.47 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.32/0.47 = ( coinductive_LCons @ A
% 0.32/0.47 @ ( coindu1381640503_llist @ A @ A @ ( coinductive_lhd @ A @ Ys )
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : X2
% 0.32/0.47 @ Xs )
% 0.32/0.47 @ ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A
% 0.32/0.47 @ ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ ( undefined @ ( coinductive_llist @ A ) )
% 0.32/0.47 @ ^ [Uu2: A,Uv2: coinductive_llist @ A] : Uv2
% 0.32/0.47 @ Ys )
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( coinductive_lappend @ A @ Xs5 @ Ys )
% 0.32/0.47 @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lappend.ctr(2)
% 0.32/0.47 thf(fact_206_llist__of__tllist_Ocode,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( tLList798109904tllist @ A @ B )
% 0.32/0.47 = ( tLList200813139tllist @ B @ ( coinductive_llist @ A ) @ A
% 0.32/0.47 @ ^ [X2: B] : ( coinductive_LNil @ A )
% 0.32/0.47 @ ^ [X2: A,Xs5: tLList446370796tllist @ A @ B] : ( coinductive_LCons @ A @ X2 @ ( tLList798109904tllist @ A @ B @ Xs5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.code
% 0.32/0.47 thf(fact_207_lappendt__LNil,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Tr: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList98099029ppendt @ A @ B @ ( coinductive_LNil @ A ) @ Tr )
% 0.32/0.47 = Tr ) ).
% 0.32/0.47
% 0.32/0.47 % lappendt_LNil
% 0.32/0.47 thf(fact_208_TNil__eq__tllist__of__llist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B4: B,B5: B,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( ( tLList57907754e_TNil @ B @ A @ B4 )
% 0.32/0.47 = ( tLList1672613558_llist @ B @ A @ B5 @ Xs ) )
% 0.32/0.47 = ( ( B4 = B5 )
% 0.32/0.47 & ( Xs
% 0.32/0.47 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % TNil_eq_tllist_of_llist
% 0.32/0.47 thf(fact_209_tllist__of__llist__LNil,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,B4: B] :
% 0.32/0.47 ( ( tLList1672613558_llist @ B @ A @ B4 @ ( coinductive_LNil @ A ) )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ B4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist_LNil
% 0.32/0.47 thf(fact_210_tllist__of__llist__eq,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,B5: B,Xs: coinductive_llist @ A,B4: B] :
% 0.32/0.47 ( ( ( tLList1672613558_llist @ B @ A @ B5 @ Xs )
% 0.32/0.47 = ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 0.32/0.47 = ( ( B4 = B5 )
% 0.32/0.47 & ( Xs
% 0.32/0.47 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist_eq
% 0.32/0.47 thf(fact_211_llist__of__tllist__TNil,axiom,
% 0.32/0.47 ! [A: $tType,Aa: $tType,X: A] :
% 0.32/0.47 ( ( tLList798109904tllist @ Aa @ A @ ( tLList57907754e_TNil @ A @ Aa @ X ) )
% 0.32/0.47 = ( coinductive_LNil @ Aa ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist_TNil
% 0.32/0.47 thf(fact_212_lappend_Ocode,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coinductive_lappend @ A )
% 0.32/0.47 = ( ^ [Xs6: coinductive_llist @ A,Ys4: coinductive_llist @ A] :
% 0.32/0.47 ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ Ys4
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( coinductive_LCons @ A @ X2 @ ( coinductive_lappend @ A @ Xs5 @ Ys4 ) )
% 0.32/0.47 @ Xs6 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lappend.code
% 0.32/0.47 thf(fact_213_ltl__def,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coinductive_ltl @ A )
% 0.32/0.47 = ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ ( coinductive_LNil @ A )
% 0.32/0.47 @ ^ [X213: A,X223: coinductive_llist @ A] : X223 ) ) ).
% 0.32/0.47
% 0.32/0.47 % ltl_def
% 0.32/0.47 thf(fact_214_lhd__LNil,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coinductive_lhd @ A @ ( coinductive_LNil @ A ) )
% 0.32/0.47 = ( undefined @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % lhd_LNil
% 0.32/0.47 thf(fact_215_llist__of__tllist__eq__LNil,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( ( tLList798109904tllist @ A @ B @ Xs )
% 0.32/0.47 = ( coinductive_LNil @ A ) )
% 0.32/0.47 = ( tLList1968894004s_TNil @ A @ B @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist_eq_LNil
% 0.32/0.47 thf(fact_216_llist__of__tllist_Octr_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 0.32/0.47 => ( ( tLList798109904tllist @ A @ B @ Xs )
% 0.32/0.47 = ( coinductive_LNil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_tllist.ctr(1)
% 0.32/0.47 thf(fact_217_tllist__of__llist__eq__lappendt__conv,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,A2: B,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( ( tLList1672613558_llist @ B @ A @ A2 @ Xs )
% 0.32/0.47 = ( tLList98099029ppendt @ A @ B @ Ys @ Zs2 ) )
% 0.32/0.47 = ( ? [Xs5: coinductive_llist @ A,A6: B] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 = ( coinductive_lappend @ A @ Ys @ Xs5 ) )
% 0.32/0.47 & ( Zs2
% 0.32/0.47 = ( tLList1672613558_llist @ B @ A @ A6 @ Xs5 ) )
% 0.32/0.47 & ( ( coinductive_lfinite @ A @ Ys )
% 0.32/0.47 => ( A2 = A6 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist_of_llist_eq_lappendt_conv
% 0.32/0.47 thf(fact_218_lappend_Osimps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.32/0.47 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 | ~ ( coinductive_lnull @ A @ Ys ) )
% 0.32/0.47 => ( ( coinductive_lhd @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.32/0.47 = ( coindu1381640503_llist @ A @ A @ ( coinductive_lhd @ A @ Ys )
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : X2
% 0.32/0.47 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lappend.simps(3)
% 0.32/0.47 thf(fact_219_lappend_Osimps_I4_J,axiom,
% 0.32/0.47 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.32/0.47 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.32/0.47 | ~ ( coinductive_lnull @ A @ Ys ) )
% 0.32/0.47 => ( ( coinductive_ltl @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.32/0.47 = ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A
% 0.32/0.47 @ ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ ( undefined @ ( coinductive_llist @ A ) )
% 0.32/0.47 @ ^ [Uu2: A,Uv2: coinductive_llist @ A] : Uv2
% 0.32/0.47 @ Ys )
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( coinductive_lappend @ A @ Xs5 @ Ys )
% 0.32/0.47 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lappend.simps(4)
% 0.32/0.47 thf(fact_220_lfilter_Osimps,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coinductive_lfilter @ A )
% 0.32/0.47 = ( ^ [P5: A > $o] :
% 0.32/0.47 ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ ( coinductive_LNil @ A )
% 0.32/0.47 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( if @ ( coinductive_llist @ A ) @ ( P5 @ X2 ) @ ( coinductive_LCons @ A @ X2 @ ( coinductive_lfilter @ A @ P5 @ Xs5 ) ) @ ( coinductive_lfilter @ A @ P5 @ Xs5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lfilter.simps
% 0.32/0.47 thf(fact_221_tllist_Osimps_I21_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 0.32/0.47 ( ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 0.32/0.47 = ( insert @ A @ X21 @ ( tLList1719791291e_tset @ A @ B @ X22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.simps(21)
% 0.32/0.47 thf(fact_222_lfilter__K__True,axiom,
% 0.32/0.47 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( coinductive_lfilter @ A
% 0.32/0.47 @ ^ [Uu: A] : $true
% 0.32/0.47 @ Xs )
% 0.32/0.47 = Xs ) ).
% 0.32/0.47
% 0.32/0.47 % lfilter_K_True
% 0.32/0.47 thf(fact_223_lfitler__K__False,axiom,
% 0.32/0.47 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( coinductive_lfilter @ A
% 0.32/0.47 @ ^ [Uu: A] : $false
% 0.32/0.47 @ Xs )
% 0.32/0.47 = ( coinductive_LNil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % lfitler_K_False
% 0.32/0.47 thf(fact_224_lset__lfilter,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( coinductive_lset @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 0.32/0.47 = ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs ) )
% 0.32/0.47 & ( P @ X2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lset_lfilter
% 0.32/0.47 thf(fact_225_insert__def,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( insert @ A )
% 0.32/0.47 = ( ^ [A4: A] :
% 0.32/0.47 ( sup_sup @ ( set @ A )
% 0.32/0.47 @ ( collect @ A
% 0.32/0.47 @ ^ [X2: A] : ( X2 = A4 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % insert_def
% 0.32/0.47 thf(fact_226_insert__compr,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( insert @ A )
% 0.32/0.47 = ( ^ [A4: A,B8: set @ A] :
% 0.32/0.47 ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( X2 = A4 )
% 0.32/0.47 | ( member @ A @ X2 @ B8 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % insert_compr
% 0.32/0.47 thf(fact_227_insert__Collect,axiom,
% 0.32/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.32/0.47 ( ( insert @ A @ A2 @ ( collect @ A @ P ) )
% 0.32/0.47 = ( collect @ A
% 0.32/0.47 @ ^ [U: A] :
% 0.32/0.47 ( ( U != A2 )
% 0.32/0.47 => ( P @ U ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % insert_Collect
% 0.32/0.47 thf(fact_228_lfilter__lfilter,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,Q: A > $o,Xs: coinductive_llist @ A] :
% 0.32/0.47 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ Q @ Xs ) )
% 0.32/0.47 = ( coinductive_lfilter @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) )
% 0.32/0.47 @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % lfilter_lfilter
% 0.32/0.47 thf(fact_229_set2__tllist__tllist__of__llist,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: coinductive_llist @ B,B4: A] :
% 0.32/0.47 ( ( ( coinductive_lfinite @ B @ Xs )
% 0.32/0.47 => ( ( tLList457864275tllist @ B @ A @ ( tLList1672613558_llist @ A @ B @ B4 @ Xs ) )
% 0.32/0.47 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/0.47 & ( ~ ( coinductive_lfinite @ B @ Xs )
% 0.32/0.47 => ( ( tLList457864275tllist @ B @ A @ ( tLList1672613558_llist @ A @ B @ B4 @ Xs ) )
% 0.32/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % set2_tllist_tllist_of_llist
% 0.32/0.47 thf(fact_230_lfilter__repeat,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,X: A] :
% 0.32/0.47 ( ( ( P @ X )
% 0.32/0.47 => ( ( coinductive_lfilter @ A @ P
% 0.32/0.47 @ ( coinductive_iterates @ A
% 0.32/0.47 @ ^ [X2: A] : X2
% 0.32/0.47 @ X ) )
% 0.32/0.47 = ( coinductive_iterates @ A
% 0.32/0.47 @ ^ [X2: A] : X2
% 0.32/0.47 @ X ) ) )
% 0.32/0.47 & ( ~ ( P @ X )
% 0.32/0.47 => ( ( coinductive_lfilter @ A @ P
% 0.32/0.47 @ ( coinductive_iterates @ A
% 0.32/0.47 @ ^ [X2: A] : X2
% 0.32/0.47 @ X ) )
% 0.32/0.47 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lfilter_repeat
% 0.32/0.47 thf(fact_231_singleton__conv,axiom,
% 0.32/0.47 ! [A: $tType,A2: A] :
% 0.32/0.47 ( ( collect @ A
% 0.32/0.47 @ ^ [X2: A] : ( X2 = A2 ) )
% 0.32/0.47 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % singleton_conv
% 0.32/0.47 thf(fact_232_singleton__conv2,axiom,
% 0.32/0.47 ! [A: $tType,A2: A] :
% 0.32/0.47 ( ( collect @ A
% 0.32/0.47 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.32/0.47 @ A2 ) )
% 0.32/0.47 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % singleton_conv2
% 0.32/0.47 thf(fact_233_lset__repeat,axiom,
% 0.32/0.47 ! [A: $tType,X: A] :
% 0.32/0.47 ( ( coinductive_lset @ A
% 0.32/0.47 @ ( coinductive_iterates @ A
% 0.32/0.47 @ ^ [X2: A] : X2
% 0.32/0.47 @ X ) )
% 0.32/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lset_repeat
% 0.32/0.47 thf(fact_234_Collect__conv__if,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,A2: A] :
% 0.32/0.47 ( ( ( P @ A2 )
% 0.32/0.47 => ( ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( X2 = A2 )
% 0.32/0.47 & ( P @ X2 ) ) )
% 0.32/0.47 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/0.47 & ( ~ ( P @ A2 )
% 0.32/0.47 => ( ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( X2 = A2 )
% 0.32/0.47 & ( P @ X2 ) ) )
% 0.32/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_conv_if
% 0.32/0.47 thf(fact_235_Collect__conv__if2,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,A2: A] :
% 0.32/0.47 ( ( ( P @ A2 )
% 0.32/0.47 => ( ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( A2 = X2 )
% 0.32/0.47 & ( P @ X2 ) ) )
% 0.32/0.47 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/0.47 & ( ~ ( P @ A2 )
% 0.32/0.47 => ( ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( A2 = X2 )
% 0.32/0.47 & ( P @ X2 ) ) )
% 0.32/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_conv_if2
% 0.32/0.47 thf(fact_236_empty__def,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.32/0.47 = ( collect @ A
% 0.32/0.47 @ ^ [X2: A] : $false ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_def
% 0.32/0.47 thf(fact_237_tllist_Osimps_I20_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,X1: B] :
% 0.32/0.47 ( ( tLList1719791291e_tset @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.32/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.simps(20)
% 0.32/0.47 thf(fact_238_tllist_Osimps_I22_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,X1: B] :
% 0.32/0.47 ( ( tLList457864275tllist @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 0.32/0.47 = ( insert @ B @ X1 @ ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tllist.simps(22)
% 0.32/0.47 thf(fact_239_lfinite__lconcat,axiom,
% 0.32/0.47 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 0.32/0.47 ( ( coinductive_lfinite @ A @ ( coinductive_lconcat @ A @ Xss ) )
% 0.32/0.47 = ( ( coinductive_lfinite @ ( coinductive_llist @ A )
% 0.32/0.47 @ ( coinductive_lfilter @ ( coinductive_llist @ A )
% 0.32/0.47 @ ^ [Xs6: coinductive_llist @ A] :
% 0.32/0.47 ~ ( coinductive_lnull @ A @ Xs6 )
% 0.32/0.47 @ Xss ) )
% 0.32/0.47 & ! [X2: coinductive_llist @ A] :
% 0.32/0.47 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( coinductive_lset @ ( coinductive_llist @ A ) @ Xss ) )
% 0.32/0.47 => ( coinductive_lfinite @ A @ X2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lfinite_lconcat
% 0.32/0.47 thf(fact_240_lconcat__repeat__LNil,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coinductive_lconcat @ A
% 0.32/0.47 @ ( coinductive_iterates @ ( coinductive_llist @ A )
% 0.32/0.47 @ ^ [X2: coinductive_llist @ A] : X2
% 0.32/0.47 @ ( coinductive_LNil @ A ) ) )
% 0.32/0.47 = ( coinductive_LNil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % lconcat_repeat_LNil
% 0.32/0.47 thf(fact_241_lconcat_Osimps,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coinductive_lconcat @ A )
% 0.32/0.47 = ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A )
% 0.32/0.47 @ ^ [Xs6: coinductive_llist @ A,Xss2: coinductive_llist @ ( coinductive_llist @ A )] : ( coinductive_lappend @ A @ Xs6 @ ( coinductive_lconcat @ A @ Xss2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lconcat.simps
% 0.32/0.47 thf(fact_242_lconcat__lfilter__neq__LNil,axiom,
% 0.32/0.47 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 0.32/0.47 ( ( coinductive_lconcat @ A
% 0.32/0.47 @ ( coinductive_lfilter @ ( coinductive_llist @ A )
% 0.32/0.47 @ ^ [Xs6: coinductive_llist @ A] :
% 0.32/0.47 ~ ( coinductive_lnull @ A @ Xs6 )
% 0.32/0.47 @ Xss ) )
% 0.32/0.47 = ( coinductive_lconcat @ A @ Xss ) ) ).
% 0.32/0.47
% 0.32/0.47 % lconcat_lfilter_neq_LNil
% 0.32/0.47 thf(fact_243_lnull__lconcat,axiom,
% 0.32/0.47 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 0.32/0.47 ( ( coinductive_lnull @ A @ ( coinductive_lconcat @ A @ Xss ) )
% 0.32/0.47 = ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( coinductive_lset @ ( coinductive_llist @ A ) @ Xss ) @ ( collect @ ( coinductive_llist @ A ) @ ( coinductive_lnull @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lnull_lconcat
% 0.32/0.47 thf(fact_244_tset__ttl,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] : ( ord_less_eq @ ( set @ A ) @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs ) ) @ ( tLList1719791291e_tset @ A @ B @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % tset_ttl
% 0.32/0.47 thf(fact_245_conj__subset__def,axiom,
% 0.32/0.47 ! [A: $tType,A3: set @ A,P: A > $o,Q: A > $o] :
% 0.32/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3
% 0.32/0.47 @ ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) ) ) )
% 0.32/0.47 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( collect @ A @ P ) )
% 0.32/0.47 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( collect @ A @ Q ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % conj_subset_def
% 0.32/0.47 thf(fact_246_prop__restrict,axiom,
% 0.32/0.47 ! [A: $tType,X: A,Z5: set @ A,X5: set @ A,P: A > $o] :
% 0.32/0.47 ( ( member @ A @ X @ Z5 )
% 0.32/0.47 => ( ( ord_less_eq @ ( set @ A ) @ Z5
% 0.32/0.47 @ ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ X5 )
% 0.32/0.47 & ( P @ X2 ) ) ) )
% 0.32/0.47 => ( P @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prop_restrict
% 0.32/0.47 thf(fact_247_Collect__restrict,axiom,
% 0.32/0.47 ! [A: $tType,X5: set @ A,P: A > $o] :
% 0.32/0.47 ( ord_less_eq @ ( set @ A )
% 0.32/0.47 @ ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ X5 )
% 0.32/0.47 & ( P @ X2 ) ) )
% 0.32/0.47 @ X5 ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_restrict
% 0.32/0.47 thf(fact_248_subset__Collect__iff,axiom,
% 0.32/0.47 ! [A: $tType,B9: set @ A,A3: set @ A,P: A > $o] :
% 0.32/0.47 ( ( ord_less_eq @ ( set @ A ) @ B9 @ A3 )
% 0.32/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B9
% 0.32/0.47 @ ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ A3 )
% 0.32/0.47 & ( P @ X2 ) ) ) )
% 0.32/0.47 = ( ! [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ B9 )
% 0.32/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_Collect_iff
% 0.32/0.47 thf(fact_249_subset__CollectI,axiom,
% 0.32/0.47 ! [A: $tType,B9: set @ A,A3: set @ A,Q: A > $o,P: A > $o] :
% 0.32/0.47 ( ( ord_less_eq @ ( set @ A ) @ B9 @ A3 )
% 0.32/0.47 => ( ! [X3: A] :
% 0.32/0.47 ( ( member @ A @ X3 @ B9 )
% 0.32/0.47 => ( ( Q @ X3 )
% 0.32/0.47 => ( P @ X3 ) ) )
% 0.32/0.47 => ( ord_less_eq @ ( set @ A )
% 0.32/0.47 @ ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ B9 )
% 0.32/0.47 & ( Q @ X2 ) ) )
% 0.32/0.47 @ ( collect @ A
% 0.32/0.47 @ ^ [X2: A] :
% 0.32/0.47 ( ( member @ A @ X2 @ A3 )
% 0.32/0.47 & ( P @ X2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_CollectI
% 0.32/0.47
% 0.32/0.47 %----Helper facts (3)
% 0.32/0.47 thf(help_If_3_1_T,axiom,
% 0.32/0.47 ! [P: $o] :
% 0.32/0.47 ( ( P = $true )
% 0.32/0.47 | ( P = $false ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_T,axiom,
% 0.32/0.47 ! [A: $tType,X: A,Y: A] :
% 0.32/0.47 ( ( if @ A @ $false @ X @ Y )
% 0.32/0.47 = Y ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_T,axiom,
% 0.32/0.47 ! [A: $tType,X: A,Y: A] :
% 0.32/0.47 ( ( if @ A @ $true @ X @ Y )
% 0.32/0.47 = X ) ).
% 0.32/0.47
% 0.32/0.47 %----Conjectures (1)
% 0.32/0.47 thf(conj_0,conjecture,
% 0.32/0.47 ( ( tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ ( tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs ) @ ys )
% 0.32/0.47 = ( tLList1380991092t_all2 @ e @ b @ f @ d
% 0.32/0.47 @ ^ [X2: e] : ( p @ ( f2 @ X2 ) )
% 0.32/0.47 @ ^ [X2: f] : ( q @ ( g @ X2 ) )
% 0.32/0.47 @ xs
% 0.32/0.47 @ ys ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 2.91/1.53 ---- Embedded in THF ---
% 2.91/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.91/1.53 %%% Generated on Tue Feb 24 06:10:57 EST 2026
% 2.91/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.91/1.53 %%% Logic specification used:
% 2.91/1.53 %%% thf(spec, logic, $$dhol).
% 2.91/1.53
% 2.91/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2EYh0nHoAB/DTF2DTF25576.p
% 2.91/1.53 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist, type, tLList446370796tllist: ($tType > ($tType > $tType))).
% 2.91/1.53 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.91/1.53 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.91/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.91/1.53 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.91/1.53 thf(ty_tf_f, type, f: $tType).
% 2.91/1.53 thf(ty_tf_e, type, e: $tType).
% 2.91/1.53 thf(ty_tf_d, type, d: $tType).
% 2.91/1.53 thf(ty_tf_c, type, c: $tType).
% 2.91/1.53 thf(ty_tf_b, type, b: $tType).
% 2.91/1.53 thf(ty_tf_a, type, a: $tType).
% 2.91/1.53 thf(sy_c_Coinductive__List_Oiterates, type, coinductive_iterates: (!> [A:$tType]: (((A > A) > (A > (coinductive_llist @ A)))))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Olconcat, type, coinductive_lconcat: (!> [A:$tType]: (((coinductive_llist @ (coinductive_llist @ A)) > (coinductive_llist @ A))))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Olfilter, type, coinductive_lfilter: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Ollist_Ocase__llist, type, coindu1381640503_llist: (!> [B:$tType,A:$tType]: ((B > ((A > ((coinductive_llist @ A) > B)) > ((coinductive_llist @ A) > B)))))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Ollist_Olhd, type, coinductive_lhd: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Ollist_Olnull, type, coinductive_lnull: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Ollist_Olset, type, coinductive_lset: (!> [A:$tType]: (((coinductive_llist @ A) > (set @ A))))).
% 2.91/1.53 thf(sy_c_Coinductive__List_Ollist_Oltl, type, coinductive_ltl: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.91/1.53 thf(sy_c_Fun_Oid, type, id: (!> [A:$tType]: ((A > A)))).
% 2.91/1.53 thf(sy_c_HOL_Odefault__class_Odefault, type, default_default: (!> [A:$tType]: (A))).
% 2.91/1.53 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.91/1.53 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.91/1.53 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.91/1.53 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.91/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.91/1.53 thf(sy_c_Product__Type_OUnity, type, product_Unity: product_unit).
% 2.91/1.53 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit, type, product_rec_unit: (!> [T:$tType]: ((T > (product_unit > T))))).
% 2.91/1.53 thf(sy_c_Product__Type_Ounit_Ocase__unit, type, product_case_unit: (!> [A:$tType]: ((A > (product_unit > A))))).
% 2.91/1.53 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 2.91/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.91/1.53 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Olappendt, type, tLList98099029ppendt: (!> [A:$tType,B:$tType]: (((coinductive_llist @ A) > (((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ B)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ollist__of__tllist, type, tLList798109904tllist: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > (coinductive_llist @ A))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otappend, type, tLList192138471append: (!> [A:$tType,B:$tType,C:$tType]: ((((tLList446370796tllist @ A) @ B) > ((B > ((tLList446370796tllist @ A) @ C)) > ((tLList446370796tllist @ A) @ C)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otcast, type, tLList222516140_tcast: (!> [A:$tType,B:$tType,C:$tType]: ((((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ C))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otconcat, type, tLList365522113concat: (!> [B:$tType,A:$tType]: ((B > (((tLList446370796tllist @ (coinductive_llist @ A)) @ B) > ((tLList446370796tllist @ A) @ B)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otconcat_H, type, tLList1329345514concat: (!> [B:$tType,A:$tType]: (((product_unit > B) > (((tLList446370796tllist @ (coinductive_llist @ A)) @ B) > ((tLList446370796tllist @ A) @ B)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Oterminal0, type, tLList1825092077minal0: (!> [A:$tType]: (A))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otfilter, type, tLList1813626245filter: (!> [B:$tType,A:$tType]: ((B > ((A > $o) > (((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ B))))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otfilter_H, type, tLList1122525870filter: (!> [B:$tType,A:$tType]: (((product_unit > B) > ((A > $o) > (((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ B))))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTCons, type, tLList1992840728_TCons: (!> [A:$tType,B:$tType]: ((A > (((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ B)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTNil, type, tLList57907754e_TNil: (!> [B:$tType,A:$tType]: ((B > ((tLList446370796tllist @ A) @ B))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocase__tllist, type, tLList200813139tllist: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > (((tLList446370796tllist @ A) @ B) > C)) > (((tLList446370796tllist @ A) @ B) > C)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocorec__tllist, type, tLList1614408749tllist: (!> [E:$tType,B:$tType,A:$tType]: (((E > $o) > ((E > B) > ((E > A) > ((E > $o) > ((E > ((tLList446370796tllist @ A) @ B)) > ((E > E) > (E > ((tLList446370796tllist @ A) @ B))))))))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ois__TNil, type, tLList1968894004s_TNil: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > $o)))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Opred__tllist, type, tLList11265572tllist: (!> [A:$tType,B:$tType]: (((A > $o) > ((B > $o) > (((tLList446370796tllist @ A) @ B) > $o)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oset2__tllist, type, tLList457864275tllist: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > (set @ B))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oterminal, type, tLList2110128105rminal: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > B)))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Othd, type, tLList_Mirabelle_thd: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > A)))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otllist__all2, type, tLList1380991092t_all2: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > (((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ C) @ D) > $o))))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otmap, type, tLList1669959861e_tmap: (!> [A:$tType,Aa:$tType,B:$tType,Ba:$tType]: (((A > Aa) > ((B > Ba) > (((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ Aa) @ Ba))))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otset, type, tLList1719791291e_tset: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > (set @ A))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ottl, type, tLList_Mirabelle_ttl: (!> [A:$tType,B:$tType]: ((((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ B))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist__of__llist, type, tLList1672613558_llist: (!> [B:$tType,A:$tType]: ((B > ((coinductive_llist @ A) > ((tLList446370796tllist @ A) @ B)))))).
% 2.91/1.53 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ounfold__tllist, type, tLList636831159tllist: (!> [A:$tType,B:$tType,C:$tType]: (((A > $o) > ((A > B) > ((A > C) > ((A > A) > (A > ((tLList446370796tllist @ C) @ B))))))))).
% 2.91/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.91/1.53 thf(sy_v_P, type, p: (a > (b > $o))).
% 2.91/1.53 thf(sy_v_Q, type, q: (c > (d > $o))).
% 2.91/1.53 thf(sy_v_f, type, f2: (e > a)).
% 2.91/1.53 thf(sy_v_g, type, g: (f > c)).
% 2.91/1.53 thf(sy_v_xs, type, xs: ((tLList446370796tllist @ e) @ f)).
% 2.91/1.53 thf(sy_v_ys, type, ys: ((tLList446370796tllist @ b) @ d)).
% 2.91/1.53 thf(fact_0_tllist_Orel__map_I2_J, axiom, (! [A:$tType,B:$tType,E:$tType,F:$tType,D:$tType,C:$tType,S1a:(A > (E > $o)),S2a:(B > (F > $o)),X:((tLList446370796tllist @ A) @ B),G1:(C > E),G2:(D > F),Y:((tLList446370796tllist @ C) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ E) @ B) @ F) @ S1a) @ S2a) @ X) @ (((((((tLList1669959861e_tmap @ C) @ E) @ D) @ F) @ G1) @ G2) @ Y)) = ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ (^ [X2:A,Y2:C]: (((S1a @ X2) @ (G1 @ Y2))))) @ (^ [X2:B,Y2:D]: (((S2a @ X2) @ (G2 @ Y2))))) @ X) @ Y))))).
% 2.91/1.53 thf(fact_1_tllist_Orel__map_I1_J, axiom, (! [A:$tType,B:$tType,E:$tType,F:$tType,D:$tType,C:$tType,S1b:(E > (C > $o)),S2b:(F > (D > $o)),I1:(A > E),I2:(B > F),X:((tLList446370796tllist @ A) @ B),Y:((tLList446370796tllist @ C) @ D)]: ((((((((((tLList1380991092t_all2 @ E) @ C) @ F) @ D) @ S1b) @ S2b) @ (((((((tLList1669959861e_tmap @ A) @ E) @ B) @ F) @ I1) @ I2) @ X)) @ Y) = ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ (^ [X2:A]: ((S1b @ (I1 @ X2))))) @ (^ [X2:B]: ((S2b @ (I2 @ X2))))) @ X) @ Y))))).
% 2.91/1.53 thf(fact_2_tllist_Orel__eq, axiom, (! [B:$tType,A:$tType]: ((((((((tLList1380991092t_all2 @ A) @ A) @ B) @ B) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ (^ [Y3:B,Z:B]: ((Y3 = Z)))) = (^ [Y3:((tLList446370796tllist @ A) @ B),Z:((tLList446370796tllist @ A) @ B)]: ((Y3 = Z))))))).
% 2.91/1.53 thf(fact_3_tllist_Orel__refl, axiom, (! [D:$tType,C:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X:((tLList446370796tllist @ C) @ D)]: (((! [X3:C]: (((R1a @ X3) @ X3))) => ((! [X3:D]: (((R2a @ X3) @ X3))) => ((((((((tLList1380991092t_all2 @ C) @ C) @ D) @ D) @ R1a) @ R2a) @ X) @ X)))))).
% 2.91/1.53 thf(fact_4_tllist_Omap__ident, axiom, (! [B:$tType,A:$tType,T2:((tLList446370796tllist @ A) @ B)]: (((((((((tLList1669959861e_tmap @ A) @ A) @ B) @ B) @ (^ [X2:A]: (X2))) @ (^ [X2:B]: (X2))) @ T2) = T2)))).
% 2.91/1.53 thf(fact_5_tllist_Omap__cong__pred, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X:((tLList446370796tllist @ A) @ B),Ya:((tLList446370796tllist @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G2:(B > D)]: (((X = Ya) => ((((((tLList11265572tllist @ A) @ B) @ (^ [Z1:A]: (((F1 @ Z1) = (G1 @ Z1))))) @ (^ [Z2:B]: (((F2 @ Z2) = (G2 @ Z2))))) @ Ya) => ((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ G1) @ G2) @ Ya))))))).
% 2.91/1.53 thf(fact_6_ttl__tmap, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,F3:(C > A),G:(D > B),Xs:((tLList446370796tllist @ C) @ D)]: (((((tLList_Mirabelle_ttl @ A) @ B) @ (((((((tLList1669959861e_tmap @ C) @ A) @ D) @ B) @ F3) @ G) @ Xs)) = (((((((tLList1669959861e_tmap @ C) @ A) @ D) @ B) @ F3) @ G) @ (((tLList_Mirabelle_ttl @ C) @ D) @ Xs)))))).
% 2.91/1.53 thf(fact_7_tllist__all2__TCons, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X21:A,X22:((tLList446370796tllist @ A) @ B),Y21:C,Y22:((tLList446370796tllist @ C) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) @ ((((tLList1992840728_TCons @ C) @ D) @ Y21) @ Y22)) = (((R1 @ X21) @ Y21) & ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X22) @ Y22)))))).
% 2.91/1.53 thf(fact_8_tllist__all2__TNil, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X1:B,Y1:D]: ((((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) @ (((tLList57907754e_TNil @ D) @ C) @ Y1)) = ((R2 @ X1) @ Y1))))).
% 2.91/1.53 thf(fact_9_tllist_Omap__disc__iff, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,F1:(A > C),F2:(B > D),A2:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ C) @ D) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ A2)) = (((tLList1968894004s_TNil @ A) @ B) @ A2))))).
% 2.91/1.53 thf(fact_10_tllist_Osimps_I15_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,F1:(A > C),F2:(B > D),X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = ((((tLList1992840728_TCons @ C) @ D) @ (F1 @ X21)) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X22)))))).
% 2.91/1.53 thf(fact_11_TCons__eq__tmap__conv, axiom, (! [D:$tType,B:$tType,A:$tType,C:$tType,Y:A,Ys:((tLList446370796tllist @ A) @ B),F3:(C > A),G:(D > B),Xs:((tLList446370796tllist @ C) @ D)]: (((((((tLList1992840728_TCons @ A) @ B) @ Y) @ Ys) = (((((((tLList1669959861e_tmap @ C) @ A) @ D) @ B) @ F3) @ G) @ Xs)) = (? [Z3:C,Zs:((tLList446370796tllist @ C) @ D)]: (((Xs = ((((tLList1992840728_TCons @ C) @ D) @ Z3) @ Zs)) & (((F3 @ Z3) = Y) & ((((((((tLList1669959861e_tmap @ C) @ A) @ D) @ B) @ F3) @ G) @ Zs) = Ys))))))))).
% 2.91/1.53 thf(fact_12_tmap__eq__TCons__conv, axiom, (! [D:$tType,B:$tType,A:$tType,C:$tType,F3:(C > A),G:(D > B),Xs:((tLList446370796tllist @ C) @ D),Y:A,Ys:((tLList446370796tllist @ A) @ B)]: ((((((((((tLList1669959861e_tmap @ C) @ A) @ D) @ B) @ F3) @ G) @ Xs) = ((((tLList1992840728_TCons @ A) @ B) @ Y) @ Ys)) = (? [Z3:C,Zs:((tLList446370796tllist @ C) @ D)]: (((Xs = ((((tLList1992840728_TCons @ C) @ D) @ Z3) @ Zs)) & (((F3 @ Z3) = Y) & ((((((((tLList1669959861e_tmap @ C) @ A) @ D) @ B) @ F3) @ G) @ Zs) = Ys))))))))).
% 2.91/1.53 thf(fact_13_tllist_Osimps_I14_J, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F1:(A > C),F2:(B > D),X1:B]: (((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (((tLList57907754e_TNil @ D) @ C) @ (F2 @ X1)))))).
% 2.91/1.53 thf(fact_14_TNil__eq__tmap__conv, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:B,F3:(C > A),G:(D > B),Xs:((tLList446370796tllist @ C) @ D)]: ((((((tLList57907754e_TNil @ B) @ A) @ Y) = (((((((tLList1669959861e_tmap @ C) @ A) @ D) @ B) @ F3) @ G) @ Xs)) = (? [Y4:D]: (((Xs = (((tLList57907754e_TNil @ D) @ C) @ Y4)) & ((G @ Y4) = Y)))))))).
% 2.91/1.53 thf(fact_15_tmap__eq__TNil__conv, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,F3:(C > A),G:(D > B),Xs:((tLList446370796tllist @ C) @ D),Y:B]: ((((((((((tLList1669959861e_tmap @ C) @ A) @ D) @ B) @ F3) @ G) @ Xs) = (((tLList57907754e_TNil @ B) @ A) @ Y)) = (? [Y4:D]: (((Xs = (((tLList57907754e_TNil @ D) @ C) @ Y4)) & ((G @ Y4) = Y)))))))).
% 2.91/1.53 thf(fact_16_tllist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),X21:A,Y21:C,R2:(B > (D > $o)),X22:((tLList446370796tllist @ A) @ B),Y22:((tLList446370796tllist @ C) @ D)]: ((((R1 @ X21) @ Y21) => (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X22) @ Y22) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) @ ((((tLList1992840728_TCons @ C) @ D) @ Y21) @ Y22))))))).
% 2.91/1.53 thf(fact_17_tllist_Oinject_I1_J, axiom, (! [A:$tType,B:$tType,X1:B,Y1:B]: ((((((tLList57907754e_TNil @ B) @ A) @ X1) = (((tLList57907754e_TNil @ B) @ A) @ Y1)) = (X1 = Y1))))).
% 2.91/1.53 thf(fact_18_tllist_Oinject_I2_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B),Y21:A,Y22:((tLList446370796tllist @ A) @ B)]: (((((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22) = ((((tLList1992840728_TCons @ A) @ B) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.91/1.53 thf(fact_19_tllist_Opred__inject_I1_J, axiom, (! [A:$tType,B:$tType,P1:(A > $o),P2:(B > $o),A2:B]: (((((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ (((tLList57907754e_TNil @ B) @ A) @ A2)) = (P2 @ A2))))).
% 2.91/1.53 thf(fact_20_tllist_Opred__inject_I2_J, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P2:(B > $o),A2:A,Aa2:((tLList446370796tllist @ A) @ B)]: (((((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ ((((tLList1992840728_TCons @ A) @ B) @ A2) @ Aa2)) = ((P1 @ A2) & (((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ Aa2)))))).
% 2.91/1.53 thf(fact_21_tllist_Osel_I5_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList_Mirabelle_ttl @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = X22)))).
% 2.91/1.53 thf(fact_22_tllist_Osel_I4_J, axiom, (! [A:$tType,B:$tType,X1:B]: (((((tLList_Mirabelle_ttl @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (((tLList57907754e_TNil @ B) @ A) @ X1))))).
% 2.91/1.53 thf(fact_23_tllist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: ((~ ((((tLList1968894004s_TNil @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22))))))).
% 2.91/1.53 thf(fact_24_tllist_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,X1:B]: ((((tLList1968894004s_TNil @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ X1))))).
% 2.91/1.53 thf(fact_25_tllist_OdiscI_I2_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B),X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((Tllist = ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) => (~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist))))))).
% 2.91/1.53 thf(fact_26_tllist_OdiscI_I1_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B),X1:B]: (((Tllist = (((tLList57907754e_TNil @ B) @ A) @ X1)) => (((tLList1968894004s_TNil @ A) @ B) @ Tllist))))).
% 2.91/1.53 thf(fact_27_tllist_Odistinct_I1_J, axiom, (! [B:$tType,A:$tType,X1:B,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList57907754e_TNil @ B) @ A) @ X1) != ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22))))).
% 2.91/1.53 thf(fact_28_is__TNil__ttl, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ Xs) => (((tLList1968894004s_TNil @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Xs)))))).
% 2.91/1.53 thf(fact_29_tllist_Oexhaust, axiom, (! [B:$tType,A:$tType,Y:((tLList446370796tllist @ A) @ B)]: (((! [X12:B]: ((Y != (((tLList57907754e_TNil @ B) @ A) @ X12)))) => (~ ((! [X212:A,X222:((tLList446370796tllist @ A) @ B)]: ((Y != ((((tLList1992840728_TCons @ A) @ B) @ X212) @ X222)))))))))).
% 2.91/1.53 thf(fact_30_is__TNil__def, axiom, (! [B:$tType,A:$tType]: ((((tLList1968894004s_TNil @ A) @ B) = (^ [Tllist2:((tLList446370796tllist @ A) @ B)]: ((? [X13:B]: ((Tllist2 = (((tLList57907754e_TNil @ B) @ A) @ X13)))))))))).
% 2.91/1.53 thf(fact_31_tllist__all2__cases, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,P:(A > (B > $o)),Q:(C > (D > $o)),Xs:((tLList446370796tllist @ A) @ C),Ys:((tLList446370796tllist @ B) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ B) @ C) @ D) @ P) @ Q) @ Xs) @ Ys) => ((! [B2:C]: (((Xs = (((tLList57907754e_TNil @ C) @ A) @ B2)) => (! [B3:D]: (((Ys = (((tLList57907754e_TNil @ D) @ B) @ B3)) => (~ (((Q @ B2) @ B3))))))))) => (~ ((! [X3:A,Xs2:((tLList446370796tllist @ A) @ C)]: (((Xs = ((((tLList1992840728_TCons @ A) @ C) @ X3) @ Xs2)) => (! [Y5:B,Ys2:((tLList446370796tllist @ B) @ D)]: (((Ys = ((((tLList1992840728_TCons @ B) @ D) @ Y5) @ Ys2)) => (((P @ X3) @ Y5) => (~ (((((((((tLList1380991092t_all2 @ A) @ B) @ C) @ D) @ P) @ Q) @ Xs2) @ Ys2))))))))))))))))).
% 2.91/1.53 thf(fact_32_tllist_Orel__cases, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),A2:((tLList446370796tllist @ A) @ B),B4:((tLList446370796tllist @ C) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ A2) @ B4) => ((! [X3:B]: (((A2 = (((tLList57907754e_TNil @ B) @ A) @ X3)) => (! [Y5:D]: (((B4 = (((tLList57907754e_TNil @ D) @ C) @ Y5)) => (~ (((R2 @ X3) @ Y5))))))))) => (~ ((! [X1a:A,X23:((tLList446370796tllist @ A) @ B)]: (((A2 = ((((tLList1992840728_TCons @ A) @ B) @ X1a) @ X23)) => (! [Y1a:C,Y23:((tLList446370796tllist @ C) @ D)]: (((B4 = ((((tLList1992840728_TCons @ C) @ D) @ Y1a) @ Y23)) => (((R1 @ X1a) @ Y1a) => (~ (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X23) @ Y23))))))))))))))))).
% 2.91/1.53 thf(fact_33_tllist_Orel__distinct_I1_J, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X1:B,Y21:C,Y22:((tLList446370796tllist @ C) @ D)]: ((~ (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) @ ((((tLList1992840728_TCons @ C) @ D) @ Y21) @ Y22))))))).
% 2.91/1.53 thf(fact_34_tllist_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),Y21:A,Y22:((tLList446370796tllist @ A) @ B),X1:D]: ((~ (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ ((((tLList1992840728_TCons @ A) @ B) @ Y21) @ Y22)) @ (((tLList57907754e_TNil @ D) @ C) @ X1))))))).
% 2.91/1.53 thf(fact_35_tllist_Omap__sel_I3_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),F1:(A > C),F2:(B > D)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => ((((tLList_Mirabelle_ttl @ C) @ D) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ A2)) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ (((tLList_Mirabelle_ttl @ A) @ B) @ A2))))))).
% 2.91/1.53 thf(fact_36_tllist_Opred__True, axiom, (! [B:$tType,A:$tType]: ((((((tLList11265572tllist @ A) @ B) @ (^ [Uu:A]: ($true))) @ (^ [Uu:B]: ($true))) = (^ [Uu:((tLList446370796tllist @ A) @ B)]: ($true)))))).
% 2.91/1.53 thf(fact_37_tllist__all2__TNil2, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType,P:(A > (B > $o)),Q:(C > (D > $o)),Ts:((tLList446370796tllist @ A) @ C),B5:D]: ((((((((((tLList1380991092t_all2 @ A) @ B) @ C) @ D) @ P) @ Q) @ Ts) @ (((tLList57907754e_TNil @ D) @ B) @ B5)) = (? [B6:C]: (((Ts = (((tLList57907754e_TNil @ C) @ A) @ B6)) & ((Q @ B6) @ B5)))))))).
% 2.91/1.53 thf(fact_38_tllist__all2__TNil1, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,P:(A > (B > $o)),Q:(C > (D > $o)),B4:C,Ts:((tLList446370796tllist @ B) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ B) @ C) @ D) @ P) @ Q) @ (((tLList57907754e_TNil @ C) @ A) @ B4)) @ Ts) = (? [B7:D]: (((Ts = (((tLList57907754e_TNil @ D) @ B) @ B7)) & ((Q @ B4) @ B7)))))))).
% 2.91/1.53 thf(fact_39_tllist_Orel__intros_I1_J, axiom, (! [B:$tType,A:$tType,C:$tType,D:$tType,R2:(B > (D > $o)),X1:B,Y1:D,R1:(A > (C > $o))]: ((((R2 @ X1) @ Y1) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) @ (((tLList57907754e_TNil @ D) @ C) @ Y1)))))).
% 2.91/1.53 thf(fact_40_tllist__all2__TCons2, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,P:(A > (B > $o)),Q:(C > (D > $o)),Ts2:((tLList446370796tllist @ A) @ C),X:B,Ts:((tLList446370796tllist @ B) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ B) @ C) @ D) @ P) @ Q) @ Ts2) @ ((((tLList1992840728_TCons @ B) @ D) @ X) @ Ts)) = (? [X4:A,Ts3:((tLList446370796tllist @ A) @ C)]: (((Ts2 = ((((tLList1992840728_TCons @ A) @ C) @ X4) @ Ts3)) & (((P @ X4) @ X) & ((((((((tLList1380991092t_all2 @ A) @ B) @ C) @ D) @ P) @ Q) @ Ts3) @ Ts))))))))).
% 2.91/1.53 thf(fact_41_tllist__all2__TCons1, axiom, (! [D:$tType,A:$tType,C:$tType,B:$tType,P:(A > (B > $o)),Q:(C > (D > $o)),X:A,Ts:((tLList446370796tllist @ A) @ C),Ts2:((tLList446370796tllist @ B) @ D)]: ((((((((((tLList1380991092t_all2 @ A) @ B) @ C) @ D) @ P) @ Q) @ ((((tLList1992840728_TCons @ A) @ C) @ X) @ Ts)) @ Ts2) = (? [X4:B,Ts3:((tLList446370796tllist @ B) @ D)]: (((Ts2 = ((((tLList1992840728_TCons @ B) @ D) @ X4) @ Ts3)) & (((P @ X) @ X4) & ((((((((tLList1380991092t_all2 @ A) @ B) @ C) @ D) @ P) @ Q) @ Ts) @ Ts3))))))))).
% 2.91/1.53 thf(fact_42_tllist_Ocollapse_I2_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist))) => (((((tLList1992840728_TCons @ A) @ B) @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist)) = Tllist))))).
% 2.91/1.53 thf(fact_43_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.91/1.53 thf(fact_44_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 2.91/1.53 thf(fact_45_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.91/1.53 thf(fact_46_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G:(A > B)]: (((! [X3:A]: (((F3 @ X3) = (G @ X3)))) => (F3 = G))))).
% 2.91/1.53 thf(fact_47_tconcat__TNil, axiom, (! [A:$tType,B:$tType,B4:B,B5:B]: ((((((tLList365522113concat @ B) @ A) @ B4) @ (((tLList57907754e_TNil @ B) @ (coinductive_llist @ A)) @ B5)) = (((tLList57907754e_TNil @ B) @ A) @ B5))))).
% 2.91/1.53 thf(fact_48_ttl__def, axiom, (! [B:$tType,A:$tType]: ((((tLList_Mirabelle_ttl @ A) @ B) = (((((tLList200813139tllist @ B) @ ((tLList446370796tllist @ A) @ B)) @ A) @ ((tLList57907754e_TNil @ B) @ A)) @ (^ [X213:A,X223:((tLList446370796tllist @ A) @ B)]: (X223))))))).
% 2.91/1.53 thf(fact_49_tllist_Omap__sel_I2_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),F1:(A > C),F2:(B > D)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => ((((tLList_Mirabelle_thd @ C) @ D) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ A2)) = (F1 @ (((tLList_Mirabelle_thd @ A) @ B) @ A2))))))).
% 2.91/1.53 thf(fact_50_tmap__is__TNil, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B),F3:(A > C),G:(B > D)]: (((((tLList1968894004s_TNil @ A) @ B) @ Xs) => ((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F3) @ G) @ Xs) = (((tLList57907754e_TNil @ D) @ C) @ (G @ (((tLList2110128105rminal @ A) @ B) @ Xs)))))))).
% 2.91/1.53 thf(fact_51_ttl__unfold__tllist, axiom, (! [B:$tType,A:$tType,C:$tType,IS_TNIL:(C > $o),A2:C,TNIL:(C > B),THD:(C > A),TTL:(C > C)]: ((((IS_TNIL @ A2) => ((((tLList_Mirabelle_ttl @ A) @ B) @ ((((((((tLList636831159tllist @ C) @ B) @ A) @ IS_TNIL) @ TNIL) @ THD) @ TTL) @ A2)) = (((tLList57907754e_TNil @ B) @ A) @ (TNIL @ A2)))) & ((~ ((IS_TNIL @ A2))) => ((((tLList_Mirabelle_ttl @ A) @ B) @ ((((((((tLList636831159tllist @ C) @ B) @ A) @ IS_TNIL) @ TNIL) @ THD) @ TTL) @ A2)) = ((((((((tLList636831159tllist @ C) @ B) @ A) @ IS_TNIL) @ TNIL) @ THD) @ TTL) @ (TTL @ A2)))))))).
% 2.91/1.53 thf(fact_52_tllist_Ocorec__code, axiom, (! [B:$tType,A:$tType,E:$tType]: (((((tLList1614408749tllist @ E) @ B) @ A) = (^ [P3:(E > $o),G12:(E > B),G21:(E > A),Q22:(E > $o),G221:(E > ((tLList446370796tllist @ A) @ B)),G222:(E > E),A4:E]: (((((if @ ((tLList446370796tllist @ A) @ B)) @ (P3 @ A4)) @ (((tLList57907754e_TNil @ B) @ A) @ (G12 @ A4))) @ ((((tLList1992840728_TCons @ A) @ B) @ (G21 @ A4)) @ ((((if @ ((tLList446370796tllist @ A) @ B)) @ (Q22 @ A4)) @ (G221 @ A4)) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P3) @ G12) @ G21) @ Q22) @ G221) @ G222) @ (G222 @ A4))))))))))).
% 2.91/1.53 thf(fact_53_unfold__tllist_Ocode, axiom, (! [B:$tType,C:$tType,A:$tType]: (((((tLList636831159tllist @ A) @ B) @ C) = (^ [P3:(A > $o),G12:(A > B),G21:(A > C),G22:(A > A),A4:A]: (((((if @ ((tLList446370796tllist @ C) @ B)) @ (P3 @ A4)) @ (((tLList57907754e_TNil @ B) @ C) @ (G12 @ A4))) @ ((((tLList1992840728_TCons @ C) @ B) @ (G21 @ A4)) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P3) @ G12) @ G21) @ G22) @ (G22 @ A4)))))))))).
% 2.91/1.53 thf(fact_54_tconcat_H__code_I1_J, axiom, (! [A:$tType,B:$tType,B4:(product_unit > B),B5:B]: ((((((tLList1329345514concat @ B) @ A) @ B4) @ (((tLList57907754e_TNil @ B) @ (coinductive_llist @ A)) @ B5)) = (((tLList57907754e_TNil @ B) @ A) @ B5))))).
% 2.91/1.53 thf(fact_55_tllist_Ocollapse_I1_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ Tllist) => ((((tLList57907754e_TNil @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ Tllist)) = Tllist))))).
% 2.91/1.53 thf(fact_56_terminal__TCons, axiom, (! [A:$tType,B:$tType,X:B,Xs:((tLList446370796tllist @ B) @ A)]: (((((tLList2110128105rminal @ B) @ A) @ ((((tLList1992840728_TCons @ B) @ A) @ X) @ Xs)) = (((tLList2110128105rminal @ B) @ A) @ Xs))))).
% 2.91/1.53 thf(fact_57_terminal__ttl, axiom, (! [A:$tType,B:$tType,Xs:((tLList446370796tllist @ B) @ A)]: (((((tLList2110128105rminal @ B) @ A) @ (((tLList_Mirabelle_ttl @ B) @ A) @ Xs)) = (((tLList2110128105rminal @ B) @ A) @ Xs))))).
% 2.91/1.53 thf(fact_58_unfold__tllist_Odisc__iff_I1_J, axiom, (! [C:$tType,B:$tType,A:$tType,P4:(A > $o),G1:(A > B),G212:(A > C),G223:(A > A),A2:A]: (((((tLList1968894004s_TNil @ C) @ B) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2)) = (P4 @ A2))))).
% 2.91/1.53 thf(fact_59_unfold__tllist_Odisc__iff_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,P4:(A > $o),G1:(A > B),G212:(A > C),G223:(A > A),A2:A]: (((~ ((((tLList1968894004s_TNil @ C) @ B) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2)))) = (~ ((P4 @ A2))))))).
% 2.91/1.53 thf(fact_60_tllist_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,B:$tType,E:$tType,P4:(E > $o),G1:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E),A2:E]: (((((tLList1968894004s_TNil @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (P4 @ A2))))).
% 2.91/1.53 thf(fact_61_tllist_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,B:$tType,E:$tType,P4:(E > $o),G1:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E),A2:E]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))) = (~ ((P4 @ A2))))))).
% 2.91/1.53 thf(fact_62_unfold__tllist__eq__TNil, axiom, (! [A:$tType,B:$tType,C:$tType,IS_TNIL:(C > $o),TNIL:(C > B),THD:(C > A),TTL:(C > C),A2:C,B4:B]: (((((((((((tLList636831159tllist @ C) @ B) @ A) @ IS_TNIL) @ TNIL) @ THD) @ TTL) @ A2) = (((tLList57907754e_TNil @ B) @ A) @ B4)) = ((IS_TNIL @ A2) & (B4 = (TNIL @ A2))))))).
% 2.91/1.53 thf(fact_63_TNil__eq__unfold__tllist, axiom, (! [A:$tType,B:$tType,C:$tType,B4:B,IS_TNIL:(C > $o),TNIL:(C > B),THD:(C > A),TTL:(C > C),A2:C]: ((((((tLList57907754e_TNil @ B) @ A) @ B4) = ((((((((tLList636831159tllist @ C) @ B) @ A) @ IS_TNIL) @ TNIL) @ THD) @ TTL) @ A2)) = ((IS_TNIL @ A2) & (B4 = (TNIL @ A2))))))).
% 2.91/1.53 thf(fact_64_unfold__tllist_Osimps_I3_J, axiom, (! [C:$tType,B:$tType,A:$tType,P4:(A > $o),A2:A,G1:(A > B),G212:(A > C),G223:(A > A)]: (((P4 @ A2) => ((((tLList2110128105rminal @ C) @ B) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2)) = (G1 @ A2)))))).
% 2.91/1.53 thf(fact_65_unfold__tllist_Osimps_I4_J, axiom, (! [B:$tType,C:$tType,A:$tType,P4:(A > $o),A2:A,G1:(A > B),G212:(A > C),G223:(A > A)]: (((~ ((P4 @ A2))) => ((((tLList_Mirabelle_thd @ C) @ B) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2)) = (G212 @ A2)))))).
% 2.91/1.53 thf(fact_66_tllist_Ocorec__sel_I1_J, axiom, (! [Aa:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G1:(E > A),G212:(E > Aa),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ Aa) @ A)),G2222:(E > E)]: (((P4 @ A2) => ((((tLList2110128105rminal @ Aa) @ A) @ ((((((((((tLList1614408749tllist @ E) @ A) @ Aa) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (G1 @ A2)))))).
% 2.91/1.53 thf(fact_67_tllist_Ocorec__sel_I2_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G1:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((~ ((P4 @ A2))) => ((((tLList_Mirabelle_thd @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (G212 @ A2)))))).
% 2.91/1.53 thf(fact_68_tconcat__code, axiom, (! [B:$tType,A:$tType]: ((((tLList365522113concat @ A) @ B) = (^ [B6:A]: ((((tLList1329345514concat @ A) @ B) @ (^ [Uu:product_unit]: (B6))))))))).
% 2.91/1.53 thf(fact_69_tllist_Ocase__eq__if, axiom, (! [A:$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))))))))).
% 2.91/1.53 thf(fact_70_tllist_Ocase__distrib, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,H:(C > D),F1:(B > C),F2:(A > (((tLList446370796tllist @ A) @ B) > C)),Tllist:((tLList446370796tllist @ A) @ B)]: (((H @ ((((((tLList200813139tllist @ B) @ C) @ A) @ F1) @ F2) @ Tllist)) = ((((((tLList200813139tllist @ B) @ D) @ A) @ (^ [X2:B]: ((H @ (F1 @ X2))))) @ (^ [X13:A,X24:((tLList446370796tllist @ A) @ B)]: ((H @ ((F2 @ X13) @ X24))))) @ Tllist))))).
% 2.91/1.53 thf(fact_71_tllist_Ocoinduct__strong, axiom, (! [B:$tType,A:$tType,R:(((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ A) @ B) > $o)),Tllist:((tLList446370796tllist @ A) @ B),Tllist3:((tLList446370796tllist @ A) @ B)]: ((((R @ Tllist) @ Tllist3) => ((! [Tllist4:((tLList446370796tllist @ A) @ B),Tllist5:((tLList446370796tllist @ A) @ B)]: ((((R @ Tllist4) @ Tllist5) => (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) = (((tLList1968894004s_TNil @ A) @ B) @ Tllist5)) & (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) => ((((tLList1968894004s_TNil @ A) @ B) @ Tllist5) => ((((tLList2110128105rminal @ A) @ B) @ Tllist4) = (((tLList2110128105rminal @ A) @ B) @ Tllist5)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist4))) => ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist5))) => (((((tLList_Mirabelle_thd @ A) @ B) @ Tllist4) = (((tLList_Mirabelle_thd @ A) @ B) @ Tllist5)) & (((R @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist4)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist5)) | ((((tLList_Mirabelle_ttl @ A) @ B) @ Tllist4) = (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist5))))))))))) => (Tllist = Tllist3)))))).
% 2.91/1.53 thf(fact_72_tllist_Ocoinduct, axiom, (! [B:$tType,A:$tType,R:(((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ A) @ B) > $o)),Tllist:((tLList446370796tllist @ A) @ B),Tllist3:((tLList446370796tllist @ A) @ B)]: ((((R @ Tllist) @ Tllist3) => ((! [Tllist4:((tLList446370796tllist @ A) @ B),Tllist5:((tLList446370796tllist @ A) @ B)]: ((((R @ Tllist4) @ Tllist5) => (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) = (((tLList1968894004s_TNil @ A) @ B) @ Tllist5)) & (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) => ((((tLList1968894004s_TNil @ A) @ B) @ Tllist5) => ((((tLList2110128105rminal @ A) @ B) @ Tllist4) = (((tLList2110128105rminal @ A) @ B) @ Tllist5)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist4))) => ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist5))) => (((((tLList_Mirabelle_thd @ A) @ B) @ Tllist4) = (((tLList_Mirabelle_thd @ A) @ B) @ Tllist5)) & ((R @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist4)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist5)))))))))) => (Tllist = Tllist3)))))).
% 2.91/1.53 thf(fact_73_tllist_Oexpand, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B),Tllist3:((tLList446370796tllist @ A) @ B)]: ((((((tLList1968894004s_TNil @ A) @ B) @ Tllist) = (((tLList1968894004s_TNil @ A) @ B) @ Tllist3)) => (((((tLList1968894004s_TNil @ A) @ B) @ Tllist) => ((((tLList1968894004s_TNil @ A) @ B) @ Tllist3) => ((((tLList2110128105rminal @ A) @ B) @ Tllist) = (((tLList2110128105rminal @ A) @ B) @ Tllist3)))) => (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist))) => ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist3))) => (((((tLList_Mirabelle_thd @ A) @ B) @ Tllist) = (((tLList_Mirabelle_thd @ A) @ B) @ Tllist3)) & ((((tLList_Mirabelle_ttl @ A) @ B) @ Tllist) = (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist3))))) => (Tllist = Tllist3))))))).
% 2.91/1.53 thf(fact_74_tllist_Osplit__sel__asm, axiom, (! [C:$tType,B:$tType,A:$tType,P:(C > $o),F1:(B > C),F2:(A > (((tLList446370796tllist @ A) @ B) > C)),Tllist:((tLList446370796tllist @ A) @ B)]: (((P @ ((((((tLList200813139tllist @ B) @ C) @ A) @ F1) @ F2) @ Tllist)) = (~ ((((Tllist = (((tLList57907754e_TNil @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ Tllist))) & (~ ((P @ (F1 @ (((tLList2110128105rminal @ A) @ B) @ Tllist)))))) | ((Tllist = ((((tLList1992840728_TCons @ A) @ B) @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))) & (~ ((P @ ((F2 @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))))))))))))).
% 2.91/1.53 thf(fact_75_tllist_Osplit__sel, axiom, (! [C:$tType,B:$tType,A:$tType,P:(C > $o),F1:(B > C),F2:(A > (((tLList446370796tllist @ A) @ B) > C)),Tllist:((tLList446370796tllist @ A) @ B)]: (((P @ ((((((tLList200813139tllist @ B) @ C) @ A) @ F1) @ F2) @ Tllist)) = (((Tllist = (((tLList57907754e_TNil @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ Tllist))) => (P @ (F1 @ (((tLList2110128105rminal @ A) @ B) @ Tllist)))) & ((Tllist = ((((tLList1992840728_TCons @ A) @ B) @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))) => (P @ ((F2 @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))))))))).
% 2.91/1.53 thf(fact_76_terminal__TNil, axiom, (! [Aa:$tType,A:$tType,X1:A]: (((((tLList2110128105rminal @ Aa) @ A) @ (((tLList57907754e_TNil @ A) @ Aa) @ X1)) = X1)))).
% 2.91/1.53 thf(fact_77_tllist_Osel_I3_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList_Mirabelle_thd @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = X21)))).
% 2.91/1.53 thf(fact_78_unfold__tllist_Odisc_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,P4:(A > $o),A2:A,G1:(A > B),G212:(A > C),G223:(A > A)]: (((P4 @ A2) => (((tLList1968894004s_TNil @ C) @ B) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2)))))).
% 2.91/1.53 thf(fact_79_unfold__tllist_Odisc_I2_J, axiom, (! [B:$tType,C:$tType,A:$tType,P4:(A > $o),A2:A,G1:(A > B),G212:(A > C),G223:(A > A)]: (((~ ((P4 @ A2))) => (~ ((((tLList1968894004s_TNil @ C) @ B) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2)))))))).
% 2.91/1.53 thf(fact_80_tllist_Ocorec__disc_I1_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G1:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((P4 @ A2) => (((tLList1968894004s_TNil @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))))).
% 2.91/1.53 thf(fact_81_tllist_Ocorec__disc_I2_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G1:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((~ ((P4 @ A2))) => (~ ((((tLList1968894004s_TNil @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))))))).
% 2.91/1.53 thf(fact_82_tllist__all2__coinduct, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,X5:(((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ C) @ D) > $o)),Xs:((tLList446370796tllist @ A) @ B),Ys:((tLList446370796tllist @ C) @ D),R:(B > (D > $o)),P:(A > (C > $o))]: ((((X5 @ Xs) @ Ys) => ((! [Xs3:((tLList446370796tllist @ A) @ B),Ys3:((tLList446370796tllist @ C) @ D)]: ((((X5 @ Xs3) @ Ys3) => (((((tLList1968894004s_TNil @ A) @ B) @ Xs3) = (((tLList1968894004s_TNil @ C) @ D) @ Ys3)) & (((((tLList1968894004s_TNil @ A) @ B) @ Xs3) => ((((tLList1968894004s_TNil @ C) @ D) @ Ys3) => ((R @ (((tLList2110128105rminal @ A) @ B) @ Xs3)) @ (((tLList2110128105rminal @ C) @ D) @ Ys3)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs3))) => ((~ ((((tLList1968894004s_TNil @ C) @ D) @ Ys3))) => (((P @ (((tLList_Mirabelle_thd @ A) @ B) @ Xs3)) @ (((tLList_Mirabelle_thd @ C) @ D) @ Ys3)) & (((X5 @ (((tLList_Mirabelle_ttl @ A) @ B) @ Xs3)) @ (((tLList_Mirabelle_ttl @ C) @ D) @ Ys3)) | ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ P) @ R) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Xs3)) @ (((tLList_Mirabelle_ttl @ C) @ D) @ Ys3))))))))))) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ P) @ R) @ Xs) @ Ys)))))).
% 2.91/1.53 thf(fact_83_tllist_Orel__coinduct, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,P:(((tLList446370796tllist @ A) @ B) > (((tLList446370796tllist @ C) @ D) > $o)),X:((tLList446370796tllist @ A) @ B),Y:((tLList446370796tllist @ C) @ D),R2:(B > (D > $o)),R1:(A > (C > $o))]: ((((P @ X) @ Y) => ((! [Tllist4:((tLList446370796tllist @ A) @ B),Tllist5:((tLList446370796tllist @ C) @ D)]: ((((P @ Tllist4) @ Tllist5) => (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) = (((tLList1968894004s_TNil @ C) @ D) @ Tllist5)) & (((((tLList1968894004s_TNil @ A) @ B) @ Tllist4) => ((((tLList1968894004s_TNil @ C) @ D) @ Tllist5) => ((R2 @ (((tLList2110128105rminal @ A) @ B) @ Tllist4)) @ (((tLList2110128105rminal @ C) @ D) @ Tllist5)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist4))) => ((~ ((((tLList1968894004s_TNil @ C) @ D) @ Tllist5))) => (((R1 @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist4)) @ (((tLList_Mirabelle_thd @ C) @ D) @ Tllist5)) & ((P @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist4)) @ (((tLList_Mirabelle_ttl @ C) @ D) @ Tllist5)))))))))) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X) @ Y)))))).
% 2.91/1.53 thf(fact_84_tllist_Orel__sel, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType]: ((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) = (^ [R12:(A > (C > $o)),R22:(B > (D > $o)),A4:((tLList446370796tllist @ A) @ B),B6:((tLList446370796tllist @ C) @ D)]: ((((((tLList1968894004s_TNil @ A) @ B) @ A4) = (((tLList1968894004s_TNil @ C) @ D) @ B6)) & (((((tLList1968894004s_TNil @ A) @ B) @ A4) => ((((tLList1968894004s_TNil @ C) @ D) @ B6) => ((R22 @ (((tLList2110128105rminal @ A) @ B) @ A4)) @ (((tLList2110128105rminal @ C) @ D) @ B6)))) & ((~ ((((tLList1968894004s_TNil @ A) @ B) @ A4))) => ((~ ((((tLList1968894004s_TNil @ C) @ D) @ B6))) => (((R12 @ (((tLList_Mirabelle_thd @ A) @ B) @ A4)) @ (((tLList_Mirabelle_thd @ C) @ D) @ B6)) & ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R12) @ R22) @ (((tLList_Mirabelle_ttl @ A) @ B) @ A4)) @ (((tLList_Mirabelle_ttl @ C) @ D) @ B6))))))))))))).
% 2.91/1.53 thf(fact_85_tllist_Oexhaust__sel, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B)]: (((Tllist != (((tLList57907754e_TNil @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ Tllist))) => (Tllist = ((((tLList1992840728_TCons @ A) @ B) @ (((tLList_Mirabelle_thd @ A) @ B) @ Tllist)) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Tllist))))))).
% 2.91/1.53 thf(fact_86_unfold__tllist_Octr_I1_J, axiom, (! [C:$tType,B:$tType,A:$tType,P4:(A > $o),A2:A,G1:(A > B),G212:(A > C),G223:(A > A)]: (((P4 @ A2) => (((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2) = (((tLList57907754e_TNil @ B) @ C) @ (G1 @ A2))))))).
% 2.91/1.53 thf(fact_87_tllist_Osimps_I5_J, axiom, (! [A:$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))))).
% 2.91/1.53 thf(fact_88_tllist_Ocorec_I1_J, axiom, (! [A:$tType,B:$tType,E:$tType,P4:(E > $o),A2:E,G1:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((P4 @ A2) => (((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2) = (((tLList57907754e_TNil @ B) @ A) @ (G1 @ A2))))))).
% 2.91/1.53 thf(fact_89_unfold__tllist_Octr_I2_J, axiom, (! [B:$tType,C:$tType,A:$tType,P4:(A > $o),A2:A,G1:(A > B),G212:(A > C),G223:(A > A)]: (((~ ((P4 @ A2))) => (((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2) = ((((tLList1992840728_TCons @ C) @ B) @ (G212 @ A2)) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ (G223 @ A2)))))))).
% 2.91/1.53 thf(fact_90_tllist_Osimps_I6_J, axiom, (! [C:$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))))).
% 2.91/1.53 thf(fact_91_tllist_Ocorec_I2_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,G1:(E > B),G212:(E > A),Q222:(E > $o),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((~ ((P4 @ A2))) => (((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2) = ((((tLList1992840728_TCons @ A) @ B) @ (G212 @ A2)) @ ((((if @ ((tLList446370796tllist @ A) @ B)) @ (Q222 @ A2)) @ (G2212 @ A2)) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.91/1.53 thf(fact_92_unfold__tllist_Osimps_I5_J, axiom, (! [B:$tType,C:$tType,A:$tType,P4:(A > $o),A2:A,G1:(A > B),G212:(A > C),G223:(A > A)]: (((~ ((P4 @ A2))) => ((((tLList_Mirabelle_ttl @ C) @ B) @ ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ A2)) = ((((((((tLList636831159tllist @ A) @ B) @ C) @ P4) @ G1) @ G212) @ G223) @ (G223 @ A2))))))).
% 2.91/1.54 thf(fact_93_tllist_Ocorec__sel_I3_J, axiom, (! [B:$tType,A:$tType,E:$tType,P4:(E > $o),A2:E,Q222:(E > $o),G1:(E > B),G212:(E > A),G2212:(E > ((tLList446370796tllist @ A) @ B)),G2222:(E > E)]: (((~ ((P4 @ A2))) => (((Q222 @ A2) => ((((tLList_Mirabelle_ttl @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (G2212 @ A2))) & ((~ ((Q222 @ A2))) => ((((tLList_Mirabelle_ttl @ A) @ B) @ ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((((tLList1614408749tllist @ E) @ B) @ A) @ P4) @ G1) @ G212) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.91/1.54 thf(fact_94_tllist_Omap__sel_I1_J, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),F1:(A > C),F2:(B > D)]: (((((tLList1968894004s_TNil @ A) @ B) @ A2) => ((((tLList2110128105rminal @ C) @ D) @ (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ A2)) = (F2 @ (((tLList2110128105rminal @ A) @ B) @ A2))))))).
% 2.91/1.54 thf(fact_95_terminal__def, axiom, (! [B:$tType,A:$tType]: ((((tLList2110128105rminal @ A) @ B) = (((((tLList200813139tllist @ B) @ B) @ A) @ (^ [X13:B]: (X13))) @ (^ [X_dummy:A]: ((tLList1825092077minal0 @ (((tLList446370796tllist @ A) @ B) > B))))))))).
% 2.91/1.54 thf(fact_96_tllist_Osel_I2_J, axiom, (! [A:$tType,Aa:$tType,X21:Aa,X22:((tLList446370796tllist @ Aa) @ A)]: (((((tLList2110128105rminal @ Aa) @ A) @ ((((tLList1992840728_TCons @ Aa) @ A) @ X21) @ X22)) = ((tLList1825092077minal0 @ (((tLList446370796tllist @ Aa) @ A) > A)) @ X22))))).
% 2.91/1.54 thf(fact_97_terminal0__terminal, axiom, (! [B:$tType,A:$tType]: (((tLList1825092077minal0 @ (((tLList446370796tllist @ A) @ B) > B)) = ((tLList2110128105rminal @ A) @ B))))).
% 2.91/1.54 thf(fact_98_set2__tllist__induct, axiom, (! [A:$tType,B:$tType,X:A,Xs:((tLList446370796tllist @ B) @ A),P:(A > (((tLList446370796tllist @ B) @ A) > $o))]: (((((member @ A) @ X) @ (((tLList457864275tllist @ B) @ A) @ Xs)) => ((! [Xs3:((tLList446370796tllist @ B) @ A)]: (((((tLList1968894004s_TNil @ B) @ A) @ Xs3) => ((P @ (((tLList2110128105rminal @ B) @ A) @ Xs3)) @ Xs3)))) => ((! [Xs3:((tLList446370796tllist @ B) @ A),Y5:A]: (((~ ((((tLList1968894004s_TNil @ B) @ A) @ Xs3))) => ((((member @ A) @ Y5) @ (((tLList457864275tllist @ B) @ A) @ (((tLList_Mirabelle_ttl @ B) @ A) @ Xs3))) => (((P @ Y5) @ (((tLList_Mirabelle_ttl @ B) @ A) @ Xs3)) => ((P @ Y5) @ Xs3)))))) => ((P @ X) @ Xs))))))).
% 2.91/1.54 thf(fact_99_tllist__set__induct, axiom, (! [B:$tType,A:$tType,X:A,Xs:((tLList446370796tllist @ A) @ B),P:(A > (((tLList446370796tllist @ A) @ B) > $o))]: (((((member @ A) @ X) @ (((tLList1719791291e_tset @ A) @ B) @ Xs)) => ((! [Xs3:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs3))) => ((P @ (((tLList_Mirabelle_thd @ A) @ B) @ Xs3)) @ Xs3)))) => ((! [Xs3:((tLList446370796tllist @ A) @ B),Y5:A]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs3))) => ((((member @ A) @ Y5) @ (((tLList1719791291e_tset @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Xs3))) => (((P @ Y5) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Xs3)) => ((P @ Y5) @ Xs3)))))) => ((P @ X) @ Xs))))))).
% 2.91/1.54 thf(fact_100_tconcat__TCons, axiom, (! [B:$tType,A:$tType,B4:B,A2:(coinductive_llist @ A),Tr:((tLList446370796tllist @ (coinductive_llist @ A)) @ B)]: ((((((tLList365522113concat @ B) @ A) @ B4) @ ((((tLList1992840728_TCons @ (coinductive_llist @ A)) @ B) @ A2) @ Tr)) = ((((tLList98099029ppendt @ A) @ B) @ A2) @ ((((tLList365522113concat @ B) @ A) @ B4) @ Tr)))))).
% 2.91/1.54 thf(fact_101_tconcat_H__def, axiom, (! [A:$tType,B:$tType]: ((((tLList1329345514concat @ B) @ A) = (^ [B6:(product_unit > B)]: ((((tLList365522113concat @ B) @ A) @ (B6 @ product_Unity)))))))).
% 2.91/1.54 thf(fact_102_tllist_Orel__cong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,X:((tLList446370796tllist @ A) @ B),Ya:((tLList446370796tllist @ A) @ B),Y:((tLList446370796tllist @ C) @ D),Xa:((tLList446370796tllist @ C) @ D),R1:(A > (C > $o)),R1a:(A > (C > $o)),R2:(B > (D > $o)),R2a:(B > (D > $o))]: (((X = Ya) => ((Y = Xa) => ((! [Z12:A,Y12:C]: (((((member @ A) @ Z12) @ (((tLList1719791291e_tset @ A) @ B) @ Ya)) => ((((member @ C) @ Y12) @ (((tLList1719791291e_tset @ C) @ D) @ Xa)) => (((R1 @ Z12) @ Y12) = ((R1a @ Z12) @ Y12)))))) => ((! [Z22:B,Y23:D]: (((((member @ B) @ Z22) @ (((tLList457864275tllist @ A) @ B) @ Ya)) => ((((member @ D) @ Y23) @ (((tLList457864275tllist @ C) @ D) @ Xa)) => (((R2 @ Z22) @ Y23) = ((R2a @ Z22) @ Y23)))))) => (((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X) @ Y) = ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ Ya) @ Xa))))))))).
% 2.91/1.54 thf(fact_103_tllist_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X:((tLList446370796tllist @ A) @ B),Y:((tLList446370796tllist @ C) @ D),R1a:(A > (C > $o)),R2a:(B > (D > $o))]: ((((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1) @ R2) @ X) @ Y) => ((! [Z12:A,Y12:C]: (((((member @ A) @ Z12) @ (((tLList1719791291e_tset @ A) @ B) @ X)) => ((((member @ C) @ Y12) @ (((tLList1719791291e_tset @ C) @ D) @ Y)) => (((R1 @ Z12) @ Y12) => ((R1a @ Z12) @ Y12)))))) => ((! [Z22:B,Y23:D]: (((((member @ B) @ Z22) @ (((tLList457864275tllist @ A) @ B) @ X)) => ((((member @ D) @ Y23) @ (((tLList457864275tllist @ C) @ D) @ Y)) => (((R2 @ Z22) @ Y23) => ((R2a @ Z22) @ Y23)))))) => ((((((((tLList1380991092t_all2 @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ X) @ Y))))))).
% 2.91/1.54 thf(fact_104_tllist_Orel__refl__strong, axiom, (! [B:$tType,A:$tType,X:((tLList446370796tllist @ A) @ B),R1a:(A > (A > $o)),R2a:(B > (B > $o))]: (((! [Z12:A]: (((((member @ A) @ Z12) @ (((tLList1719791291e_tset @ A) @ B) @ X)) => ((R1a @ Z12) @ Z12)))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ (((tLList457864275tllist @ A) @ B) @ X)) => ((R2a @ Z22) @ Z22)))) => ((((((((tLList1380991092t_all2 @ A) @ A) @ B) @ B) @ R1a) @ R2a) @ X) @ X)))))).
% 2.91/1.54 thf(fact_105_tllist_Omap__cong, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X:((tLList446370796tllist @ A) @ B),Ya:((tLList446370796tllist @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G2:(B > D)]: (((X = Ya) => ((! [Z12:A]: (((((member @ A) @ Z12) @ (((tLList1719791291e_tset @ A) @ B) @ Ya)) => ((F1 @ Z12) = (G1 @ Z12))))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ (((tLList457864275tllist @ A) @ B) @ Ya)) => ((F2 @ Z22) = (G2 @ Z22))))) => ((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ G1) @ G2) @ Ya)))))))).
% 2.91/1.54 thf(fact_106_tllist_Omap__cong0, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X:((tLList446370796tllist @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G2:(B > D)]: (((! [Z12:A]: (((((member @ A) @ Z12) @ (((tLList1719791291e_tset @ A) @ B) @ X)) => ((F1 @ Z12) = (G1 @ Z12))))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ (((tLList457864275tllist @ A) @ B) @ X)) => ((F2 @ Z22) = (G2 @ Z22))))) => ((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ G1) @ G2) @ X))))))).
% 2.91/1.54 thf(fact_107_tllist_Oinj__map__strong, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,X:((tLList446370796tllist @ A) @ B),Xa:((tLList446370796tllist @ A) @ B),F1:(A > C),F1a:(A > C),F2:(B > D),F2a:(B > D)]: (((! [Z12:A,Z1a:A]: (((((member @ A) @ Z12) @ (((tLList1719791291e_tset @ A) @ B) @ X)) => ((((member @ A) @ Z1a) @ (((tLList1719791291e_tset @ A) @ B) @ Xa)) => (((F1 @ Z12) = (F1a @ Z1a)) => (Z12 = Z1a)))))) => ((! [Z22:B,Z2a:B]: (((((member @ B) @ Z22) @ (((tLList457864275tllist @ A) @ B) @ X)) => ((((member @ B) @ Z2a) @ (((tLList457864275tllist @ A) @ B) @ Xa)) => (((F2 @ Z22) = (F2a @ Z2a)) => (Z22 = Z2a)))))) => (((((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1) @ F2) @ X) = (((((((tLList1669959861e_tmap @ A) @ C) @ B) @ D) @ F1a) @ F2a) @ Xa)) => (X = Xa))))))).
% 2.91/1.54 thf(fact_108_tllist_Opred__mono__strong, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P2:(B > $o),X:((tLList446370796tllist @ A) @ B),P1a:(A > $o),P2a:(B > $o)]: (((((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ X) => ((! [Z12:A]: (((((member @ A) @ Z12) @ (((tLList1719791291e_tset @ A) @ B) @ X)) => ((P1 @ Z12) => (P1a @ Z12))))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ (((tLList457864275tllist @ A) @ B) @ X)) => ((P2 @ Z22) => (P2a @ Z22))))) => (((((tLList11265572tllist @ A) @ B) @ P1a) @ P2a) @ X))))))).
% 2.91/1.54 thf(fact_109_tllist_Opred__cong, axiom, (! [B:$tType,A:$tType,X:((tLList446370796tllist @ A) @ B),Ya:((tLList446370796tllist @ A) @ B),P1:(A > $o),P1a:(A > $o),P2:(B > $o),P2a:(B > $o)]: (((X = Ya) => ((! [Z12:A]: (((((member @ A) @ Z12) @ (((tLList1719791291e_tset @ A) @ B) @ Ya)) => ((P1 @ Z12) = (P1a @ Z12))))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ (((tLList457864275tllist @ A) @ B) @ Ya)) => ((P2 @ Z22) = (P2a @ Z22))))) => ((((((tLList11265572tllist @ A) @ B) @ P1) @ P2) @ X) = (((((tLList11265572tllist @ A) @ B) @ P1a) @ P2a) @ Ya)))))))).
% 2.91/1.54 thf(fact_110_tllist_Oset__cases_I1_J, axiom, (! [B:$tType,A:$tType,E2:A,A2:((tLList446370796tllist @ A) @ B)]: (((((member @ A) @ E2) @ (((tLList1719791291e_tset @ A) @ B) @ A2)) => ((! [Z22:((tLList446370796tllist @ A) @ B)]: ((A2 != ((((tLList1992840728_TCons @ A) @ B) @ E2) @ Z22)))) => (~ ((! [Z12:A,Z22:((tLList446370796tllist @ A) @ B)]: (((A2 = ((((tLList1992840728_TCons @ A) @ B) @ Z12) @ Z22)) => (~ ((((member @ A) @ E2) @ (((tLList1719791291e_tset @ A) @ B) @ Z22)))))))))))))).
% 2.91/1.54 thf(fact_111_tllist_Oset__induct_I1_J, axiom, (! [B:$tType,A:$tType,X:A,A2:((tLList446370796tllist @ A) @ B),P:(A > (((tLList446370796tllist @ A) @ B) > $o))]: (((((member @ A) @ X) @ (((tLList1719791291e_tset @ A) @ B) @ A2)) => ((! [Z12:A,Z22:((tLList446370796tllist @ A) @ B)]: (((P @ Z12) @ ((((tLList1992840728_TCons @ A) @ B) @ Z12) @ Z22)))) => ((! [Z12:A,Z22:((tLList446370796tllist @ A) @ B),Xa2:A]: (((((member @ A) @ Xa2) @ (((tLList1719791291e_tset @ A) @ B) @ Z22)) => (((P @ Xa2) @ Z22) => ((P @ Xa2) @ ((((tLList1992840728_TCons @ A) @ B) @ Z12) @ Z22)))))) => ((P @ X) @ A2))))))).
% 2.91/1.54 thf(fact_112_tllist_Oset__intros_I2_J, axiom, (! [B:$tType,A:$tType,X:A,A22:((tLList446370796tllist @ A) @ B),A1:A]: (((((member @ A) @ X) @ (((tLList1719791291e_tset @ A) @ B) @ A22)) => (((member @ A) @ X) @ (((tLList1719791291e_tset @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ A1) @ A22))))))).
% 2.91/1.54 thf(fact_113_tllist_Oset__intros_I1_J, axiom, (! [B:$tType,A:$tType,A1:A,A22:((tLList446370796tllist @ A) @ B)]: ((((member @ A) @ A1) @ (((tLList1719791291e_tset @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ A1) @ A22)))))).
% 2.91/1.54 thf(fact_114_in__tset__ttlD, axiom, (! [B:$tType,A:$tType,X:A,Xs:((tLList446370796tllist @ A) @ B)]: (((((member @ A) @ X) @ (((tLList1719791291e_tset @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Xs))) => (((member @ A) @ X) @ (((tLList1719791291e_tset @ A) @ B) @ Xs)))))).
% 2.91/1.54 thf(fact_115_tllist_Oset__intros_I3_J, axiom, (! [A:$tType,B:$tType,Aa2:B]: ((((member @ B) @ Aa2) @ (((tLList457864275tllist @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ Aa2)))))).
% 2.91/1.54 thf(fact_116_tllist_Osimps_I23_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList457864275tllist @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = (((tLList457864275tllist @ A) @ B) @ X22))))).
% 2.91/1.54 thf(fact_117_tllist_Oset__intros_I4_J, axiom, (! [B:$tType,A:$tType,Xc:B,A2a:((tLList446370796tllist @ A) @ B),A1a:A]: (((((member @ B) @ Xc) @ (((tLList457864275tllist @ A) @ B) @ A2a)) => (((member @ B) @ Xc) @ (((tLList457864275tllist @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ A1a) @ A2a))))))).
% 2.91/1.54 thf(fact_118_tllist_Odisc__eq__case_I2_J, axiom, (! [B:$tType,A:$tType,Tllist:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Tllist))) = ((((((tLList200813139tllist @ B) @ $o) @ A) @ (^ [Uu:B]: ($false))) @ (^ [Uu:A,Uv:((tLList446370796tllist @ A) @ B)]: ($true))) @ Tllist))))).
% 2.91/1.54 thf(fact_119_tllist_Odisc__eq__case_I1_J, axiom, (! [B:$tType,A:$tType]: ((((tLList1968894004s_TNil @ A) @ B) = (((((tLList200813139tllist @ B) @ $o) @ A) @ (^ [Uu:B]: ($true))) @ (^ [Uu:A,Uv:((tLList446370796tllist @ A) @ B)]: ($false))))))).
% 2.91/1.54 thf(fact_120_tllist_Oset__sel_I2_J, axiom, (! [B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),X:A]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => ((((member @ A) @ X) @ (((tLList1719791291e_tset @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ A2))) => (((member @ A) @ X) @ (((tLList1719791291e_tset @ A) @ B) @ A2))))))).
% 2.91/1.54 thf(fact_121_tllist_Oset__sel_I1_J, axiom, (! [B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => (((member @ A) @ (((tLList_Mirabelle_thd @ A) @ B) @ A2)) @ (((tLList1719791291e_tset @ A) @ B) @ A2)))))).
% 2.91/1.54 thf(fact_122_tllist_Oset__sel_I3_J, axiom, (! [B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ A2) => (((member @ B) @ (((tLList2110128105rminal @ A) @ B) @ A2)) @ (((tLList457864275tllist @ A) @ B) @ A2)))))).
% 2.91/1.54 thf(fact_123_tllist_Oset__cases_I2_J, axiom, (! [B:$tType,A:$tType,E2:B,A2:((tLList446370796tllist @ A) @ B)]: (((((member @ B) @ E2) @ (((tLList457864275tllist @ A) @ B) @ A2)) => ((A2 != (((tLList57907754e_TNil @ B) @ A) @ E2)) => (~ ((! [Z12:A,Z22:((tLList446370796tllist @ A) @ B)]: (((A2 = ((((tLList1992840728_TCons @ A) @ B) @ Z12) @ Z22)) => (~ ((((member @ B) @ E2) @ (((tLList457864275tllist @ A) @ B) @ Z22)))))))))))))).
% 2.91/1.54 thf(fact_124_tllist_Oset__induct_I2_J, axiom, (! [A:$tType,Aa:$tType,X:A,A2:((tLList446370796tllist @ Aa) @ A),P:(A > (((tLList446370796tllist @ Aa) @ A) > $o))]: (((((member @ A) @ X) @ (((tLList457864275tllist @ Aa) @ A) @ A2)) => ((! [Z4:A]: (((P @ Z4) @ (((tLList57907754e_TNil @ A) @ Aa) @ Z4)))) => ((! [Z12:Aa,Z22:((tLList446370796tllist @ Aa) @ A),Xb:A]: (((((member @ A) @ Xb) @ (((tLList457864275tllist @ Aa) @ A) @ Z22)) => (((P @ Xb) @ Z22) => ((P @ Xb) @ ((((tLList1992840728_TCons @ Aa) @ A) @ Z12) @ Z22)))))) => ((P @ X) @ A2))))))).
% 2.91/1.54 thf(fact_125_tllist_Oset__sel_I4_J, axiom, (! [B:$tType,A:$tType,A2:((tLList446370796tllist @ A) @ B),Xc:B]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ A2))) => ((((member @ B) @ Xc) @ (((tLList457864275tllist @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ A2))) => (((member @ B) @ Xc) @ (((tLList457864275tllist @ A) @ B) @ A2))))))).
% 2.91/1.54 thf(fact_126_tconcat_H__code_I2_J, axiom, (! [B:$tType,C:$tType,B4:(product_unit > B),A2:(coinductive_llist @ C),Tr:((tLList446370796tllist @ (coinductive_llist @ C)) @ B)]: ((((((tLList1329345514concat @ B) @ C) @ B4) @ ((((tLList1992840728_TCons @ (coinductive_llist @ C)) @ B) @ A2) @ Tr)) = ((((tLList98099029ppendt @ C) @ B) @ A2) @ ((((tLList1329345514concat @ B) @ C) @ B4) @ Tr)))))).
% 2.91/1.54 thf(fact_127_unit__abs__eta__conv, axiom, (! [A:$tType,F3:(product_unit > A)]: (((^ [U:product_unit]: ((F3 @ product_Unity))) = F3)))).
% 2.91/1.54 thf(fact_128_is__TNil__tfilter, axiom, (! [B:$tType,A:$tType,Y:B,P:(A > $o),Xs:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ (((((tLList1813626245filter @ B) @ A) @ Y) @ P) @ Xs)) = (! [X2:A]: (((((member @ A) @ X2) @ (((tLList1719791291e_tset @ A) @ B) @ Xs)) => (~ ((P @ X2)))))))))).
% 2.91/1.54 thf(fact_129_old_Ounit_Oexhaust, axiom, (! [Y:product_unit]: ((Y = product_Unity)))).
% 2.91/1.54 thf(fact_130_old_Ounit_Oinducts, axiom, (! [P:(product_unit > $o),Unit:product_unit]: (((P @ product_Unity) => (P @ Unit))))).
% 2.91/1.54 thf(fact_131_unit__all__impI, axiom, (! [P:(product_unit > $o),Q:(product_unit > $o)]: ((((P @ product_Unity) => (Q @ product_Unity)) => (! [X6:product_unit]: (((P @ X6) => (Q @ X6)))))))).
% 2.91/1.54 thf(fact_132_tfilter__TNil, axiom, (! [A:$tType,B:$tType,B5:B,P:(A > $o),B4:B]: (((((((tLList1813626245filter @ B) @ A) @ B5) @ P) @ (((tLList57907754e_TNil @ B) @ A) @ B4)) = (((tLList57907754e_TNil @ B) @ A) @ B4))))).
% 2.91/1.54 thf(fact_133_tfilter__TCons, axiom, (! [B:$tType,A:$tType,P:(A > $o),A2:A,B4:B,Tr:((tLList446370796tllist @ A) @ B)]: ((((P @ A2) => ((((((tLList1813626245filter @ B) @ A) @ B4) @ P) @ ((((tLList1992840728_TCons @ A) @ B) @ A2) @ Tr)) = ((((tLList1992840728_TCons @ A) @ B) @ A2) @ (((((tLList1813626245filter @ B) @ A) @ B4) @ P) @ Tr)))) & ((~ ((P @ A2))) => ((((((tLList1813626245filter @ B) @ A) @ B4) @ P) @ ((((tLList1992840728_TCons @ A) @ B) @ A2) @ Tr)) = (((((tLList1813626245filter @ B) @ A) @ B4) @ P) @ Tr))))))).
% 2.91/1.54 thf(fact_134_eq__sym__Unity__conv, axiom, (! [X:$o]: (((X = (product_Unity = product_Unity)) = X)))).
% 2.91/1.54 thf(fact_135_old_Ounit_Orec, axiom, (! [T:$tType,F1:T]: (((((product_rec_unit @ T) @ F1) @ product_Unity) = F1)))).
% 2.91/1.54 thf(fact_136_default__unit__def, axiom, ((default_default @ product_unit) = product_Unity)).
% 2.91/1.54 thf(fact_137_tfilter_H__def, axiom, (! [A:$tType,B:$tType]: ((((tLList1122525870filter @ B) @ A) = (^ [B6:(product_unit > B)]: ((((tLList1813626245filter @ B) @ A) @ (B6 @ product_Unity)))))))).
% 2.91/1.54 thf(fact_138_tfilter__code, axiom, (! [B:$tType,A:$tType]: ((((tLList1813626245filter @ A) @ B) = (^ [B6:A]: ((((tLList1122525870filter @ A) @ B) @ (^ [Uu:product_unit]: (B6))))))))).
% 2.91/1.54 thf(fact_139_tfilter_H__code_I1_J, axiom, (! [A:$tType,B:$tType,B5:(product_unit > B),P:(A > $o),B4:B]: (((((((tLList1122525870filter @ B) @ A) @ B5) @ P) @ (((tLList57907754e_TNil @ B) @ A) @ B4)) = (((tLList57907754e_TNil @ B) @ A) @ B4))))).
% 2.91/1.54 thf(fact_140_tfilter_H__code_I2_J, axiom, (! [B:$tType,A:$tType,P:(A > $o),A2:A,B5:(product_unit > B),Tr:((tLList446370796tllist @ A) @ B)]: ((((P @ A2) => ((((((tLList1122525870filter @ B) @ A) @ B5) @ P) @ ((((tLList1992840728_TCons @ A) @ B) @ A2) @ Tr)) = ((((tLList1992840728_TCons @ A) @ B) @ A2) @ (((((tLList1122525870filter @ B) @ A) @ B5) @ P) @ Tr)))) & ((~ ((P @ A2))) => ((((((tLList1122525870filter @ B) @ A) @ B5) @ P) @ ((((tLList1992840728_TCons @ A) @ B) @ A2) @ Tr)) = (((((tLList1122525870filter @ B) @ A) @ B5) @ P) @ Tr))))))).
% 2.91/1.54 thf(fact_141_tllist_Opred__set, axiom, (! [B:$tType,A:$tType]: ((((tLList11265572tllist @ A) @ B) = (^ [P12:(A > $o),P22:(B > $o),X2:((tLList446370796tllist @ A) @ B)]: (((! [Y2:A]: (((((member @ A) @ Y2) @ (((tLList1719791291e_tset @ A) @ B) @ X2)) => (P12 @ Y2)))) & (! [Y2:B]: (((((member @ B) @ Y2) @ (((tLList457864275tllist @ A) @ B) @ X2)) => (P22 @ Y2))))))))))).
% 2.91/1.54 thf(fact_142_old_Ounit_Ocase, axiom, (! [A:$tType,F3:A]: (((((product_case_unit @ A) @ F3) @ product_Unity) = F3)))).
% 2.91/1.54 thf(fact_143_lappendt__LCons, axiom, (! [B:$tType,A:$tType,X:A,Xs:(coinductive_llist @ A),Tr:((tLList446370796tllist @ A) @ B)]: ((((((tLList98099029ppendt @ A) @ B) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ Tr) = ((((tLList1992840728_TCons @ A) @ B) @ X) @ ((((tLList98099029ppendt @ A) @ B) @ Xs) @ Tr)))))).
% 2.91/1.54 thf(fact_144_terminal__lappendt__lfinite, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),Ys:((tLList446370796tllist @ A) @ B)]: ((((coinductive_lfinite @ A) @ Xs) => ((((tLList2110128105rminal @ A) @ B) @ ((((tLList98099029ppendt @ A) @ B) @ Xs) @ Ys)) = (((tLList2110128105rminal @ A) @ B) @ Ys)))))).
% 2.91/1.54 thf(fact_145_unit_Ocase__distrib, axiom, (! [A:$tType,B:$tType,H:(A > B),F3:A,Unit:product_unit]: (((H @ (((product_case_unit @ A) @ F3) @ Unit)) = (((product_case_unit @ B) @ (H @ F3)) @ Unit))))).
% 2.91/1.54 thf(fact_146_case__unit__Unity, axiom, (! [A:$tType]: (((product_case_unit @ A) = (^ [F4:A,U:product_unit]: (F4)))))).
% 2.91/1.54 thf(fact_147_tfilter__empty__conv, axiom, (! [A:$tType,B:$tType,Y:B,P:(A > $o),Xs:((tLList446370796tllist @ A) @ B),Y6:B]: ((((((((tLList1813626245filter @ B) @ A) @ Y) @ P) @ Xs) = (((tLList57907754e_TNil @ B) @ A) @ Y6)) = ((! [X2:A]: (((((member @ A) @ X2) @ (((tLList1719791291e_tset @ A) @ B) @ Xs)) => (~ ((P @ X2)))))) & ((((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) => ((((tLList2110128105rminal @ A) @ B) @ Xs) = Y6)) & ((~ (((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)))) => (Y = Y6)))))))).
% 2.91/1.54 thf(fact_148_terminal__tmap, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B),F3:(A > D),G:(B > C)]: ((((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) => ((((tLList2110128105rminal @ D) @ C) @ (((((((tLList1669959861e_tmap @ A) @ D) @ B) @ C) @ F3) @ G) @ Xs)) = (G @ (((tLList2110128105rminal @ A) @ B) @ Xs))))))).
% 2.91/1.54 thf(fact_149_tfilter__eq__TConsD, axiom, (! [B:$tType,A:$tType,A2:B,P:(A > $o),Ys:((tLList446370796tllist @ A) @ B),X:A,Xs:((tLList446370796tllist @ A) @ B)]: ((((((((tLList1813626245filter @ B) @ A) @ A2) @ P) @ Ys) = ((((tLList1992840728_TCons @ A) @ B) @ X) @ Xs)) => (? [Us:(coinductive_llist @ A),Vs:((tLList446370796tllist @ A) @ B)]: (((Ys = ((((tLList98099029ppendt @ A) @ B) @ Us) @ ((((tLList1992840728_TCons @ A) @ B) @ X) @ Vs))) & (((coinductive_lfinite @ A) @ Us) & ((! [X6:A]: (((((member @ A) @ X6) @ ((coinductive_lset @ A) @ Us)) => (~ ((P @ X6)))))) & ((P @ X) & (Xs = (((((tLList1813626245filter @ B) @ A) @ A2) @ P) @ Vs)))))))))))).
% 2.91/1.54 thf(fact_150_llist__of__tllist__TCons, axiom, (! [B:$tType,A:$tType,Xa:A,X:((tLList446370796tllist @ A) @ B)]: (((((tLList798109904tllist @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ Xa) @ X)) = (((coinductive_LCons @ A) @ Xa) @ (((tLList798109904tllist @ A) @ B) @ X)))))).
% 2.91/1.54 thf(fact_151_lset__llist__of__tllist, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: ((((coinductive_lset @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) = (((tLList1719791291e_tset @ A) @ B) @ Xs))))).
% 2.91/1.54 thf(fact_152_is__TNil__tfinite, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ Xs) => ((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)))))).
% 2.91/1.54 thf(fact_153_tfinite__induct, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B),P:(((tLList446370796tllist @ A) @ B) > $o)]: ((((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) => ((! [Y5:B]: ((P @ (((tLList57907754e_TNil @ B) @ A) @ Y5)))) => ((! [X3:A,Xs3:((tLList446370796tllist @ A) @ B)]: ((((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs3)) => ((P @ Xs3) => (P @ ((((tLList1992840728_TCons @ A) @ B) @ X3) @ Xs3)))))) => (P @ Xs))))))).
% 2.91/1.54 thf(fact_154_tset__lappendt__lfinite, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),Ys:((tLList446370796tllist @ A) @ B)]: ((((coinductive_lfinite @ A) @ Xs) => ((((tLList1719791291e_tset @ A) @ B) @ ((((tLList98099029ppendt @ A) @ B) @ Xs) @ Ys)) = (((sup_sup @ (set @ A)) @ ((coinductive_lset @ A) @ Xs)) @ (((tLList1719791291e_tset @ A) @ B) @ Ys))))))).
% 2.91/1.54 thf(fact_155_tfinite__tappend, axiom, (! [B:$tType,C:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ C),F3:(C > ((tLList446370796tllist @ A) @ B))]: ((((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ (((((tLList192138471append @ A) @ C) @ B) @ Xs) @ F3))) = (((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ C) @ Xs)) & ((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ (F3 @ (((tLList2110128105rminal @ A) @ C) @ Xs))))))))).
% 2.91/1.54 thf(fact_156_terminal__tappend, axiom, (! [A:$tType,B:$tType,Xs:((tLList446370796tllist @ B) @ A),F3:(A > ((tLList446370796tllist @ B) @ A))]: (((((coinductive_lfinite @ B) @ (((tLList798109904tllist @ B) @ A) @ Xs)) => ((((tLList2110128105rminal @ B) @ A) @ (((((tLList192138471append @ B) @ A) @ A) @ Xs) @ F3)) = (((tLList2110128105rminal @ B) @ A) @ (F3 @ (((tLList2110128105rminal @ B) @ A) @ Xs))))) & ((~ (((coinductive_lfinite @ B) @ (((tLList798109904tllist @ B) @ A) @ Xs)))) => ((((tLList2110128105rminal @ B) @ A) @ (((((tLList192138471append @ B) @ A) @ A) @ Xs) @ F3)) = (((tLList2110128105rminal @ B) @ A) @ Xs))))))).
% 2.91/1.54 thf(fact_157_tappend__TNil2, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((((((tLList192138471append @ A) @ B) @ B) @ Xs) @ ((tLList57907754e_TNil @ B) @ A)) = Xs)))).
% 2.91/1.54 thf(fact_158_tappend__TNil, axiom, (! [A:$tType,B:$tType,C:$tType,B4:C,F3:(C > ((tLList446370796tllist @ A) @ B))]: (((((((tLList192138471append @ A) @ C) @ B) @ (((tLList57907754e_TNil @ C) @ A) @ B4)) @ F3) = (F3 @ B4))))).
% 2.91/1.54 thf(fact_159_tappend__TCons, axiom, (! [B:$tType,A:$tType,C:$tType,A2:A,Tr:((tLList446370796tllist @ A) @ C),F3:(C > ((tLList446370796tllist @ A) @ B))]: (((((((tLList192138471append @ A) @ C) @ B) @ ((((tLList1992840728_TCons @ A) @ C) @ A2) @ Tr)) @ F3) = ((((tLList1992840728_TCons @ A) @ B) @ A2) @ (((((tLList192138471append @ A) @ C) @ B) @ Tr) @ F3)))))).
% 2.91/1.54 thf(fact_160_tappend__assoc, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,Xs:((tLList446370796tllist @ A) @ D),F3:(D > ((tLList446370796tllist @ A) @ C)),G:(C > ((tLList446370796tllist @ A) @ B))]: (((((((tLList192138471append @ A) @ C) @ B) @ (((((tLList192138471append @ A) @ D) @ C) @ Xs) @ F3)) @ G) = (((((tLList192138471append @ A) @ D) @ B) @ Xs) @ (^ [B6:D]: ((((((tLList192138471append @ A) @ C) @ B) @ (F3 @ B6)) @ G)))))))).
% 2.91/1.54 thf(fact_161_tappend__inf, axiom, (! [C:$tType,B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B),F3:(B > ((tLList446370796tllist @ A) @ C))]: (((~ (((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)))) => ((((((tLList192138471append @ A) @ B) @ C) @ Xs) @ F3) = ((((tLList222516140_tcast @ A) @ B) @ C) @ Xs)))))).
% 2.91/1.54 thf(fact_162_Collect__disj__eq, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X2:A]: (((P @ X2) | (Q @ X2))))) = (((sup_sup @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.91/1.54 thf(fact_163_Un__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B8:(set @ A)]: (((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A5) | (((member @ A) @ X2) @ B8))))))))))).
% 2.91/1.54 thf(fact_164_lhd__llist__of__tllist, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs))) => (((coinductive_lhd @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) = (((tLList_Mirabelle_thd @ A) @ B) @ Xs)))))).
% 2.91/1.54 thf(fact_165_terminal__tinfinite, axiom, (! [A:$tType,B:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((~ (((coinductive_lfinite @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)))) => ((((tLList2110128105rminal @ A) @ B) @ Xs) = (undefined @ B)))))).
% 2.91/1.54 thf(fact_166_llist__of__tllist__inverse, axiom, (! [B:$tType,A:$tType,B4:((tLList446370796tllist @ A) @ B)]: ((((((tLList1672613558_llist @ B) @ A) @ (((tLList2110128105rminal @ A) @ B) @ B4)) @ (((tLList798109904tllist @ A) @ B) @ B4)) = B4)))).
% 2.91/1.54 thf(fact_167_tllist__of__llist__inject, axiom, (! [A:$tType,B:$tType,B4:B,Xs:(coinductive_llist @ A),C2:B,Ys:(coinductive_llist @ A)]: (((((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs) = ((((tLList1672613558_llist @ B) @ A) @ C2) @ Ys)) = ((Xs = Ys) & (((coinductive_lfinite @ A) @ Ys) => (B4 = C2))))))).
% 2.91/1.54 thf(fact_168_tllist__of__llist__inverse, axiom, (! [B:$tType,A:$tType,B4:B,Xs:(coinductive_llist @ A)]: (((((tLList798109904tllist @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = Xs)))).
% 2.91/1.54 thf(fact_169_tllist__of__llist__LCons, axiom, (! [B:$tType,A:$tType,B4:B,Xa:A,X:(coinductive_llist @ A)]: ((((((tLList1672613558_llist @ B) @ A) @ B4) @ (((coinductive_LCons @ A) @ Xa) @ X)) = ((((tLList1992840728_TCons @ A) @ B) @ Xa) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ X)))))).
% 2.91/1.54 thf(fact_170_terminal__tllist__of__llist__lfinite, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),B4:B]: ((((coinductive_lfinite @ A) @ Xs) => ((((tLList2110128105rminal @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = B4))))).
% 2.91/1.54 thf(fact_171_tset__tllist__of__llist, axiom, (! [B:$tType,A:$tType,B4:B,Xs:(coinductive_llist @ A)]: (((((tLList1719791291e_tset @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = ((coinductive_lset @ A) @ Xs))))).
% 2.91/1.54 thf(fact_172_thd__tllist__of__llist, axiom, (! [B:$tType,A:$tType,B4:B,Xs:(coinductive_llist @ A)]: (((((tLList_Mirabelle_thd @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = ((coinductive_lhd @ A) @ Xs))))).
% 2.91/1.54 thf(fact_173_terminal__tllist__of__llist, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ B),Y:A]: (((((coinductive_lfinite @ B) @ Xs) => ((((tLList2110128105rminal @ B) @ A) @ ((((tLList1672613558_llist @ A) @ B) @ Y) @ Xs)) = Y)) & ((~ (((coinductive_lfinite @ B) @ Xs))) => ((((tLList2110128105rminal @ B) @ A) @ ((((tLList1672613558_llist @ A) @ B) @ Y) @ Xs)) = (undefined @ A))))))).
% 2.91/1.54 thf(fact_174_tllist__of__llist__cong, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),Xs4:(coinductive_llist @ A),B4:B,B5:B]: (((Xs = Xs4) => ((((coinductive_lfinite @ A) @ Xs4) => (B4 = B5)) => (((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs) = ((((tLList1672613558_llist @ B) @ A) @ B5) @ Xs4))))))).
% 2.91/1.54 thf(fact_175_llist__of__tllist_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs))) => (((coinductive_lhd @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) = ((((((tLList200813139tllist @ B) @ A) @ A) @ (^ [X2:B]: ((undefined @ A)))) @ (^ [X2:A,Xs5:((tLList446370796tllist @ A) @ B)]: (X2))) @ Xs)))))).
% 2.91/1.54 thf(fact_176_llist__of__tllist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs))) => ((((tLList798109904tllist @ A) @ B) @ Xs) = (((coinductive_LCons @ A) @ ((((((tLList200813139tllist @ B) @ A) @ A) @ (^ [X2:B]: ((undefined @ A)))) @ (^ [X2:A,Xs5:((tLList446370796tllist @ A) @ B)]: (X2))) @ Xs)) @ ((((((tLList200813139tllist @ B) @ (coinductive_llist @ A)) @ A) @ (^ [X2:B]: ((undefined @ (coinductive_llist @ A))))) @ (^ [X2:A]: (((tLList798109904tllist @ A) @ B)))) @ Xs))))))).
% 2.91/1.54 thf(fact_177_thd__TNil, axiom, (! [B:$tType,A:$tType,B4:B]: (((((tLList_Mirabelle_thd @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ B4)) = (undefined @ A))))).
% 2.91/1.54 thf(fact_178_thd__def, axiom, (! [B:$tType,A:$tType]: ((((tLList_Mirabelle_thd @ A) @ B) = (((((tLList200813139tllist @ B) @ A) @ A) @ (^ [X_dummy:B]: ((undefined @ A)))) @ (^ [X213:A,X223:((tLList446370796tllist @ A) @ B)]: (X213))))))).
% 2.91/1.54 thf(fact_179_terminal0_Oraw__induct, axiom, (! [C:$tType,D:$tType,P:(((tLList446370796tllist @ C) @ D) > (D > $o)),Xs:((tLList446370796tllist @ C) @ D),Y:D]: (((! [Terminal0:(((tLList446370796tllist @ C) @ D) > D)]: (((! [X6:((tLList446370796tllist @ C) @ D)]: ((((Terminal0 @ X6) != (undefined @ D)) => ((P @ X6) @ (Terminal0 @ X6))))) => (! [Xs3:((tLList446370796tllist @ C) @ D),Xsa:D]: (((((((tLList1968894004s_TNil @ C) @ D) @ Xs3) => (((((((tLList200813139tllist @ D) @ D) @ C) @ (id @ D)) @ (undefined @ (C > (((tLList446370796tllist @ C) @ D) > D)))) @ Xs3) = Xsa)) & ((~ ((((tLList1968894004s_TNil @ C) @ D) @ Xs3))) => ((Terminal0 @ (((tLList_Mirabelle_ttl @ C) @ D) @ Xs3)) = Xsa))) => ((Xsa != (undefined @ D)) => ((P @ Xs3) @ Xsa)))))))) => ((((tLList1825092077minal0 @ (((tLList446370796tllist @ C) @ D) > D)) @ Xs) = Y) => ((Y != (undefined @ D)) => ((P @ Xs) @ Y))))))).
% 2.91/1.54 thf(fact_180_terminal0_Osimps, axiom, (! [D:$tType,C:$tType]: (((tLList1825092077minal0 @ (((tLList446370796tllist @ C) @ D) > D)) = (^ [Xs6:((tLList446370796tllist @ C) @ D)]: (((((if @ D) @ (((tLList1968894004s_TNil @ C) @ D) @ Xs6)) @ ((((((tLList200813139tllist @ D) @ D) @ C) @ (id @ D)) @ (undefined @ (C > (((tLList446370796tllist @ C) @ D) > D)))) @ Xs6)) @ ((tLList1825092077minal0 @ (((tLList446370796tllist @ C) @ D) > D)) @ (((tLList_Mirabelle_ttl @ C) @ D) @ Xs6))))))))).
% 2.91/1.54 thf(fact_181_tllist__of__llist_Ocode, axiom, (! [A:$tType,B:$tType]: ((((tLList1672613558_llist @ B) @ A) = (^ [B6:B]: (((((coindu1381640503_llist @ ((tLList446370796tllist @ A) @ B)) @ A) @ (((tLList57907754e_TNil @ B) @ A) @ B6)) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: (((((tLList1992840728_TCons @ A) @ B) @ X2) @ ((((tLList1672613558_llist @ B) @ A) @ B6) @ Xs5))))))))))).
% 2.91/1.54 thf(fact_182_tllist_Omap__id, axiom, (! [B:$tType,A:$tType,T2:((tLList446370796tllist @ A) @ B)]: (((((((((tLList1669959861e_tmap @ A) @ A) @ B) @ B) @ (id @ A)) @ (id @ B)) @ T2) = T2)))).
% 2.91/1.54 thf(fact_183_tllist_Omap__id0, axiom, (! [B:$tType,A:$tType]: ((((((((tLList1669959861e_tmap @ A) @ A) @ B) @ B) @ (id @ A)) @ (id @ B)) = (id @ ((tLList446370796tllist @ A) @ B)))))).
% 2.91/1.54 thf(fact_184_lhd__def, axiom, (! [A:$tType]: (((coinductive_lhd @ A) = ((((coindu1381640503_llist @ A) @ A) @ (undefined @ A)) @ (^ [X213:A,X223:(coinductive_llist @ A)]: (X213))))))).
% 2.91/1.54 thf(fact_185_tllist__of__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),B4:B]: (((~ (((coinductive_lnull @ A) @ Xs))) => (((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs) = ((((tLList1992840728_TCons @ A) @ B) @ (((((coindu1381640503_llist @ A) @ A) @ (undefined @ A)) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: (X2))) @ Xs)) @ (((((coindu1381640503_llist @ ((tLList446370796tllist @ A) @ B)) @ A) @ (undefined @ ((tLList446370796tllist @ A) @ B))) @ (^ [X2:A]: ((((tLList1672613558_llist @ B) @ A) @ B4)))) @ Xs))))))).
% 2.91/1.54 thf(fact_186_llist__of__tllist_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs))) => (((coinductive_ltl @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) = ((((((tLList200813139tllist @ B) @ (coinductive_llist @ A)) @ A) @ (^ [X2:B]: ((undefined @ (coinductive_llist @ A))))) @ (^ [X2:A]: (((tLList798109904tllist @ A) @ B)))) @ Xs)))))).
% 2.91/1.54 thf(fact_187_tllist__of__llist_Odisc__iff_I2_J, axiom, (! [B:$tType,A:$tType,B4:B,Xs:(coinductive_llist @ A)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)))) = (~ (((coinductive_lnull @ A) @ Xs))))))).
% 2.91/1.54 thf(fact_188_tllist__of__llist_Odisc__iff_I1_J, axiom, (! [B:$tType,A:$tType,B4:B,Xs:(coinductive_llist @ A)]: (((((tLList1968894004s_TNil @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = ((coinductive_lnull @ A) @ Xs))))).
% 2.91/1.54 thf(fact_189_llist__of__tllist_Odisc__iff_I2_J, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((~ (((coinductive_lnull @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)))) = (~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs))))))).
% 2.91/1.54 thf(fact_190_llist__of__tllist_Odisc__iff_I1_J, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: ((((coinductive_lnull @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) = (((tLList1968894004s_TNil @ A) @ B) @ Xs))))).
% 2.91/1.54 thf(fact_191_terminal__tllist__of__llist__lnull, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),B4:B]: ((((coinductive_lnull @ A) @ Xs) => ((((tLList2110128105rminal @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = B4))))).
% 2.91/1.54 thf(fact_192_ttl__tllist__of__llist, axiom, (! [B:$tType,A:$tType,B4:B,Xs:(coinductive_llist @ A)]: (((((tLList_Mirabelle_ttl @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = ((((tLList1672613558_llist @ B) @ A) @ B4) @ ((coinductive_ltl @ A) @ Xs)))))).
% 2.91/1.54 thf(fact_193_ltl__llist__of__tllist, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: ((((coinductive_ltl @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)) = (((tLList798109904tllist @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Xs)))))).
% 2.91/1.54 thf(fact_194_llist_Odisc__eq__case_I2_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ Llist))) = (((((coindu1381640503_llist @ $o) @ A) @ $false) @ (^ [Uu:A,Uv:(coinductive_llist @ A)]: ($true))) @ Llist))))).
% 2.91/1.54 thf(fact_195_llist_Odisc__eq__case_I1_J, axiom, (! [A:$tType]: (((coinductive_lnull @ A) = ((((coindu1381640503_llist @ $o) @ A) @ $true) @ (^ [Uu:A,Uv:(coinductive_llist @ A)]: ($false))))))).
% 2.91/1.54 thf(fact_196_tllist__of__llist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),B4:B]: (((~ (((coinductive_lnull @ A) @ Xs))) => (~ ((((tLList1968894004s_TNil @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)))))))).
% 2.91/1.54 thf(fact_197_tllist__of__llist_Odisc_I1_J, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),B4:B]: ((((coinductive_lnull @ A) @ Xs) => (((tLList1968894004s_TNil @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)))))).
% 2.91/1.54 thf(fact_198_llist__of__tllist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((~ ((((tLList1968894004s_TNil @ A) @ B) @ Xs))) => (~ (((coinductive_lnull @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)))))))).
% 2.91/1.54 thf(fact_199_llist__of__tllist_Odisc_I1_J, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ Xs) => ((coinductive_lnull @ A) @ (((tLList798109904tllist @ A) @ B) @ Xs)))))).
% 2.91/1.54 thf(fact_200_tllist__of__llist_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),B4:B]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((((tLList_Mirabelle_ttl @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = (((((coindu1381640503_llist @ ((tLList446370796tllist @ A) @ B)) @ A) @ (undefined @ ((tLList446370796tllist @ A) @ B))) @ (^ [X2:A]: ((((tLList1672613558_llist @ B) @ A) @ B4)))) @ Xs)))))).
% 2.91/1.54 thf(fact_201_tllist__of__llist_Octr_I1_J, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),B4:B]: ((((coinductive_lnull @ A) @ Xs) => (((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs) = (((tLList57907754e_TNil @ B) @ A) @ (((((coindu1381640503_llist @ B) @ A) @ B4) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: ((undefined @ B)))) @ Xs))))))).
% 2.91/1.54 thf(fact_202_tllist__of__llist_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),B4:B]: ((((coinductive_lnull @ A) @ Xs) => ((((tLList2110128105rminal @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = (((((coindu1381640503_llist @ B) @ A) @ B4) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: ((undefined @ B)))) @ Xs)))))).
% 2.91/1.54 thf(fact_203_tllist__of__llist_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),B4:B]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((((tLList_Mirabelle_thd @ A) @ B) @ ((((tLList1672613558_llist @ B) @ A) @ B4) @ Xs)) = (((((coindu1381640503_llist @ A) @ A) @ (undefined @ A)) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: (X2))) @ Xs)))))).
% 2.91/1.54 thf(fact_204_llist_Ocase__distrib, axiom, (! [B:$tType,C:$tType,A:$tType,H:(B > C),F1:B,F2:(A > ((coinductive_llist @ A) > B)),Llist:(coinductive_llist @ A)]: (((H @ (((((coindu1381640503_llist @ B) @ A) @ F1) @ F2) @ Llist)) = (((((coindu1381640503_llist @ C) @ A) @ (H @ F1)) @ (^ [X13:A,X24:(coinductive_llist @ A)]: ((H @ ((F2 @ X13) @ X24))))) @ Llist))))).
% 2.91/1.54 thf(fact_205_lappend_Octr_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = (((coinductive_LCons @ A) @ (((((coindu1381640503_llist @ A) @ A) @ ((coinductive_lhd @ A) @ Ys)) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: (X2))) @ Xs)) @ (((((coindu1381640503_llist @ (coinductive_llist @ A)) @ A) @ (((((coindu1381640503_llist @ (coinductive_llist @ A)) @ A) @ (undefined @ (coinductive_llist @ A))) @ (^ [Uu2:A,Uv2:(coinductive_llist @ A)]: (Uv2))) @ Ys)) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: ((((coinductive_lappend @ A) @ Xs5) @ Ys)))) @ Xs))))))).
% 2.91/1.54 thf(fact_206_llist__of__tllist_Ocode, axiom, (! [B:$tType,A:$tType]: ((((tLList798109904tllist @ A) @ B) = (((((tLList200813139tllist @ B) @ (coinductive_llist @ A)) @ A) @ (^ [X2:B]: ((coinductive_LNil @ A)))) @ (^ [X2:A,Xs5:((tLList446370796tllist @ A) @ B)]: ((((coinductive_LCons @ A) @ X2) @ (((tLList798109904tllist @ A) @ B) @ Xs5))))))))).
% 2.91/1.54 thf(fact_207_lappendt__LNil, axiom, (! [B:$tType,A:$tType,Tr:((tLList446370796tllist @ A) @ B)]: ((((((tLList98099029ppendt @ A) @ B) @ (coinductive_LNil @ A)) @ Tr) = Tr)))).
% 2.91/1.54 thf(fact_208_TNil__eq__tllist__of__llist, axiom, (! [B:$tType,A:$tType,B4:B,B5:B,Xs:(coinductive_llist @ A)]: ((((((tLList57907754e_TNil @ B) @ A) @ B4) = ((((tLList1672613558_llist @ B) @ A) @ B5) @ Xs)) = ((B4 = B5) & (Xs = (coinductive_LNil @ A))))))).
% 2.91/1.54 thf(fact_209_tllist__of__llist__LNil, axiom, (! [A:$tType,B:$tType,B4:B]: ((((((tLList1672613558_llist @ B) @ A) @ B4) @ (coinductive_LNil @ A)) = (((tLList57907754e_TNil @ B) @ A) @ B4))))).
% 2.91/1.54 thf(fact_210_tllist__of__llist__eq, axiom, (! [B:$tType,A:$tType,B5:B,Xs:(coinductive_llist @ A),B4:B]: (((((((tLList1672613558_llist @ B) @ A) @ B5) @ Xs) = (((tLList57907754e_TNil @ B) @ A) @ B4)) = ((B4 = B5) & (Xs = (coinductive_LNil @ A))))))).
% 2.91/1.54 thf(fact_211_llist__of__tllist__TNil, axiom, (! [A:$tType,Aa:$tType,X:A]: (((((tLList798109904tllist @ Aa) @ A) @ (((tLList57907754e_TNil @ A) @ Aa) @ X)) = (coinductive_LNil @ Aa))))).
% 2.91/1.54 thf(fact_212_lappend_Ocode, axiom, (! [A:$tType]: (((coinductive_lappend @ A) = (^ [Xs6:(coinductive_llist @ A),Ys4:(coinductive_llist @ A)]: ((((((coindu1381640503_llist @ (coinductive_llist @ A)) @ A) @ Ys4) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: ((((coinductive_LCons @ A) @ X2) @ (((coinductive_lappend @ A) @ Xs5) @ Ys4))))) @ Xs6))))))).
% 2.91/1.54 thf(fact_213_ltl__def, axiom, (! [A:$tType]: (((coinductive_ltl @ A) = ((((coindu1381640503_llist @ (coinductive_llist @ A)) @ A) @ (coinductive_LNil @ A)) @ (^ [X213:A,X223:(coinductive_llist @ A)]: (X223))))))).
% 2.91/1.54 thf(fact_214_lhd__LNil, axiom, (! [A:$tType]: ((((coinductive_lhd @ A) @ (coinductive_LNil @ A)) = (undefined @ A))))).
% 2.91/1.54 thf(fact_215_llist__of__tllist__eq__LNil, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: ((((((tLList798109904tllist @ A) @ B) @ Xs) = (coinductive_LNil @ A)) = (((tLList1968894004s_TNil @ A) @ B) @ Xs))))).
% 2.91/1.54 thf(fact_216_llist__of__tllist_Octr_I1_J, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: (((((tLList1968894004s_TNil @ A) @ B) @ Xs) => ((((tLList798109904tllist @ A) @ B) @ Xs) = (coinductive_LNil @ A)))))).
% 2.91/1.54 thf(fact_217_tllist__of__llist__eq__lappendt__conv, axiom, (! [B:$tType,A:$tType,A2:B,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs2:((tLList446370796tllist @ A) @ B)]: (((((((tLList1672613558_llist @ B) @ A) @ A2) @ Xs) = ((((tLList98099029ppendt @ A) @ B) @ Ys) @ Zs2)) = (? [Xs5:(coinductive_llist @ A),A6:B]: (((Xs = (((coinductive_lappend @ A) @ Ys) @ Xs5)) & ((Zs2 = ((((tLList1672613558_llist @ B) @ A) @ A6) @ Xs5)) & (((coinductive_lfinite @ A) @ Ys) => (A2 = A6)))))))))).
% 2.91/1.54 thf(fact_218_lappend_Osimps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))) => (((coinductive_lhd @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((((coindu1381640503_llist @ A) @ A) @ ((coinductive_lhd @ A) @ Ys)) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: (X2))) @ Xs)))))).
% 2.91/1.54 thf(fact_219_lappend_Osimps_I4_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))) => (((coinductive_ltl @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((((coindu1381640503_llist @ (coinductive_llist @ A)) @ A) @ (((((coindu1381640503_llist @ (coinductive_llist @ A)) @ A) @ (undefined @ (coinductive_llist @ A))) @ (^ [Uu2:A,Uv2:(coinductive_llist @ A)]: (Uv2))) @ Ys)) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: ((((coinductive_lappend @ A) @ Xs5) @ Ys)))) @ Xs)))))).
% 2.91/1.54 thf(fact_220_lfilter_Osimps, axiom, (! [A:$tType]: (((coinductive_lfilter @ A) = (^ [P5:(A > $o)]: (((((coindu1381640503_llist @ (coinductive_llist @ A)) @ A) @ (coinductive_LNil @ A)) @ (^ [X2:A,Xs5:(coinductive_llist @ A)]: (((((if @ (coinductive_llist @ A)) @ (P5 @ X2)) @ (((coinductive_LCons @ A) @ X2) @ (((coinductive_lfilter @ A) @ P5) @ Xs5))) @ (((coinductive_lfilter @ A) @ P5) @ Xs5))))))))))).
% 2.91/1.54 thf(fact_221_tllist_Osimps_I21_J, axiom, (! [B:$tType,A:$tType,X21:A,X22:((tLList446370796tllist @ A) @ B)]: (((((tLList1719791291e_tset @ A) @ B) @ ((((tLList1992840728_TCons @ A) @ B) @ X21) @ X22)) = (((insert @ A) @ X21) @ (((tLList1719791291e_tset @ A) @ B) @ X22)))))).
% 2.91/1.54 thf(fact_222_lfilter__K__True, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ (^ [Uu:A]: ($true))) @ Xs) = Xs)))).
% 2.91/1.54 thf(fact_223_lfitler__K__False, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ (^ [Uu:A]: ($false))) @ Xs) = (coinductive_LNil @ A))))).
% 2.91/1.54 thf(fact_224_lset__lfilter, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((coinductive_lset @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)) = ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs)) & (P @ X2))))))))).
% 2.91/1.54 thf(fact_225_insert__def, axiom, (! [A:$tType]: (((insert @ A) = (^ [A4:A]: (((sup_sup @ (set @ A)) @ ((collect @ A) @ (^ [X2:A]: ((X2 = A4))))))))))).
% 2.91/1.54 thf(fact_226_insert__compr, axiom, (! [A:$tType]: (((insert @ A) = (^ [A4:A,B8:(set @ A)]: (((collect @ A) @ (^ [X2:A]: (((X2 = A4) | (((member @ A) @ X2) @ B8))))))))))).
% 2.91/1.54 thf(fact_227_insert__Collect, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((insert @ A) @ A2) @ ((collect @ A) @ P)) = ((collect @ A) @ (^ [U:A]: (((U != A2) => (P @ U))))))))).
% 2.91/1.54 thf(fact_228_lfilter__lfilter, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o),Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ P) @ (((coinductive_lfilter @ A) @ Q) @ Xs)) = (((coinductive_lfilter @ A) @ (^ [X2:A]: (((P @ X2) & (Q @ X2))))) @ Xs))))).
% 2.91/1.54 thf(fact_229_set2__tllist__tllist__of__llist, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ B),B4:A]: (((((coinductive_lfinite @ B) @ Xs) => ((((tLList457864275tllist @ B) @ A) @ ((((tLList1672613558_llist @ A) @ B) @ B4) @ Xs)) = (((insert @ A) @ B4) @ (bot_bot @ (set @ A))))) & ((~ (((coinductive_lfinite @ B) @ Xs))) => ((((tLList457864275tllist @ B) @ A) @ ((((tLList1672613558_llist @ A) @ B) @ B4) @ Xs)) = (bot_bot @ (set @ A)))))))).
% 2.91/1.54 thf(fact_230_lfilter__repeat, axiom, (! [A:$tType,P:(A > $o),X:A]: ((((P @ X) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_iterates @ A) @ (^ [X2:A]: (X2))) @ X)) = (((coinductive_iterates @ A) @ (^ [X2:A]: (X2))) @ X))) & ((~ ((P @ X))) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_iterates @ A) @ (^ [X2:A]: (X2))) @ X)) = (coinductive_LNil @ A))))))).
% 2.91/1.54 thf(fact_231_singleton__conv, axiom, (! [A:$tType,A2:A]: ((((collect @ A) @ (^ [X2:A]: ((X2 = A2)))) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.91/1.54 thf(fact_232_singleton__conv2, axiom, (! [A:$tType,A2:A]: ((((collect @ A) @ ((^ [Y3:A,Z:A]: ((Y3 = Z))) @ A2)) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.91/1.54 thf(fact_233_lset__repeat, axiom, (! [A:$tType,X:A]: ((((coinductive_lset @ A) @ (((coinductive_iterates @ A) @ (^ [X2:A]: (X2))) @ X)) = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 2.91/1.54 thf(fact_234_Collect__conv__if, axiom, (! [A:$tType,P:(A > $o),A2:A]: ((((P @ A2) => (((collect @ A) @ (^ [X2:A]: (((X2 = A2) & (P @ X2))))) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))) & ((~ ((P @ A2))) => (((collect @ A) @ (^ [X2:A]: (((X2 = A2) & (P @ X2))))) = (bot_bot @ (set @ A)))))))).
% 2.91/1.54 thf(fact_235_Collect__conv__if2, axiom, (! [A:$tType,P:(A > $o),A2:A]: ((((P @ A2) => (((collect @ A) @ (^ [X2:A]: (((A2 = X2) & (P @ X2))))) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))) & ((~ ((P @ A2))) => (((collect @ A) @ (^ [X2:A]: (((A2 = X2) & (P @ X2))))) = (bot_bot @ (set @ A)))))))).
% 2.91/1.54 thf(fact_236_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X2:A]: ($false))))))).
% 2.91/1.54 thf(fact_237_tllist_Osimps_I20_J, axiom, (! [B:$tType,A:$tType,X1:B]: (((((tLList1719791291e_tset @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (bot_bot @ (set @ A)))))).
% 2.91/1.54 thf(fact_238_tllist_Osimps_I22_J, axiom, (! [A:$tType,B:$tType,X1:B]: (((((tLList457864275tllist @ A) @ B) @ (((tLList57907754e_TNil @ B) @ A) @ X1)) = (((insert @ B) @ X1) @ (bot_bot @ (set @ B))))))).
% 2.91/1.54 thf(fact_239_lfinite__lconcat, axiom, (! [A:$tType,Xss:(coinductive_llist @ (coinductive_llist @ A))]: ((((coinductive_lfinite @ A) @ ((coinductive_lconcat @ A) @ Xss)) = (((coinductive_lfinite @ (coinductive_llist @ A)) @ (((coinductive_lfilter @ (coinductive_llist @ A)) @ (^ [Xs6:(coinductive_llist @ A)]: ((~ (((coinductive_lnull @ A) @ Xs6)))))) @ Xss)) & (! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((coinductive_lset @ (coinductive_llist @ A)) @ Xss)) => ((coinductive_lfinite @ A) @ X2))))))))).
% 2.91/1.54 thf(fact_240_lconcat__repeat__LNil, axiom, (! [A:$tType]: ((((coinductive_lconcat @ A) @ (((coinductive_iterates @ (coinductive_llist @ A)) @ (^ [X2:(coinductive_llist @ A)]: (X2))) @ (coinductive_LNil @ A))) = (coinductive_LNil @ A))))).
% 2.91/1.54 thf(fact_241_lconcat_Osimps, axiom, (! [A:$tType]: (((coinductive_lconcat @ A) = ((((coindu1381640503_llist @ (coinductive_llist @ A)) @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (^ [Xs6:(coinductive_llist @ A),Xss2:(coinductive_llist @ (coinductive_llist @ A))]: ((((coinductive_lappend @ A) @ Xs6) @ ((coinductive_lconcat @ A) @ Xss2))))))))).
% 2.91/1.54 thf(fact_242_lconcat__lfilter__neq__LNil, axiom, (! [A:$tType,Xss:(coinductive_llist @ (coinductive_llist @ A))]: ((((coinductive_lconcat @ A) @ (((coinductive_lfilter @ (coinductive_llist @ A)) @ (^ [Xs6:(coinductive_llist @ A)]: ((~ (((coinductive_lnull @ A) @ Xs6)))))) @ Xss)) = ((coinductive_lconcat @ A) @ Xss))))).
% 2.91/1.54 thf(fact_243_lnull__lconcat, axiom, (! [A:$tType,Xss:(coinductive_llist @ (coinductive_llist @ A))]: ((((coinductive_lnull @ A) @ ((coinductive_lconcat @ A) @ Xss)) = (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((coinductive_lset @ (coinductive_llist @ A)) @ Xss)) @ ((collect @ (coinductive_llist @ A)) @ (coinductive_lnull @ A))))))).
% 2.91/1.54 thf(fact_244_tset__ttl, axiom, (! [B:$tType,A:$tType,Xs:((tLList446370796tllist @ A) @ B)]: ((((ord_less_eq @ (set @ A)) @ (((tLList1719791291e_tset @ A) @ B) @ (((tLList_Mirabelle_ttl @ A) @ B) @ Xs))) @ (((tLList1719791291e_tset @ A) @ B) @ Xs))))).
% 2.91/1.54 thf(fact_245_conj__subset__def, axiom, (! [A:$tType,A3:(set @ A),P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A3) @ ((collect @ A) @ (^ [X2:A]: (((P @ X2) & (Q @ X2)))))) = ((((ord_less_eq @ (set @ A)) @ A3) @ ((collect @ A) @ P)) & (((ord_less_eq @ (set @ A)) @ A3) @ ((collect @ A) @ Q))))))).
% 2.91/1.54 thf(fact_246_prop__restrict, axiom, (! [A:$tType,X:A,Z5:(set @ A),X5:(set @ A),P:(A > $o)]: (((((member @ A) @ X) @ Z5) => ((((ord_less_eq @ (set @ A)) @ Z5) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ X5) & (P @ X2)))))) => (P @ X)))))).
% 2.91/1.54 thf(fact_247_Collect__restrict, axiom, (! [A:$tType,X5:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ X5) & (P @ X2)))))) @ X5)))).
% 2.91/1.54 thf(fact_248_subset__Collect__iff, axiom, (! [A:$tType,B9:(set @ A),A3:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B9) @ A3) => ((((ord_less_eq @ (set @ A)) @ B9) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A3) & (P @ X2)))))) = (! [X2:A]: (((((member @ A) @ X2) @ B9) => (P @ X2))))))))).
% 2.91/1.54 thf(fact_249_subset__CollectI, axiom, (! [A:$tType,B9:(set @ A),A3:(set @ A),Q:(A > $o),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B9) @ A3) => ((! [X3:A]: (((((member @ A) @ X3) @ B9) => ((Q @ X3) => (P @ X3))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ B9) & (Q @ X2)))))) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A3) & (P @ X2))))))))))).
% 2.91/1.54 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.91/1.54 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.91/1.54 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.91/1.54 thf(conj_0, conjecture, (((((((((tLList1380991092t_all2 @ a) @ b) @ c) @ d) @ p) @ q) @ (((((((tLList1669959861e_tmap @ e) @ a) @ f) @ c) @ f2) @ g) @ xs)) @ ys) = ((((((((tLList1380991092t_all2 @ e) @ b) @ f) @ d) @ (^ [X2:e]: ((p @ (f2 @ X2))))) @ (^ [X2:f]: ((q @ (g @ X2))))) @ xs) @ ys))).
% 2.91/1.54 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2EYh0nHoAB/DTF2DTF25576.p
% 2.91/1.54 ------------------------
% 2.91/1.56 ---- Cleaned THF ---
% 2.91/1.56 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist,type,
% 2.91/1.56 tLList446370796tllist: $tType > $tType > $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_t_Coinductive__List_Ollist,type,
% 2.91/1.56 coinductive_llist: $tType > $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_t_Product__Type_Ounit,type,
% 2.91/1.56 product_unit: $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_t_Set_Oset,type,
% 2.91/1.56 set: $tType > $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_t_itself,type,
% 2.91/1.56 itself: $tType > $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_tf_f,type,
% 2.91/1.56 f: $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_tf_e,type,
% 2.91/1.56 e: $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_tf_d,type,
% 2.91/1.56 d: $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_tf_c,type,
% 2.91/1.56 c: $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_tf_b,type,
% 2.91/1.56 b: $tType ).
% 2.91/1.56
% 2.91/1.56 thf(ty_tf_a,type,
% 2.91/1.56 a: $tType ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Oiterates,type,
% 2.91/1.56 coinductive_iterates:
% 2.91/1.56 !>[A: $tType] : ( ( A > A ) > A > ( coinductive_llist @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Olappend,type,
% 2.91/1.56 coinductive_lappend:
% 2.91/1.56 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Olconcat,type,
% 2.91/1.56 coinductive_lconcat:
% 2.91/1.56 !>[A: $tType] : ( ( coinductive_llist @ ( coinductive_llist @ A ) ) > ( coinductive_llist @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Olfilter,type,
% 2.91/1.56 coinductive_lfilter:
% 2.91/1.56 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Olfinite,type,
% 2.91/1.56 coinductive_lfinite:
% 2.91/1.56 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.91/1.56 coinductive_LCons:
% 2.91/1.56 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.91/1.56 coinductive_LNil:
% 2.91/1.56 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Ollist_Ocase__llist,type,
% 2.91/1.56 coindu1381640503_llist:
% 2.91/1.56 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B ) > ( coinductive_llist @ A ) > B ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Ollist_Olhd,type,
% 2.91/1.56 coinductive_lhd:
% 2.91/1.56 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 2.91/1.56 coinductive_lnull:
% 2.91/1.56 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 2.91/1.56 coinductive_lset:
% 2.91/1.56 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Coinductive__List_Ollist_Oltl,type,
% 2.91/1.56 coinductive_ltl:
% 2.91/1.56 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Fun_Oid,type,
% 2.91/1.56 id:
% 2.91/1.56 !>[A: $tType] : ( A > A ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 2.91/1.56 default_default:
% 2.91/1.56 !>[A: $tType] : A ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_HOL_Oundefined,type,
% 2.91/1.56 undefined:
% 2.91/1.56 !>[A: $tType] : A ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_If,type,
% 2.91/1.56 if:
% 2.91/1.56 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.91/1.56 sup_sup:
% 2.91/1.56 !>[A: $tType] : ( A > A > A ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.91/1.56 bot_bot:
% 2.91/1.56 !>[A: $tType] : A ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.91/1.56 ord_less_eq:
% 2.91/1.56 !>[A: $tType] : ( A > A > $o ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Product__Type_OUnity,type,
% 2.91/1.56 product_Unity: product_unit ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 2.91/1.56 product_rec_unit:
% 2.91/1.56 !>[T: $tType] : ( T > product_unit > T ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Product__Type_Ounit_Ocase__unit,type,
% 2.91/1.56 product_case_unit:
% 2.91/1.56 !>[A: $tType] : ( A > product_unit > A ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Pure_Otype,type,
% 2.91/1.56 type:
% 2.91/1.56 !>[A: $tType] : ( itself @ A ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Set_OCollect,type,
% 2.91/1.56 collect:
% 2.91/1.56 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_Set_Oinsert,type,
% 2.91/1.56 insert:
% 2.91/1.56 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Olappendt,type,
% 2.91/1.56 tLList98099029ppendt:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( coinductive_llist @ A ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ollist__of__tllist,type,
% 2.91/1.56 tLList798109904tllist:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( coinductive_llist @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otappend,type,
% 2.91/1.56 tLList192138471append:
% 2.91/1.56 !>[A: $tType,B: $tType,C: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( B > ( tLList446370796tllist @ A @ C ) ) > ( tLList446370796tllist @ A @ C ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otcast,type,
% 2.91/1.56 tLList222516140_tcast:
% 2.91/1.56 !>[A: $tType,B: $tType,C: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ C ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otconcat,type,
% 2.91/1.56 tLList365522113concat:
% 2.91/1.56 !>[B: $tType,A: $tType] : ( B > ( tLList446370796tllist @ ( coinductive_llist @ A ) @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otconcat_H,type,
% 2.91/1.56 tLList1329345514concat:
% 2.91/1.56 !>[B: $tType,A: $tType] : ( ( product_unit > B ) > ( tLList446370796tllist @ ( coinductive_llist @ A ) @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Oterminal0,type,
% 2.91/1.56 tLList1825092077minal0:
% 2.91/1.56 !>[A: $tType] : A ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otfilter,type,
% 2.91/1.56 tLList1813626245filter:
% 2.91/1.56 !>[B: $tType,A: $tType] : ( B > ( A > $o ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otfilter_H,type,
% 2.91/1.56 tLList1122525870filter:
% 2.91/1.56 !>[B: $tType,A: $tType] : ( ( product_unit > B ) > ( A > $o ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTCons,type,
% 2.91/1.56 tLList1992840728_TCons:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( A > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_OTNil,type,
% 2.91/1.56 tLList57907754e_TNil:
% 2.91/1.56 !>[B: $tType,A: $tType] : ( B > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocase__tllist,type,
% 2.91/1.56 tLList200813139tllist:
% 2.91/1.56 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > ( tLList446370796tllist @ A @ B ) > C ) > ( tLList446370796tllist @ A @ B ) > C ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ocorec__tllist,type,
% 2.91/1.56 tLList1614408749tllist:
% 2.91/1.56 !>[E: $tType,B: $tType,A: $tType] : ( ( E > $o ) > ( E > B ) > ( E > A ) > ( E > $o ) > ( E > ( tLList446370796tllist @ A @ B ) ) > ( E > E ) > E > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ois__TNil,type,
% 2.91/1.56 tLList1968894004s_TNil:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > $o ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Opred__tllist,type,
% 2.91/1.56 tLList11265572tllist:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( tLList446370796tllist @ A @ B ) > $o ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oset2__tllist,type,
% 2.91/1.56 tLList457864275tllist:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( set @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Oterminal,type,
% 2.91/1.56 tLList2110128105rminal:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > B ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Othd,type,
% 2.91/1.56 tLList_Mirabelle_thd:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > A ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otllist__all2,type,
% 2.91/1.56 tLList1380991092t_all2:
% 2.91/1.56 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otmap,type,
% 2.91/1.56 tLList1669959861e_tmap:
% 2.91/1.56 !>[A: $tType,Aa: $tType,B: $tType,Ba: $tType] : ( ( A > Aa ) > ( B > Ba ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ Aa @ Ba ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Otset,type,
% 2.91/1.56 tLList1719791291e_tset:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( set @ A ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist_Ottl,type,
% 2.91/1.56 tLList_Mirabelle_ttl:
% 2.91/1.56 !>[A: $tType,B: $tType] : ( ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist__of__llist,type,
% 2.91/1.56 tLList1672613558_llist:
% 2.91/1.56 !>[B: $tType,A: $tType] : ( B > ( coinductive_llist @ A ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ounfold__tllist,type,
% 2.91/1.56 tLList636831159tllist:
% 2.91/1.56 !>[A: $tType,B: $tType,C: $tType] : ( ( A > $o ) > ( A > B ) > ( A > C ) > ( A > A ) > A > ( tLList446370796tllist @ C @ B ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_c_member,type,
% 2.91/1.56 member:
% 2.91/1.56 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.91/1.56
% 2.91/1.56 thf(sy_v_P,type,
% 2.91/1.56 p: a > b > $o ).
% 2.91/1.56
% 2.91/1.56 thf(sy_v_Q,type,
% 2.91/1.56 q: c > d > $o ).
% 2.91/1.56
% 2.91/1.56 thf(sy_v_f,type,
% 2.91/1.56 f2: e > a ).
% 2.91/1.56
% 2.91/1.56 thf(sy_v_g,type,
% 2.91/1.56 g: f > c ).
% 2.91/1.56
% 2.91/1.56 thf(sy_v_xs,type,
% 2.91/1.56 xs: tLList446370796tllist @ e @ f ).
% 2.91/1.56
% 2.91/1.56 thf(sy_v_ys,type,
% 2.91/1.56 ys: tLList446370796tllist @ b @ d ).
% 2.91/1.56
% 2.91/1.56 thf(fact_0_tllist_Orel__map_I2_J,axiom,
% 2.91/1.56 ! [A: $tType,B: $tType,E: $tType,F: $tType,D: $tType,C: $tType,S1a: A > E > $o,S2a: B > F > $o,X: tLList446370796tllist @ A @ B,G1: C > E,G2: D > F,Y: tLList446370796tllist @ C @ D] :
% 2.91/1.56 ( ( tLList1380991092t_all2 @ A @ E @ B @ F @ S1a @ S2a @ X @ ( tLList1669959861e_tmap @ C @ E @ D @ F @ G1 @ G2 @ Y ) )
% 2.91/1.56 = ( tLList1380991092t_all2 @ A @ C @ B @ D
% 2.91/1.56 @ ^ [X2: A,Y2: C] : ( S1a @ X2 @ ( G1 @ Y2 ) )
% 2.91/1.56 @ ^ [X2: B,Y2: D] : ( S2a @ X2 @ ( G2 @ Y2 ) )
% 2.91/1.56 @ X
% 2.91/1.56 @ Y ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_1_tllist_Orel__map_I1_J,axiom,
% 2.91/1.56 ! [A: $tType,B: $tType,E: $tType,F: $tType,D: $tType,C: $tType,S1b: E > C > $o,S2b: F > D > $o,I1: A > E,I2: B > F,X: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D] :
% 2.91/1.56 ( ( tLList1380991092t_all2 @ E @ C @ F @ D @ S1b @ S2b @ ( tLList1669959861e_tmap @ A @ E @ B @ F @ I1 @ I2 @ X ) @ Y )
% 2.91/1.56 = ( tLList1380991092t_all2 @ A @ C @ B @ D
% 2.91/1.56 @ ^ [X2: A] : ( S1b @ ( I1 @ X2 ) )
% 2.91/1.56 @ ^ [X2: B] : ( S2b @ ( I2 @ X2 ) )
% 2.91/1.56 @ X
% 2.91/1.56 @ Y ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_2_tllist_Orel__eq,axiom,
% 2.91/1.56 ! [B: $tType,A: $tType] :
% 2.91/1.56 ( ( tLList1380991092t_all2 @ A @ A @ B @ B
% 2.91/1.56 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 2.91/1.56 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) )
% 2.91/1.56 = ( ^ [Y3: tLList446370796tllist @ A @ B,Z: tLList446370796tllist @ A @ B] : ( Y3 = Z ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_3_tllist_Orel__refl,axiom,
% 2.91/1.56 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X: tLList446370796tllist @ C @ D] :
% 2.91/1.56 ( ! [X3: C] : ( R1a @ X3 @ X3 )
% 2.91/1.56 => ( ! [X3: D] : ( R2a @ X3 @ X3 )
% 2.91/1.56 => ( tLList1380991092t_all2 @ C @ C @ D @ D @ R1a @ R2a @ X @ X ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_4_tllist_Omap__ident,axiom,
% 2.91/1.56 ! [B: $tType,A: $tType,T2: tLList446370796tllist @ A @ B] :
% 2.91/1.56 ( ( tLList1669959861e_tmap @ A @ A @ B @ B
% 2.91/1.56 @ ^ [X2: A] : X2
% 2.91/1.56 @ ^ [X2: B] : X2
% 2.91/1.56 @ T2 )
% 2.91/1.56 = T2 ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_5_tllist_Omap__cong__pred,axiom,
% 2.91/1.56 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 2.91/1.56 ( ( X = Ya )
% 2.91/1.56 => ( ( tLList11265572tllist @ A @ B
% 2.91/1.56 @ ^ [Z1: A] :
% 2.91/1.56 ( ( F1 @ Z1 )
% 2.91/1.56 = ( G1 @ Z1 ) )
% 2.91/1.56 @ ^ [Z2: B] :
% 2.91/1.56 ( ( F2 @ Z2 )
% 2.91/1.56 = ( G2 @ Z2 ) )
% 2.91/1.56 @ Ya )
% 2.91/1.56 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X )
% 2.91/1.56 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_6_ttl__tmap,axiom,
% 2.91/1.56 ! [B: $tType,A: $tType,D: $tType,C: $tType,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D] :
% 2.91/1.56 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs ) )
% 2.91/1.56 = ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ ( tLList_Mirabelle_ttl @ C @ D @ Xs ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_7_tllist__all2__TCons,axiom,
% 2.91/1.56 ! [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] :
% 2.91/1.56 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) )
% 2.91/1.56 = ( ( R1 @ X21 @ Y21 )
% 2.91/1.56 & ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_8_tllist__all2__TNil,axiom,
% 2.91/1.56 ! [C: $tType,A: $tType,B: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,X1: B,Y1: D] :
% 2.91/1.56 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList57907754e_TNil @ D @ C @ Y1 ) )
% 2.91/1.56 = ( R2 @ X1 @ Y1 ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_9_tllist_Omap__disc__iff,axiom,
% 2.91/1.56 ! [C: $tType,D: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,A2: tLList446370796tllist @ A @ B] :
% 2.91/1.56 ( ( tLList1968894004s_TNil @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 2.91/1.56 = ( tLList1968894004s_TNil @ A @ B @ A2 ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_10_tllist_Osimps_I15_J,axiom,
% 2.91/1.56 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.56 ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.91/1.56 = ( tLList1992840728_TCons @ C @ D @ ( F1 @ X21 ) @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X22 ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_11_TCons__eq__tmap__conv,axiom,
% 2.91/1.56 ! [D: $tType,B: $tType,A: $tType,C: $tType,Y: A,Ys: tLList446370796tllist @ A @ B,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D] :
% 2.91/1.56 ( ( ( tLList1992840728_TCons @ A @ B @ Y @ Ys )
% 2.91/1.56 = ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs ) )
% 2.91/1.56 = ( ? [Z3: C,Zs: tLList446370796tllist @ C @ D] :
% 2.91/1.56 ( ( Xs
% 2.91/1.56 = ( tLList1992840728_TCons @ C @ D @ Z3 @ Zs ) )
% 2.91/1.56 & ( ( F3 @ Z3 )
% 2.91/1.56 = Y )
% 2.91/1.56 & ( ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Zs )
% 2.91/1.56 = Ys ) ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_12_tmap__eq__TCons__conv,axiom,
% 2.91/1.56 ! [D: $tType,B: $tType,A: $tType,C: $tType,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D,Y: A,Ys: tLList446370796tllist @ A @ B] :
% 2.91/1.56 ( ( ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs )
% 2.91/1.56 = ( tLList1992840728_TCons @ A @ B @ Y @ Ys ) )
% 2.91/1.56 = ( ? [Z3: C,Zs: tLList446370796tllist @ C @ D] :
% 2.91/1.56 ( ( Xs
% 2.91/1.56 = ( tLList1992840728_TCons @ C @ D @ Z3 @ Zs ) )
% 2.91/1.56 & ( ( F3 @ Z3 )
% 2.91/1.56 = Y )
% 2.91/1.56 & ( ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Zs )
% 2.91/1.56 = Ys ) ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_13_tllist_Osimps_I14_J,axiom,
% 2.91/1.56 ! [A: $tType,C: $tType,D: $tType,B: $tType,F1: A > C,F2: B > D,X1: B] :
% 2.91/1.56 ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.91/1.56 = ( tLList57907754e_TNil @ D @ C @ ( F2 @ X1 ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_14_TNil__eq__tmap__conv,axiom,
% 2.91/1.56 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: B,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D] :
% 2.91/1.56 ( ( ( tLList57907754e_TNil @ B @ A @ Y )
% 2.91/1.56 = ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs ) )
% 2.91/1.56 = ( ? [Y4: D] :
% 2.91/1.56 ( ( Xs
% 2.91/1.56 = ( tLList57907754e_TNil @ D @ C @ Y4 ) )
% 2.91/1.56 & ( ( G @ Y4 )
% 2.91/1.56 = Y ) ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_15_tmap__eq__TNil__conv,axiom,
% 2.91/1.56 ! [A: $tType,B: $tType,C: $tType,D: $tType,F3: C > A,G: D > B,Xs: tLList446370796tllist @ C @ D,Y: B] :
% 2.91/1.56 ( ( ( tLList1669959861e_tmap @ C @ A @ D @ B @ F3 @ G @ Xs )
% 2.91/1.56 = ( tLList57907754e_TNil @ B @ A @ Y ) )
% 2.91/1.56 = ( ? [Y4: D] :
% 2.91/1.56 ( ( Xs
% 2.91/1.56 = ( tLList57907754e_TNil @ D @ C @ Y4 ) )
% 2.91/1.56 & ( ( G @ Y4 )
% 2.91/1.56 = Y ) ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_16_tllist_Orel__intros_I2_J,axiom,
% 2.91/1.56 ! [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] :
% 2.91/1.56 ( ( R1 @ X21 @ Y21 )
% 2.91/1.56 => ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 )
% 2.91/1.56 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_17_tllist_Oinject_I1_J,axiom,
% 2.91/1.56 ! [A: $tType,B: $tType,X1: B,Y1: B] :
% 2.91/1.56 ( ( ( tLList57907754e_TNil @ B @ A @ X1 )
% 2.91/1.56 = ( tLList57907754e_TNil @ B @ A @ Y1 ) )
% 2.91/1.56 = ( X1 = Y1 ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_18_tllist_Oinject_I2_J,axiom,
% 2.91/1.56 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B,Y21: A,Y22: tLList446370796tllist @ A @ B] :
% 2.91/1.56 ( ( ( tLList1992840728_TCons @ A @ B @ X21 @ X22 )
% 2.91/1.56 = ( tLList1992840728_TCons @ A @ B @ Y21 @ Y22 ) )
% 2.91/1.56 = ( ( X21 = Y21 )
% 2.91/1.56 & ( X22 = Y22 ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_19_tllist_Opred__inject_I1_J,axiom,
% 2.91/1.56 ! [A: $tType,B: $tType,P1: A > $o,P2: B > $o,A2: B] :
% 2.91/1.56 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ ( tLList57907754e_TNil @ B @ A @ A2 ) )
% 2.91/1.56 = ( P2 @ A2 ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_20_tllist_Opred__inject_I2_J,axiom,
% 2.91/1.56 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,A2: A,Aa2: tLList446370796tllist @ A @ B] :
% 2.91/1.56 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ ( tLList1992840728_TCons @ A @ B @ A2 @ Aa2 ) )
% 2.91/1.56 = ( ( P1 @ A2 )
% 2.91/1.56 & ( tLList11265572tllist @ A @ B @ P1 @ P2 @ Aa2 ) ) ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_21_tllist_Osel_I5_J,axiom,
% 2.91/1.56 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.56 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.91/1.56 = X22 ) ).
% 2.91/1.56
% 2.91/1.56 thf(fact_22_tllist_Osel_I4_J,axiom,
% 2.91/1.56 ! [A: $tType,B: $tType,X1: B] :
% 2.91/1.56 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ X1 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_23_tllist_Odisc_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_24_tllist_Odisc_I1_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,X1: B] : ( tLList1968894004s_TNil @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_25_tllist_OdiscI_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( Tllist
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.91/1.57 => ~ ( tLList1968894004s_TNil @ A @ B @ Tllist ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_26_tllist_OdiscI_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,X1: B] :
% 2.91/1.57 ( ( Tllist
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.91/1.57 => ( tLList1968894004s_TNil @ A @ B @ Tllist ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_27_tllist_Odistinct_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X1: B,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList57907754e_TNil @ B @ A @ X1 )
% 2.91/1.57 != ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_28_is__TNil__ttl,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( tLList1968894004s_TNil @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_29_tllist_Oexhaust,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Y: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ! [X12: B] :
% 2.91/1.57 ( Y
% 2.91/1.57 != ( tLList57907754e_TNil @ B @ A @ X12 ) )
% 2.91/1.57 => ~ ! [X212: A,X222: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( Y
% 2.91/1.57 != ( tLList1992840728_TCons @ A @ B @ X212 @ X222 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_30_is__TNil__def,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B )
% 2.91/1.57 = ( ^ [Tllist2: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ? [X13: B] :
% 2.91/1.57 ( Tllist2
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ X13 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_31_tllist__all2__cases,axiom,
% 2.91/1.57 ! [A: $tType,C: $tType,D: $tType,B: $tType,P: A > B > $o,Q: C > D > $o,Xs: tLList446370796tllist @ A @ C,Ys: tLList446370796tllist @ B @ D] :
% 2.91/1.57 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Xs @ Ys )
% 2.91/1.57 => ( ! [B2: C] :
% 2.91/1.57 ( ( Xs
% 2.91/1.57 = ( tLList57907754e_TNil @ C @ A @ B2 ) )
% 2.91/1.57 => ! [B3: D] :
% 2.91/1.57 ( ( Ys
% 2.91/1.57 = ( tLList57907754e_TNil @ D @ B @ B3 ) )
% 2.91/1.57 => ~ ( Q @ B2 @ B3 ) ) )
% 2.91/1.57 => ~ ! [X3: A,Xs2: tLList446370796tllist @ A @ C] :
% 2.91/1.57 ( ( Xs
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ C @ X3 @ Xs2 ) )
% 2.91/1.57 => ! [Y5: B,Ys2: tLList446370796tllist @ B @ D] :
% 2.91/1.57 ( ( Ys
% 2.91/1.57 = ( tLList1992840728_TCons @ B @ D @ Y5 @ Ys2 ) )
% 2.91/1.57 => ( ( P @ X3 @ Y5 )
% 2.91/1.57 => ~ ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_32_tllist_Orel__cases,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,A2: tLList446370796tllist @ A @ B,B4: tLList446370796tllist @ C @ D] :
% 2.91/1.57 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ A2 @ B4 )
% 2.91/1.57 => ( ! [X3: B] :
% 2.91/1.57 ( ( A2
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ X3 ) )
% 2.91/1.57 => ! [Y5: D] :
% 2.91/1.57 ( ( B4
% 2.91/1.57 = ( tLList57907754e_TNil @ D @ C @ Y5 ) )
% 2.91/1.57 => ~ ( R2 @ X3 @ Y5 ) ) )
% 2.91/1.57 => ~ ! [X1a: A,X23: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( A2
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ X1a @ X23 ) )
% 2.91/1.57 => ! [Y1a: C,Y23: tLList446370796tllist @ C @ D] :
% 2.91/1.57 ( ( B4
% 2.91/1.57 = ( tLList1992840728_TCons @ C @ D @ Y1a @ Y23 ) )
% 2.91/1.57 => ( ( R1 @ X1a @ Y1a )
% 2.91/1.57 => ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X23 @ Y23 ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_33_tllist_Orel__distinct_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X1: B,Y21: C,Y22: tLList446370796tllist @ C @ D] :
% 2.91/1.57 ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList1992840728_TCons @ C @ D @ Y21 @ Y22 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_34_tllist_Orel__distinct_I2_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,Y21: A,Y22: tLList446370796tllist @ A @ B,X1: D] :
% 2.91/1.57 ~ ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList1992840728_TCons @ A @ B @ Y21 @ Y22 ) @ ( tLList57907754e_TNil @ D @ C @ X1 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_35_tllist_Omap__sel_I3_J,axiom,
% 2.91/1.57 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_ttl @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 2.91/1.57 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_36_tllist_Opred__True,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList11265572tllist @ A @ B
% 2.91/1.57 @ ^ [Uu: A] : $true
% 2.91/1.57 @ ^ [Uu: B] : $true )
% 2.91/1.57 = ( ^ [Uu: tLList446370796tllist @ A @ B] : $true ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_37_tllist__all2__TNil2,axiom,
% 2.91/1.57 ! [B: $tType,D: $tType,A: $tType,C: $tType,P: A > B > $o,Q: C > D > $o,Ts: tLList446370796tllist @ A @ C,B5: D] :
% 2.91/1.57 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Ts @ ( tLList57907754e_TNil @ D @ B @ B5 ) )
% 2.91/1.57 = ( ? [B6: C] :
% 2.91/1.57 ( ( Ts
% 2.91/1.57 = ( tLList57907754e_TNil @ C @ A @ B6 ) )
% 2.91/1.57 & ( Q @ B6 @ B5 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_38_tllist__all2__TNil1,axiom,
% 2.91/1.57 ! [A: $tType,C: $tType,B: $tType,D: $tType,P: A > B > $o,Q: C > D > $o,B4: C,Ts: tLList446370796tllist @ B @ D] :
% 2.91/1.57 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ ( tLList57907754e_TNil @ C @ A @ B4 ) @ Ts )
% 2.91/1.57 = ( ? [B7: D] :
% 2.91/1.57 ( ( Ts
% 2.91/1.57 = ( tLList57907754e_TNil @ D @ B @ B7 ) )
% 2.91/1.57 & ( Q @ B4 @ B7 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_39_tllist_Orel__intros_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,C: $tType,D: $tType,R2: B > D > $o,X1: B,Y1: D,R1: A > C > $o] :
% 2.91/1.57 ( ( R2 @ X1 @ Y1 )
% 2.91/1.57 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) @ ( tLList57907754e_TNil @ D @ C @ Y1 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_40_tllist__all2__TCons2,axiom,
% 2.91/1.57 ! [C: $tType,D: $tType,B: $tType,A: $tType,P: A > B > $o,Q: C > D > $o,Ts2: tLList446370796tllist @ A @ C,X: B,Ts: tLList446370796tllist @ B @ D] :
% 2.91/1.57 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Ts2 @ ( tLList1992840728_TCons @ B @ D @ X @ Ts ) )
% 2.91/1.57 = ( ? [X4: A,Ts3: tLList446370796tllist @ A @ C] :
% 2.91/1.57 ( ( Ts2
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ C @ X4 @ Ts3 ) )
% 2.91/1.57 & ( P @ X4 @ X )
% 2.91/1.57 & ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Ts3 @ Ts ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_41_tllist__all2__TCons1,axiom,
% 2.91/1.57 ! [D: $tType,A: $tType,C: $tType,B: $tType,P: A > B > $o,Q: C > D > $o,X: A,Ts: tLList446370796tllist @ A @ C,Ts2: tLList446370796tllist @ B @ D] :
% 2.91/1.57 ( ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ ( tLList1992840728_TCons @ A @ C @ X @ Ts ) @ Ts2 )
% 2.91/1.57 = ( ? [X4: B,Ts3: tLList446370796tllist @ B @ D] :
% 2.91/1.57 ( ( Ts2
% 2.91/1.57 = ( tLList1992840728_TCons @ B @ D @ X4 @ Ts3 ) )
% 2.91/1.57 & ( P @ X @ X4 )
% 2.91/1.57 & ( tLList1380991092t_all2 @ A @ B @ C @ D @ P @ Q @ Ts @ Ts3 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_42_tllist_Ocollapse_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.91/1.57 => ( ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) )
% 2.91/1.57 = Tllist ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_43_mem__Collect__eq,axiom,
% 2.91/1.57 ! [A: $tType,A2: A,P: A > $o] :
% 2.91/1.57 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.91/1.57 = ( P @ A2 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_44_Collect__mem__eq,axiom,
% 2.91/1.57 ! [A: $tType,A3: set @ A] :
% 2.91/1.57 ( ( collect @ A
% 2.91/1.57 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 2.91/1.57 = A3 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_45_Collect__cong,axiom,
% 2.91/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.91/1.57 ( ! [X3: A] :
% 2.91/1.57 ( ( P @ X3 )
% 2.91/1.57 = ( Q @ X3 ) )
% 2.91/1.57 => ( ( collect @ A @ P )
% 2.91/1.57 = ( collect @ A @ Q ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_46_ext,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,F3: A > B,G: A > B] :
% 2.91/1.57 ( ! [X3: A] :
% 2.91/1.57 ( ( F3 @ X3 )
% 2.91/1.57 = ( G @ X3 ) )
% 2.91/1.57 => ( F3 = G ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_47_tconcat__TNil,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,B4: B,B5: B] :
% 2.91/1.57 ( ( tLList365522113concat @ B @ A @ B4 @ ( tLList57907754e_TNil @ B @ ( coinductive_llist @ A ) @ B5 ) )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ B5 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_48_ttl__def,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList_Mirabelle_ttl @ A @ B )
% 2.91/1.57 = ( tLList200813139tllist @ B @ ( tLList446370796tllist @ A @ B ) @ A @ ( tLList57907754e_TNil @ B @ A )
% 2.91/1.57 @ ^ [X213: A,X223: tLList446370796tllist @ A @ B] : X223 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_49_tllist_Omap__sel_I2_J,axiom,
% 2.91/1.57 ! [D: $tType,C: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_thd @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 2.91/1.57 = ( F1 @ ( tLList_Mirabelle_thd @ A @ B @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_50_tmap__is__TNil,axiom,
% 2.91/1.57 ! [C: $tType,D: $tType,B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B,F3: A > C,G: B > D] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F3 @ G @ Xs )
% 2.91/1.57 = ( tLList57907754e_TNil @ D @ C @ ( G @ ( tLList2110128105rminal @ A @ B @ Xs ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_51_ttl__unfold__tllist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,C: $tType,IS_TNIL: C > $o,A2: C,TNIL: C > B,THD: C > A,TTL: C > C] :
% 2.91/1.57 ( ( ( IS_TNIL @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ A2 ) )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ ( TNIL @ A2 ) ) ) )
% 2.91/1.57 & ( ~ ( IS_TNIL @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ A2 ) )
% 2.91/1.57 = ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ ( TTL @ A2 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_52_tllist_Ocorec__code,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,E: $tType] :
% 2.91/1.57 ( ( tLList1614408749tllist @ E @ B @ A )
% 2.91/1.57 = ( ^ [P3: E > $o,G12: 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 @ ( G12 @ A4 ) ) @ ( tLList1992840728_TCons @ A @ B @ ( G21 @ A4 ) @ ( if @ ( tLList446370796tllist @ A @ B ) @ ( Q22 @ A4 ) @ ( G221 @ A4 ) @ ( tLList1614408749tllist @ E @ B @ A @ P3 @ G12 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_53_unfold__tllist_Ocode,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList636831159tllist @ A @ B @ C )
% 2.91/1.57 = ( ^ [P3: A > $o,G12: A > B,G21: A > C,G22: A > A,A4: A] : ( if @ ( tLList446370796tllist @ C @ B ) @ ( P3 @ A4 ) @ ( tLList57907754e_TNil @ B @ C @ ( G12 @ A4 ) ) @ ( tLList1992840728_TCons @ C @ B @ ( G21 @ A4 ) @ ( tLList636831159tllist @ A @ B @ C @ P3 @ G12 @ G21 @ G22 @ ( G22 @ A4 ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_54_tconcat_H__code_I1_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,B4: product_unit > B,B5: B] :
% 2.91/1.57 ( ( tLList1329345514concat @ B @ A @ B4 @ ( tLList57907754e_TNil @ B @ ( coinductive_llist @ A ) @ B5 ) )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ B5 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_55_tllist_Ocollapse_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.91/1.57 => ( ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) )
% 2.91/1.57 = Tllist ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_56_terminal__TCons,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,X: B,Xs: tLList446370796tllist @ B @ A] :
% 2.91/1.57 ( ( tLList2110128105rminal @ B @ A @ ( tLList1992840728_TCons @ B @ A @ X @ Xs ) )
% 2.91/1.57 = ( tLList2110128105rminal @ B @ A @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_57_terminal__ttl,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,Xs: tLList446370796tllist @ B @ A] :
% 2.91/1.57 ( ( tLList2110128105rminal @ B @ A @ ( tLList_Mirabelle_ttl @ B @ A @ Xs ) )
% 2.91/1.57 = ( tLList2110128105rminal @ B @ A @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_58_unfold__tllist_Odisc__iff_I1_J,axiom,
% 2.91/1.57 ! [C: $tType,B: $tType,A: $tType,P4: A > $o,G1: A > B,G212: A > C,G223: A > A,A2: A] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) )
% 2.91/1.57 = ( P4 @ A2 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_59_unfold__tllist_Odisc__iff_I2_J,axiom,
% 2.91/1.57 ! [C: $tType,B: $tType,A: $tType,P4: A > $o,G1: A > B,G212: A > C,G223: A > A,A2: A] :
% 2.91/1.57 ( ( ~ ( tLList1968894004s_TNil @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) ) )
% 2.91/1.57 = ( ~ ( P4 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_60_tllist_Ocorec__disc__iff_I1_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E,A2: E] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.91/1.57 = ( P4 @ A2 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_61_tllist_Ocorec__disc__iff_I2_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E,A2: E] :
% 2.91/1.57 ( ( ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) )
% 2.91/1.57 = ( ~ ( P4 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_62_unfold__tllist__eq__TNil,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,C: $tType,IS_TNIL: C > $o,TNIL: C > B,THD: C > A,TTL: C > C,A2: C,B4: B] :
% 2.91/1.57 ( ( ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ A2 )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 2.91/1.57 = ( ( IS_TNIL @ A2 )
% 2.91/1.57 & ( B4
% 2.91/1.57 = ( TNIL @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_63_TNil__eq__unfold__tllist,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,C: $tType,B4: B,IS_TNIL: C > $o,TNIL: C > B,THD: C > A,TTL: C > C,A2: C] :
% 2.91/1.57 ( ( ( tLList57907754e_TNil @ B @ A @ B4 )
% 2.91/1.57 = ( tLList636831159tllist @ C @ B @ A @ IS_TNIL @ TNIL @ THD @ TTL @ A2 ) )
% 2.91/1.57 = ( ( IS_TNIL @ A2 )
% 2.91/1.57 & ( B4
% 2.91/1.57 = ( TNIL @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_64_unfold__tllist_Osimps_I3_J,axiom,
% 2.91/1.57 ! [C: $tType,B: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 2.91/1.57 ( ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList2110128105rminal @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) )
% 2.91/1.57 = ( G1 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_65_unfold__tllist_Osimps_I4_J,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 2.91/1.57 ( ~ ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_thd @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) )
% 2.91/1.57 = ( G212 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_66_tllist_Ocorec__sel_I1_J,axiom,
% 2.91/1.57 ! [Aa: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > A,G212: E > Aa,Q222: E > $o,G2212: E > ( tLList446370796tllist @ Aa @ A ),G2222: E > E] :
% 2.91/1.57 ( ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList2110128105rminal @ Aa @ A @ ( tLList1614408749tllist @ E @ A @ Aa @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.91/1.57 = ( G1 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_67_tllist_Ocorec__sel_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.91/1.57 ( ~ ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.91/1.57 = ( G212 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_68_tconcat__code,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList365522113concat @ A @ B )
% 2.91/1.57 = ( ^ [B6: A] :
% 2.91/1.57 ( tLList1329345514concat @ A @ B
% 2.91/1.57 @ ^ [Uu: product_unit] : B6 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_69_tllist_Ocase__eq__if,axiom,
% 2.91/1.57 ! [A: $tType,C: $tType,B: $tType] :
% 2.91/1.57 ( ( tLList200813139tllist @ B @ C @ A )
% 2.91/1.57 = ( ^ [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 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_70_tllist_Ocase__distrib,axiom,
% 2.91/1.57 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( H @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 2.91/1.57 = ( tLList200813139tllist @ B @ D @ A
% 2.91/1.57 @ ^ [X2: B] : ( H @ ( F1 @ X2 ) )
% 2.91/1.57 @ ^ [X13: A,X24: tLList446370796tllist @ A @ B] : ( H @ ( F2 @ X13 @ X24 ) )
% 2.91/1.57 @ Tllist ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_71_tllist_Ocoinduct__strong,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,R: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) > $o,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( R @ Tllist @ Tllist3 )
% 2.91/1.57 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( R @ Tllist4 @ Tllist5 )
% 2.91/1.57 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 = ( tLList1968894004s_TNil @ A @ B @ Tllist5 ) )
% 2.91/1.57 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ Tllist4 )
% 2.91/1.57 = ( tLList2110128105rminal @ A @ B @ Tllist5 ) ) ) )
% 2.91/1.57 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 2.91/1.57 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist4 )
% 2.91/1.57 = ( tLList_Mirabelle_thd @ A @ B @ Tllist5 ) )
% 2.91/1.57 & ( ( R @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) )
% 2.91/1.57 | ( ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 )
% 2.91/1.57 = ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) ) ) ) ) ) ) )
% 2.91/1.57 => ( Tllist = Tllist3 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_72_tllist_Ocoinduct,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,R: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) > $o,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( R @ Tllist @ Tllist3 )
% 2.91/1.57 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( R @ Tllist4 @ Tllist5 )
% 2.91/1.57 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 = ( tLList1968894004s_TNil @ A @ B @ Tllist5 ) )
% 2.91/1.57 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ Tllist4 )
% 2.91/1.57 = ( tLList2110128105rminal @ A @ B @ Tllist5 ) ) ) )
% 2.91/1.57 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist5 )
% 2.91/1.57 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist4 )
% 2.91/1.57 = ( tLList_Mirabelle_thd @ A @ B @ Tllist5 ) )
% 2.91/1.57 & ( R @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist5 ) ) ) ) ) ) )
% 2.91/1.57 => ( Tllist = Tllist3 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_73_tllist_Oexpand,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B,Tllist3: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.91/1.57 = ( tLList1968894004s_TNil @ A @ B @ Tllist3 ) )
% 2.91/1.57 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.91/1.57 => ( ( tLList1968894004s_TNil @ A @ B @ Tllist3 )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ Tllist )
% 2.91/1.57 = ( tLList2110128105rminal @ A @ B @ Tllist3 ) ) ) )
% 2.91/1.57 => ( ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist )
% 2.91/1.57 => ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist3 )
% 2.91/1.57 => ( ( ( tLList_Mirabelle_thd @ A @ B @ Tllist )
% 2.91/1.57 = ( tLList_Mirabelle_thd @ A @ B @ Tllist3 ) )
% 2.91/1.57 & ( ( tLList_Mirabelle_ttl @ A @ B @ Tllist )
% 2.91/1.57 = ( tLList_Mirabelle_ttl @ A @ B @ Tllist3 ) ) ) ) )
% 2.91/1.57 => ( Tllist = Tllist3 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_74_tllist_Osplit__sel__asm,axiom,
% 2.91/1.57 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( P @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 2.91/1.57 = ( ~ ( ( ( Tllist
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 2.91/1.57 & ~ ( P @ ( F1 @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) ) )
% 2.91/1.57 | ( ( Tllist
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) )
% 2.91/1.57 & ~ ( P @ ( F2 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_75_tllist_Osplit__sel,axiom,
% 2.91/1.57 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,Tllist: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( P @ ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ Tllist ) )
% 2.91/1.57 = ( ( ( Tllist
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 2.91/1.57 => ( P @ ( F1 @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) ) )
% 2.91/1.57 & ( ( Tllist
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) )
% 2.91/1.57 => ( P @ ( F2 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_76_terminal__TNil,axiom,
% 2.91/1.57 ! [Aa: $tType,A: $tType,X1: A] :
% 2.91/1.57 ( ( tLList2110128105rminal @ Aa @ A @ ( tLList57907754e_TNil @ A @ Aa @ X1 ) )
% 2.91/1.57 = X1 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_77_tllist_Osel_I3_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.91/1.57 = X21 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_78_unfold__tllist_Odisc_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 2.91/1.57 ( ( P4 @ A2 )
% 2.91/1.57 => ( tLList1968894004s_TNil @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_79_unfold__tllist_Odisc_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 2.91/1.57 ( ~ ( P4 @ A2 )
% 2.91/1.57 => ~ ( tLList1968894004s_TNil @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_80_tllist_Ocorec__disc_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.91/1.57 ( ( P4 @ A2 )
% 2.91/1.57 => ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_81_tllist_Ocorec__disc_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.91/1.57 ( ~ ( P4 @ A2 )
% 2.91/1.57 => ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_82_tllist__all2__coinduct,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,D: $tType,C: $tType,X5: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o,Xs: tLList446370796tllist @ A @ B,Ys: tLList446370796tllist @ C @ D,R: B > D > $o,P: A > C > $o] :
% 2.91/1.57 ( ( X5 @ Xs @ Ys )
% 2.91/1.57 => ( ! [Xs3: tLList446370796tllist @ A @ B,Ys3: tLList446370796tllist @ C @ D] :
% 2.91/1.57 ( ( X5 @ Xs3 @ Ys3 )
% 2.91/1.57 => ( ( ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 2.91/1.57 = ( tLList1968894004s_TNil @ C @ D @ Ys3 ) )
% 2.91/1.57 & ( ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 2.91/1.57 => ( ( tLList1968894004s_TNil @ C @ D @ Ys3 )
% 2.91/1.57 => ( R @ ( tLList2110128105rminal @ A @ B @ Xs3 ) @ ( tLList2110128105rminal @ C @ D @ Ys3 ) ) ) )
% 2.91/1.57 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 2.91/1.57 => ( ~ ( tLList1968894004s_TNil @ C @ D @ Ys3 )
% 2.91/1.57 => ( ( P @ ( tLList_Mirabelle_thd @ A @ B @ Xs3 ) @ ( tLList_Mirabelle_thd @ C @ D @ Ys3 ) )
% 2.91/1.57 & ( ( X5 @ ( tLList_Mirabelle_ttl @ A @ B @ Xs3 ) @ ( tLList_Mirabelle_ttl @ C @ D @ Ys3 ) )
% 2.91/1.57 | ( tLList1380991092t_all2 @ A @ C @ B @ D @ P @ R @ ( tLList_Mirabelle_ttl @ A @ B @ Xs3 ) @ ( tLList_Mirabelle_ttl @ C @ D @ Ys3 ) ) ) ) ) ) ) )
% 2.91/1.57 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ P @ R @ Xs @ Ys ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_83_tllist_Orel__coinduct,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,D: $tType,C: $tType,P: ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ C @ D ) > $o,X: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,R2: B > D > $o,R1: A > C > $o] :
% 2.91/1.57 ( ( P @ X @ Y )
% 2.91/1.57 => ( ! [Tllist4: tLList446370796tllist @ A @ B,Tllist5: tLList446370796tllist @ C @ D] :
% 2.91/1.57 ( ( P @ Tllist4 @ Tllist5 )
% 2.91/1.57 => ( ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 = ( tLList1968894004s_TNil @ C @ D @ Tllist5 ) )
% 2.91/1.57 & ( ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 => ( ( tLList1968894004s_TNil @ C @ D @ Tllist5 )
% 2.91/1.57 => ( R2 @ ( tLList2110128105rminal @ A @ B @ Tllist4 ) @ ( tLList2110128105rminal @ C @ D @ Tllist5 ) ) ) )
% 2.91/1.57 & ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist4 )
% 2.91/1.57 => ( ~ ( tLList1968894004s_TNil @ C @ D @ Tllist5 )
% 2.91/1.57 => ( ( R1 @ ( tLList_Mirabelle_thd @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_thd @ C @ D @ Tllist5 ) )
% 2.91/1.57 & ( P @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist4 ) @ ( tLList_Mirabelle_ttl @ C @ D @ Tllist5 ) ) ) ) ) ) )
% 2.91/1.57 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X @ Y ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_84_tllist_Orel__sel,axiom,
% 2.91/1.57 ! [B: $tType,D: $tType,C: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList1380991092t_all2 @ A @ C @ B @ D )
% 2.91/1.57 = ( ^ [R12: A > C > $o,R22: B > D > $o,A4: tLList446370796tllist @ A @ B,B6: tLList446370796tllist @ C @ D] :
% 2.91/1.57 ( ( ( tLList1968894004s_TNil @ A @ B @ A4 )
% 2.91/1.57 = ( tLList1968894004s_TNil @ C @ D @ B6 ) )
% 2.91/1.57 & ( ( tLList1968894004s_TNil @ A @ B @ A4 )
% 2.91/1.57 => ( ( tLList1968894004s_TNil @ C @ D @ B6 )
% 2.91/1.57 => ( R22 @ ( tLList2110128105rminal @ A @ B @ A4 ) @ ( tLList2110128105rminal @ C @ D @ B6 ) ) ) )
% 2.91/1.57 & ( ~ ( tLList1968894004s_TNil @ A @ B @ A4 )
% 2.91/1.57 => ( ~ ( tLList1968894004s_TNil @ C @ D @ B6 )
% 2.91/1.57 => ( ( R12 @ ( tLList_Mirabelle_thd @ A @ B @ A4 ) @ ( tLList_Mirabelle_thd @ C @ D @ B6 ) )
% 2.91/1.57 & ( tLList1380991092t_all2 @ A @ C @ B @ D @ R12 @ R22 @ ( tLList_Mirabelle_ttl @ A @ B @ A4 ) @ ( tLList_Mirabelle_ttl @ C @ D @ B6 ) ) ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_85_tllist_Oexhaust__sel,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( Tllist
% 2.91/1.57 != ( tLList57907754e_TNil @ B @ A @ ( tLList2110128105rminal @ A @ B @ Tllist ) ) )
% 2.91/1.57 => ( Tllist
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ ( tLList_Mirabelle_thd @ A @ B @ Tllist ) @ ( tLList_Mirabelle_ttl @ A @ B @ Tllist ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_86_unfold__tllist_Octr_I1_J,axiom,
% 2.91/1.57 ! [C: $tType,B: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 2.91/1.57 ( ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ C @ ( G1 @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_87_tllist_Osimps_I5_J,axiom,
% 2.91/1.57 ! [A: $tType,C: $tType,B: $tType,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,X1: B] :
% 2.91/1.57 ( ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.91/1.57 = ( F1 @ X1 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_88_tllist_Ocorec_I1_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.91/1.57 ( ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ ( G1 @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_89_unfold__tllist_Octr_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 2.91/1.57 ( ~ ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 )
% 2.91/1.57 = ( tLList1992840728_TCons @ C @ B @ ( G212 @ A2 ) @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_90_tllist_Osimps_I6_J,axiom,
% 2.91/1.57 ! [C: $tType,B: $tType,A: $tType,F1: B > C,F2: A > ( tLList446370796tllist @ A @ B ) > C,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList200813139tllist @ B @ C @ A @ F1 @ F2 @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.91/1.57 = ( F2 @ X21 @ X22 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_91_tllist_Ocorec_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,G1: E > B,G212: E > A,Q222: E > $o,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.91/1.57 ( ~ ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ ( G212 @ A2 ) @ ( if @ ( tLList446370796tllist @ A @ B ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_92_unfold__tllist_Osimps_I5_J,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,A: $tType,P4: A > $o,A2: A,G1: A > B,G212: A > C,G223: A > A] :
% 2.91/1.57 ( ~ ( P4 @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_ttl @ C @ B @ ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ A2 ) )
% 2.91/1.57 = ( tLList636831159tllist @ A @ B @ C @ P4 @ G1 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_93_tllist_Ocorec__sel_I3_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,E: $tType,P4: E > $o,A2: E,Q222: E > $o,G1: E > B,G212: E > A,G2212: E > ( tLList446370796tllist @ A @ B ),G2222: E > E] :
% 2.91/1.57 ( ~ ( P4 @ A2 )
% 2.91/1.57 => ( ( ( Q222 @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.91/1.57 = ( G2212 @ A2 ) ) )
% 2.91/1.57 & ( ~ ( Q222 @ A2 )
% 2.91/1.57 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.91/1.57 = ( tLList1614408749tllist @ E @ B @ A @ P4 @ G1 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_94_tllist_Omap__sel_I1_J,axiom,
% 2.91/1.57 ! [C: $tType,D: $tType,B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,F1: A > C,F2: B > D] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.91/1.57 => ( ( tLList2110128105rminal @ C @ D @ ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ A2 ) )
% 2.91/1.57 = ( F2 @ ( tLList2110128105rminal @ A @ B @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_95_terminal__def,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList2110128105rminal @ A @ B )
% 2.91/1.57 = ( tLList200813139tllist @ B @ B @ A
% 2.91/1.57 @ ^ [X13: B] : X13
% 2.91/1.57 @ ^ [X_dummy: A] : ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ A @ B ) > B ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_96_tllist_Osel_I2_J,axiom,
% 2.91/1.57 ! [A: $tType,Aa: $tType,X21: Aa,X22: tLList446370796tllist @ Aa @ A] :
% 2.91/1.57 ( ( tLList2110128105rminal @ Aa @ A @ ( tLList1992840728_TCons @ Aa @ A @ X21 @ X22 ) )
% 2.91/1.57 = ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ Aa @ A ) > A ) @ X22 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_97_terminal0__terminal,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ A @ B ) > B ) )
% 2.91/1.57 = ( tLList2110128105rminal @ A @ B ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_98_set2__tllist__induct,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,X: A,Xs: tLList446370796tllist @ B @ A,P: A > ( tLList446370796tllist @ B @ A ) > $o] :
% 2.91/1.57 ( ( member @ A @ X @ ( tLList457864275tllist @ B @ A @ Xs ) )
% 2.91/1.57 => ( ! [Xs3: tLList446370796tllist @ B @ A] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ B @ A @ Xs3 )
% 2.91/1.57 => ( P @ ( tLList2110128105rminal @ B @ A @ Xs3 ) @ Xs3 ) )
% 2.91/1.57 => ( ! [Xs3: tLList446370796tllist @ B @ A,Y5: A] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ B @ A @ Xs3 )
% 2.91/1.57 => ( ( member @ A @ Y5 @ ( tLList457864275tllist @ B @ A @ ( tLList_Mirabelle_ttl @ B @ A @ Xs3 ) ) )
% 2.91/1.57 => ( ( P @ Y5 @ ( tLList_Mirabelle_ttl @ B @ A @ Xs3 ) )
% 2.91/1.57 => ( P @ Y5 @ Xs3 ) ) ) )
% 2.91/1.57 => ( P @ X @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_99_tllist__set__induct,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X: A,Xs: tLList446370796tllist @ A @ B,P: A > ( tLList446370796tllist @ A @ B ) > $o] :
% 2.91/1.57 ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ Xs ) )
% 2.91/1.57 => ( ! [Xs3: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 2.91/1.57 => ( P @ ( tLList_Mirabelle_thd @ A @ B @ Xs3 ) @ Xs3 ) )
% 2.91/1.57 => ( ! [Xs3: tLList446370796tllist @ A @ B,Y5: A] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs3 )
% 2.91/1.57 => ( ( member @ A @ Y5 @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs3 ) ) )
% 2.91/1.57 => ( ( P @ Y5 @ ( tLList_Mirabelle_ttl @ A @ B @ Xs3 ) )
% 2.91/1.57 => ( P @ Y5 @ Xs3 ) ) ) )
% 2.91/1.57 => ( P @ X @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_100_tconcat__TCons,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,A2: coinductive_llist @ A,Tr: tLList446370796tllist @ ( coinductive_llist @ A ) @ B] :
% 2.91/1.57 ( ( tLList365522113concat @ B @ A @ B4 @ ( tLList1992840728_TCons @ ( coinductive_llist @ A ) @ B @ A2 @ Tr ) )
% 2.91/1.57 = ( tLList98099029ppendt @ A @ B @ A2 @ ( tLList365522113concat @ B @ A @ B4 @ Tr ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_101_tconcat_H__def,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType] :
% 2.91/1.57 ( ( tLList1329345514concat @ B @ A )
% 2.91/1.57 = ( ^ [B6: product_unit > B] : ( tLList365522113concat @ B @ A @ ( B6 @ product_Unity ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_102_tllist_Orel__cong,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,D: $tType,C: $tType,X: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,Xa: tLList446370796tllist @ C @ D,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
% 2.91/1.57 ( ( X = Ya )
% 2.91/1.57 => ( ( Y = Xa )
% 2.91/1.57 => ( ! [Z12: A,Y12: C] :
% 2.91/1.57 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 2.91/1.57 => ( ( member @ C @ Y12 @ ( tLList1719791291e_tset @ C @ D @ Xa ) )
% 2.91/1.57 => ( ( R1 @ Z12 @ Y12 )
% 2.91/1.57 = ( R1a @ Z12 @ Y12 ) ) ) )
% 2.91/1.57 => ( ! [Z22: B,Y23: D] :
% 2.91/1.57 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 2.91/1.57 => ( ( member @ D @ Y23 @ ( tLList457864275tllist @ C @ D @ Xa ) )
% 2.91/1.57 => ( ( R2 @ Z22 @ Y23 )
% 2.91/1.57 = ( R2a @ Z22 @ Y23 ) ) ) )
% 2.91/1.57 => ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X @ Y )
% 2.91/1.57 = ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_103_tllist_Orel__mono__strong,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X: tLList446370796tllist @ A @ B,Y: tLList446370796tllist @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 2.91/1.57 ( ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1 @ R2 @ X @ Y )
% 2.91/1.57 => ( ! [Z12: A,Y12: C] :
% 2.91/1.57 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 2.91/1.57 => ( ( member @ C @ Y12 @ ( tLList1719791291e_tset @ C @ D @ Y ) )
% 2.91/1.57 => ( ( R1 @ Z12 @ Y12 )
% 2.91/1.57 => ( R1a @ Z12 @ Y12 ) ) ) )
% 2.91/1.57 => ( ! [Z22: B,Y23: D] :
% 2.91/1.57 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 2.91/1.57 => ( ( member @ D @ Y23 @ ( tLList457864275tllist @ C @ D @ Y ) )
% 2.91/1.57 => ( ( R2 @ Z22 @ Y23 )
% 2.91/1.57 => ( R2a @ Z22 @ Y23 ) ) ) )
% 2.91/1.57 => ( tLList1380991092t_all2 @ A @ C @ B @ D @ R1a @ R2a @ X @ Y ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_104_tllist_Orel__refl__strong,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 2.91/1.57 ( ! [Z12: A] :
% 2.91/1.57 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 2.91/1.57 => ( R1a @ Z12 @ Z12 ) )
% 2.91/1.57 => ( ! [Z22: B] :
% 2.91/1.57 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 2.91/1.57 => ( R2a @ Z22 @ Z22 ) )
% 2.91/1.57 => ( tLList1380991092t_all2 @ A @ A @ B @ B @ R1a @ R2a @ X @ X ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_105_tllist_Omap__cong,axiom,
% 2.91/1.57 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 2.91/1.57 ( ( X = Ya )
% 2.91/1.57 => ( ! [Z12: A] :
% 2.91/1.57 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 2.91/1.57 => ( ( F1 @ Z12 )
% 2.91/1.57 = ( G1 @ Z12 ) ) )
% 2.91/1.57 => ( ! [Z22: B] :
% 2.91/1.57 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 2.91/1.57 => ( ( F2 @ Z22 )
% 2.91/1.57 = ( G2 @ Z22 ) ) )
% 2.91/1.57 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X )
% 2.91/1.57 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_106_tllist_Omap__cong0,axiom,
% 2.91/1.57 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 2.91/1.57 ( ! [Z12: A] :
% 2.91/1.57 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 2.91/1.57 => ( ( F1 @ Z12 )
% 2.91/1.57 = ( G1 @ Z12 ) ) )
% 2.91/1.57 => ( ! [Z22: B] :
% 2.91/1.57 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 2.91/1.57 => ( ( F2 @ Z22 )
% 2.91/1.57 = ( G2 @ Z22 ) ) )
% 2.91/1.57 => ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X )
% 2.91/1.57 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ G1 @ G2 @ X ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_107_tllist_Oinj__map__strong,axiom,
% 2.91/1.57 ! [C: $tType,D: $tType,B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,Xa: tLList446370796tllist @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
% 2.91/1.57 ( ! [Z12: A,Z1a: A] :
% 2.91/1.57 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 2.91/1.57 => ( ( member @ A @ Z1a @ ( tLList1719791291e_tset @ A @ B @ Xa ) )
% 2.91/1.57 => ( ( ( F1 @ Z12 )
% 2.91/1.57 = ( F1a @ Z1a ) )
% 2.91/1.57 => ( Z12 = Z1a ) ) ) )
% 2.91/1.57 => ( ! [Z22: B,Z2a: B] :
% 2.91/1.57 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 2.91/1.57 => ( ( member @ B @ Z2a @ ( tLList457864275tllist @ A @ B @ Xa ) )
% 2.91/1.57 => ( ( ( F2 @ Z22 )
% 2.91/1.57 = ( F2a @ Z2a ) )
% 2.91/1.57 => ( Z22 = Z2a ) ) ) )
% 2.91/1.57 => ( ( ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1 @ F2 @ X )
% 2.91/1.57 = ( tLList1669959861e_tmap @ A @ C @ B @ D @ F1a @ F2a @ Xa ) )
% 2.91/1.57 => ( X = Xa ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_108_tllist_Opred__mono__strong,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,X: tLList446370796tllist @ A @ B,P1a: A > $o,P2a: B > $o] :
% 2.91/1.57 ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ X )
% 2.91/1.57 => ( ! [Z12: A] :
% 2.91/1.57 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ X ) )
% 2.91/1.57 => ( ( P1 @ Z12 )
% 2.91/1.57 => ( P1a @ Z12 ) ) )
% 2.91/1.57 => ( ! [Z22: B] :
% 2.91/1.57 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ X ) )
% 2.91/1.57 => ( ( P2 @ Z22 )
% 2.91/1.57 => ( P2a @ Z22 ) ) )
% 2.91/1.57 => ( tLList11265572tllist @ A @ B @ P1a @ P2a @ X ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_109_tllist_Opred__cong,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X: tLList446370796tllist @ A @ B,Ya: tLList446370796tllist @ A @ B,P1: A > $o,P1a: A > $o,P2: B > $o,P2a: B > $o] :
% 2.91/1.57 ( ( X = Ya )
% 2.91/1.57 => ( ! [Z12: A] :
% 2.91/1.57 ( ( member @ A @ Z12 @ ( tLList1719791291e_tset @ A @ B @ Ya ) )
% 2.91/1.57 => ( ( P1 @ Z12 )
% 2.91/1.57 = ( P1a @ Z12 ) ) )
% 2.91/1.57 => ( ! [Z22: B] :
% 2.91/1.57 ( ( member @ B @ Z22 @ ( tLList457864275tllist @ A @ B @ Ya ) )
% 2.91/1.57 => ( ( P2 @ Z22 )
% 2.91/1.57 = ( P2a @ Z22 ) ) )
% 2.91/1.57 => ( ( tLList11265572tllist @ A @ B @ P1 @ P2 @ X )
% 2.91/1.57 = ( tLList11265572tllist @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_110_tllist_Oset__cases_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,E2: A,A2: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( member @ A @ E2 @ ( tLList1719791291e_tset @ A @ B @ A2 ) )
% 2.91/1.57 => ( ! [Z22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( A2
% 2.91/1.57 != ( tLList1992840728_TCons @ A @ B @ E2 @ Z22 ) )
% 2.91/1.57 => ~ ! [Z12: A,Z22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( A2
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ Z12 @ Z22 ) )
% 2.91/1.57 => ~ ( member @ A @ E2 @ ( tLList1719791291e_tset @ A @ B @ Z22 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_111_tllist_Oset__induct_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X: A,A2: tLList446370796tllist @ A @ B,P: A > ( tLList446370796tllist @ A @ B ) > $o] :
% 2.91/1.57 ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ A2 ) )
% 2.91/1.57 => ( ! [Z12: A,Z22: tLList446370796tllist @ A @ B] : ( P @ Z12 @ ( tLList1992840728_TCons @ A @ B @ Z12 @ Z22 ) )
% 2.91/1.57 => ( ! [Z12: A,Z22: tLList446370796tllist @ A @ B,Xa2: A] :
% 2.91/1.57 ( ( member @ A @ Xa2 @ ( tLList1719791291e_tset @ A @ B @ Z22 ) )
% 2.91/1.57 => ( ( P @ Xa2 @ Z22 )
% 2.91/1.57 => ( P @ Xa2 @ ( tLList1992840728_TCons @ A @ B @ Z12 @ Z22 ) ) ) )
% 2.91/1.57 => ( P @ X @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_112_tllist_Oset__intros_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X: A,A22: tLList446370796tllist @ A @ B,A1: A] :
% 2.91/1.57 ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ A22 ) )
% 2.91/1.57 => ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1 @ A22 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_113_tllist_Oset__intros_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,A1: A,A22: tLList446370796tllist @ A @ B] : ( member @ A @ A1 @ ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1 @ A22 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_114_in__tset__ttlD,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X: A,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs ) ) )
% 2.91/1.57 => ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_115_tllist_Oset__intros_I3_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,Aa2: B] : ( member @ B @ Aa2 @ ( tLList457864275tllist @ A @ B @ ( tLList57907754e_TNil @ B @ A @ Aa2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_116_tllist_Osimps_I23_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList457864275tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.91/1.57 = ( tLList457864275tllist @ A @ B @ X22 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_117_tllist_Oset__intros_I4_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xc: B,A2a: tLList446370796tllist @ A @ B,A1a: A] :
% 2.91/1.57 ( ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ A2a ) )
% 2.91/1.57 => ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ A1a @ A2a ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_118_tllist_Odisc__eq__case_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Tllist: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( ~ ( tLList1968894004s_TNil @ A @ B @ Tllist ) )
% 2.91/1.57 = ( tLList200813139tllist @ B @ $o @ A
% 2.91/1.57 @ ^ [Uu: B] : $false
% 2.91/1.57 @ ^ [Uu: A,Uv: tLList446370796tllist @ A @ B] : $true
% 2.91/1.57 @ Tllist ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_119_tllist_Odisc__eq__case_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B )
% 2.91/1.57 = ( tLList200813139tllist @ B @ $o @ A
% 2.91/1.57 @ ^ [Uu: B] : $true
% 2.91/1.57 @ ^ [Uu: A,Uv: tLList446370796tllist @ A @ B] : $false ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_120_tllist_Oset__sel_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,X: A] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.91/1.57 => ( ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) )
% 2.91/1.57 => ( member @ A @ X @ ( tLList1719791291e_tset @ A @ B @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_121_tllist_Oset__sel_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.91/1.57 => ( member @ A @ ( tLList_Mirabelle_thd @ A @ B @ A2 ) @ ( tLList1719791291e_tset @ A @ B @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_122_tllist_Oset__sel_I3_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.91/1.57 => ( member @ B @ ( tLList2110128105rminal @ A @ B @ A2 ) @ ( tLList457864275tllist @ A @ B @ A2 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_123_tllist_Oset__cases_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,E2: B,A2: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( member @ B @ E2 @ ( tLList457864275tllist @ A @ B @ A2 ) )
% 2.91/1.57 => ( ( A2
% 2.91/1.57 != ( tLList57907754e_TNil @ B @ A @ E2 ) )
% 2.91/1.57 => ~ ! [Z12: A,Z22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( A2
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ Z12 @ Z22 ) )
% 2.91/1.57 => ~ ( member @ B @ E2 @ ( tLList457864275tllist @ A @ B @ Z22 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_124_tllist_Oset__induct_I2_J,axiom,
% 2.91/1.57 ! [A: $tType,Aa: $tType,X: A,A2: tLList446370796tllist @ Aa @ A,P: A > ( tLList446370796tllist @ Aa @ A ) > $o] :
% 2.91/1.57 ( ( member @ A @ X @ ( tLList457864275tllist @ Aa @ A @ A2 ) )
% 2.91/1.57 => ( ! [Z4: A] : ( P @ Z4 @ ( tLList57907754e_TNil @ A @ Aa @ Z4 ) )
% 2.91/1.57 => ( ! [Z12: Aa,Z22: tLList446370796tllist @ Aa @ A,Xb: A] :
% 2.91/1.57 ( ( member @ A @ Xb @ ( tLList457864275tllist @ Aa @ A @ Z22 ) )
% 2.91/1.57 => ( ( P @ Xb @ Z22 )
% 2.91/1.57 => ( P @ Xb @ ( tLList1992840728_TCons @ Aa @ A @ Z12 @ Z22 ) ) ) )
% 2.91/1.57 => ( P @ X @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_125_tllist_Oset__sel_I4_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,A2: tLList446370796tllist @ A @ B,Xc: B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ A2 )
% 2.91/1.57 => ( ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ A2 ) ) )
% 2.91/1.57 => ( member @ B @ Xc @ ( tLList457864275tllist @ A @ B @ A2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_126_tconcat_H__code_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,B4: product_unit > B,A2: coinductive_llist @ C,Tr: tLList446370796tllist @ ( coinductive_llist @ C ) @ B] :
% 2.91/1.57 ( ( tLList1329345514concat @ B @ C @ B4 @ ( tLList1992840728_TCons @ ( coinductive_llist @ C ) @ B @ A2 @ Tr ) )
% 2.91/1.57 = ( tLList98099029ppendt @ C @ B @ A2 @ ( tLList1329345514concat @ B @ C @ B4 @ Tr ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_127_unit__abs__eta__conv,axiom,
% 2.91/1.57 ! [A: $tType,F3: product_unit > A] :
% 2.91/1.57 ( ( ^ [U: product_unit] : ( F3 @ product_Unity ) )
% 2.91/1.57 = F3 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_128_is__TNil__tfilter,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Y: B,P: A > $o,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ ( tLList1813626245filter @ B @ A @ Y @ P @ Xs ) )
% 2.91/1.57 = ( ! [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ ( tLList1719791291e_tset @ A @ B @ Xs ) )
% 2.91/1.57 => ~ ( P @ X2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_129_old_Ounit_Oexhaust,axiom,
% 2.91/1.57 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_130_old_Ounit_Oinducts,axiom,
% 2.91/1.57 ! [P: product_unit > $o,Unit: product_unit] :
% 2.91/1.57 ( ( P @ product_Unity )
% 2.91/1.57 => ( P @ Unit ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_131_unit__all__impI,axiom,
% 2.91/1.57 ! [P: product_unit > $o,Q: product_unit > $o] :
% 2.91/1.57 ( ( ( P @ product_Unity )
% 2.91/1.57 => ( Q @ product_Unity ) )
% 2.91/1.57 => ! [X6: product_unit] :
% 2.91/1.57 ( ( P @ X6 )
% 2.91/1.57 => ( Q @ X6 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_132_tfilter__TNil,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,B5: B,P: A > $o,B4: B] :
% 2.91/1.57 ( ( tLList1813626245filter @ B @ A @ B5 @ P @ ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ B4 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_133_tfilter__TCons,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,P: A > $o,A2: A,B4: B,Tr: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( ( P @ A2 )
% 2.91/1.57 => ( ( tLList1813626245filter @ B @ A @ B4 @ P @ ( tLList1992840728_TCons @ A @ B @ A2 @ Tr ) )
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ A2 @ ( tLList1813626245filter @ B @ A @ B4 @ P @ Tr ) ) ) )
% 2.91/1.57 & ( ~ ( P @ A2 )
% 2.91/1.57 => ( ( tLList1813626245filter @ B @ A @ B4 @ P @ ( tLList1992840728_TCons @ A @ B @ A2 @ Tr ) )
% 2.91/1.57 = ( tLList1813626245filter @ B @ A @ B4 @ P @ Tr ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_134_eq__sym__Unity__conv,axiom,
% 2.91/1.57 ! [X: $o] :
% 2.91/1.57 ( ( X
% 2.91/1.57 = ( product_Unity = product_Unity ) )
% 2.91/1.57 = X ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_135_old_Ounit_Orec,axiom,
% 2.91/1.57 ! [T: $tType,F1: T] :
% 2.91/1.57 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 2.91/1.57 = F1 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_136_default__unit__def,axiom,
% 2.91/1.57 ( ( default_default @ product_unit )
% 2.91/1.57 = product_Unity ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_137_tfilter_H__def,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType] :
% 2.91/1.57 ( ( tLList1122525870filter @ B @ A )
% 2.91/1.57 = ( ^ [B6: product_unit > B] : ( tLList1813626245filter @ B @ A @ ( B6 @ product_Unity ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_138_tfilter__code,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList1813626245filter @ A @ B )
% 2.91/1.57 = ( ^ [B6: A] :
% 2.91/1.57 ( tLList1122525870filter @ A @ B
% 2.91/1.57 @ ^ [Uu: product_unit] : B6 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_139_tfilter_H__code_I1_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,B5: product_unit > B,P: A > $o,B4: B] :
% 2.91/1.57 ( ( tLList1122525870filter @ B @ A @ B5 @ P @ ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ B4 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_140_tfilter_H__code_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,P: A > $o,A2: A,B5: product_unit > B,Tr: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( ( P @ A2 )
% 2.91/1.57 => ( ( tLList1122525870filter @ B @ A @ B5 @ P @ ( tLList1992840728_TCons @ A @ B @ A2 @ Tr ) )
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ A2 @ ( tLList1122525870filter @ B @ A @ B5 @ P @ Tr ) ) ) )
% 2.91/1.57 & ( ~ ( P @ A2 )
% 2.91/1.57 => ( ( tLList1122525870filter @ B @ A @ B5 @ P @ ( tLList1992840728_TCons @ A @ B @ A2 @ Tr ) )
% 2.91/1.57 = ( tLList1122525870filter @ B @ A @ B5 @ P @ Tr ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_141_tllist_Opred__set,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList11265572tllist @ A @ B )
% 2.91/1.57 = ( ^ [P12: A > $o,P22: B > $o,X2: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ! [Y2: A] :
% 2.91/1.57 ( ( member @ A @ Y2 @ ( tLList1719791291e_tset @ A @ B @ X2 ) )
% 2.91/1.57 => ( P12 @ Y2 ) )
% 2.91/1.57 & ! [Y2: B] :
% 2.91/1.57 ( ( member @ B @ Y2 @ ( tLList457864275tllist @ A @ B @ X2 ) )
% 2.91/1.57 => ( P22 @ Y2 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_142_old_Ounit_Ocase,axiom,
% 2.91/1.57 ! [A: $tType,F3: A] :
% 2.91/1.57 ( ( product_case_unit @ A @ F3 @ product_Unity )
% 2.91/1.57 = F3 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_143_lappendt__LCons,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X: A,Xs: coinductive_llist @ A,Tr: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList98099029ppendt @ A @ B @ ( coinductive_LCons @ A @ X @ Xs ) @ Tr )
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ X @ ( tLList98099029ppendt @ A @ B @ Xs @ Tr ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_144_terminal__lappendt__lfinite,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Ys: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( coinductive_lfinite @ A @ Xs )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ ( tLList98099029ppendt @ A @ B @ Xs @ Ys ) )
% 2.91/1.57 = ( tLList2110128105rminal @ A @ B @ Ys ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_145_unit_Ocase__distrib,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,H: A > B,F3: A,Unit: product_unit] :
% 2.91/1.57 ( ( H @ ( product_case_unit @ A @ F3 @ Unit ) )
% 2.91/1.57 = ( product_case_unit @ B @ ( H @ F3 ) @ Unit ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_146_case__unit__Unity,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( product_case_unit @ A )
% 2.91/1.57 = ( ^ [F4: A,U: product_unit] : F4 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_147_tfilter__empty__conv,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,Y: B,P: A > $o,Xs: tLList446370796tllist @ A @ B,Y6: B] :
% 2.91/1.57 ( ( ( tLList1813626245filter @ B @ A @ Y @ P @ Xs )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ Y6 ) )
% 2.91/1.57 = ( ! [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ ( tLList1719791291e_tset @ A @ B @ Xs ) )
% 2.91/1.57 => ~ ( P @ X2 ) )
% 2.91/1.57 & ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ Xs )
% 2.91/1.57 = Y6 ) )
% 2.91/1.57 & ( ~ ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 => ( Y = Y6 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_148_terminal__tmap,axiom,
% 2.91/1.57 ! [D: $tType,C: $tType,B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B,F3: A > D,G: B > C] :
% 2.91/1.57 ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 => ( ( tLList2110128105rminal @ D @ C @ ( tLList1669959861e_tmap @ A @ D @ B @ C @ F3 @ G @ Xs ) )
% 2.91/1.57 = ( G @ ( tLList2110128105rminal @ A @ B @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_149_tfilter__eq__TConsD,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,A2: B,P: A > $o,Ys: tLList446370796tllist @ A @ B,X: A,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( ( tLList1813626245filter @ B @ A @ A2 @ P @ Ys )
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ X @ Xs ) )
% 2.91/1.57 => ? [Us: coinductive_llist @ A,Vs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( Ys
% 2.91/1.57 = ( tLList98099029ppendt @ A @ B @ Us @ ( tLList1992840728_TCons @ A @ B @ X @ Vs ) ) )
% 2.91/1.57 & ( coinductive_lfinite @ A @ Us )
% 2.91/1.57 & ! [X6: A] :
% 2.91/1.57 ( ( member @ A @ X6 @ ( coinductive_lset @ A @ Us ) )
% 2.91/1.57 => ~ ( P @ X6 ) )
% 2.91/1.57 & ( P @ X )
% 2.91/1.57 & ( Xs
% 2.91/1.57 = ( tLList1813626245filter @ B @ A @ A2 @ P @ Vs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_150_llist__of__tllist__TCons,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xa: A,X: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList798109904tllist @ A @ B @ ( tLList1992840728_TCons @ A @ B @ Xa @ X ) )
% 2.91/1.57 = ( coinductive_LCons @ A @ Xa @ ( tLList798109904tllist @ A @ B @ X ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_151_lset__llist__of__tllist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( coinductive_lset @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 = ( tLList1719791291e_tset @ A @ B @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_152_is__TNil__tfinite,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_153_tfinite__induct,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B,P: ( tLList446370796tllist @ A @ B ) > $o] :
% 2.91/1.57 ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 => ( ! [Y5: B] : ( P @ ( tLList57907754e_TNil @ B @ A @ Y5 ) )
% 2.91/1.57 => ( ! [X3: A,Xs3: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs3 ) )
% 2.91/1.57 => ( ( P @ Xs3 )
% 2.91/1.57 => ( P @ ( tLList1992840728_TCons @ A @ B @ X3 @ Xs3 ) ) ) )
% 2.91/1.57 => ( P @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_154_tset__lappendt__lfinite,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Ys: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( coinductive_lfinite @ A @ Xs )
% 2.91/1.57 => ( ( tLList1719791291e_tset @ A @ B @ ( tLList98099029ppendt @ A @ B @ Xs @ Ys ) )
% 2.91/1.57 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( tLList1719791291e_tset @ A @ B @ Ys ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_155_tfinite__tappend,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,A: $tType,Xs: tLList446370796tllist @ A @ C,F3: C > ( tLList446370796tllist @ A @ B )] :
% 2.91/1.57 ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ ( tLList192138471append @ A @ C @ B @ Xs @ F3 ) ) )
% 2.91/1.57 = ( ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ C @ Xs ) )
% 2.91/1.57 & ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ ( F3 @ ( tLList2110128105rminal @ A @ C @ Xs ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_156_terminal__tappend,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,Xs: tLList446370796tllist @ B @ A,F3: A > ( tLList446370796tllist @ B @ A )] :
% 2.91/1.57 ( ( ( coinductive_lfinite @ B @ ( tLList798109904tllist @ B @ A @ Xs ) )
% 2.91/1.57 => ( ( tLList2110128105rminal @ B @ A @ ( tLList192138471append @ B @ A @ A @ Xs @ F3 ) )
% 2.91/1.57 = ( tLList2110128105rminal @ B @ A @ ( F3 @ ( tLList2110128105rminal @ B @ A @ Xs ) ) ) ) )
% 2.91/1.57 & ( ~ ( coinductive_lfinite @ B @ ( tLList798109904tllist @ B @ A @ Xs ) )
% 2.91/1.57 => ( ( tLList2110128105rminal @ B @ A @ ( tLList192138471append @ B @ A @ A @ Xs @ F3 ) )
% 2.91/1.57 = ( tLList2110128105rminal @ B @ A @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_157_tappend__TNil2,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList192138471append @ A @ B @ B @ Xs @ ( tLList57907754e_TNil @ B @ A ) )
% 2.91/1.57 = Xs ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_158_tappend__TNil,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,C: $tType,B4: C,F3: C > ( tLList446370796tllist @ A @ B )] :
% 2.91/1.57 ( ( tLList192138471append @ A @ C @ B @ ( tLList57907754e_TNil @ C @ A @ B4 ) @ F3 )
% 2.91/1.57 = ( F3 @ B4 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_159_tappend__TCons,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,C: $tType,A2: A,Tr: tLList446370796tllist @ A @ C,F3: C > ( tLList446370796tllist @ A @ B )] :
% 2.91/1.57 ( ( tLList192138471append @ A @ C @ B @ ( tLList1992840728_TCons @ A @ C @ A2 @ Tr ) @ F3 )
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ A2 @ ( tLList192138471append @ A @ C @ B @ Tr @ F3 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_160_tappend__assoc,axiom,
% 2.91/1.57 ! [C: $tType,A: $tType,B: $tType,D: $tType,Xs: tLList446370796tllist @ A @ D,F3: D > ( tLList446370796tllist @ A @ C ),G: C > ( tLList446370796tllist @ A @ B )] :
% 2.91/1.57 ( ( tLList192138471append @ A @ C @ B @ ( tLList192138471append @ A @ D @ C @ Xs @ F3 ) @ G )
% 2.91/1.57 = ( tLList192138471append @ A @ D @ B @ Xs
% 2.91/1.57 @ ^ [B6: D] : ( tLList192138471append @ A @ C @ B @ ( F3 @ B6 ) @ G ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_161_tappend__inf,axiom,
% 2.91/1.57 ! [C: $tType,B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B,F3: B > ( tLList446370796tllist @ A @ C )] :
% 2.91/1.57 ( ~ ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 => ( ( tLList192138471append @ A @ B @ C @ Xs @ F3 )
% 2.91/1.57 = ( tLList222516140_tcast @ A @ B @ C @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_162_Collect__disj__eq,axiom,
% 2.91/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.91/1.57 ( ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( P @ X2 )
% 2.91/1.57 | ( Q @ X2 ) ) )
% 2.91/1.57 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_163_Un__def,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( sup_sup @ ( set @ A ) )
% 2.91/1.57 = ( ^ [A5: set @ A,B8: set @ A] :
% 2.91/1.57 ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ A5 )
% 2.91/1.57 | ( member @ A @ X2 @ B8 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_164_lhd__llist__of__tllist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( ( coinductive_lhd @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 = ( tLList_Mirabelle_thd @ A @ B @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_165_terminal__tinfinite,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( coinductive_lfinite @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ Xs )
% 2.91/1.57 = ( undefined @ B ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_166_llist__of__tllist__inverse,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1672613558_llist @ B @ A @ ( tLList2110128105rminal @ A @ B @ B4 ) @ ( tLList798109904tllist @ A @ B @ B4 ) )
% 2.91/1.57 = B4 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_167_tllist__of__llist__inject,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,B4: B,Xs: coinductive_llist @ A,C2: B,Ys: coinductive_llist @ A] :
% 2.91/1.57 ( ( ( tLList1672613558_llist @ B @ A @ B4 @ Xs )
% 2.91/1.57 = ( tLList1672613558_llist @ B @ A @ C2 @ Ys ) )
% 2.91/1.57 = ( ( Xs = Ys )
% 2.91/1.57 & ( ( coinductive_lfinite @ A @ Ys )
% 2.91/1.57 => ( B4 = C2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_168_tllist__of__llist__inverse,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( tLList798109904tllist @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = Xs ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_169_tllist__of__llist__LCons,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,Xa: A,X: coinductive_llist @ A] :
% 2.91/1.57 ( ( tLList1672613558_llist @ B @ A @ B4 @ ( coinductive_LCons @ A @ Xa @ X ) )
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B @ Xa @ ( tLList1672613558_llist @ B @ A @ B4 @ X ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_170_terminal__tllist__of__llist__lfinite,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ( coinductive_lfinite @ A @ Xs )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = B4 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_171_tset__tllist__of__llist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( tLList1719791291e_tset @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = ( coinductive_lset @ A @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_172_thd__tllist__of__llist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = ( coinductive_lhd @ A @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_173_terminal__tllist__of__llist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ B,Y: A] :
% 2.91/1.57 ( ( ( coinductive_lfinite @ B @ Xs )
% 2.91/1.57 => ( ( tLList2110128105rminal @ B @ A @ ( tLList1672613558_llist @ A @ B @ Y @ Xs ) )
% 2.91/1.57 = Y ) )
% 2.91/1.57 & ( ~ ( coinductive_lfinite @ B @ Xs )
% 2.91/1.57 => ( ( tLList2110128105rminal @ B @ A @ ( tLList1672613558_llist @ A @ B @ Y @ Xs ) )
% 2.91/1.57 = ( undefined @ A ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_174_tllist__of__llist__cong,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Xs4: coinductive_llist @ A,B4: B,B5: B] :
% 2.91/1.57 ( ( Xs = Xs4 )
% 2.91/1.57 => ( ( ( coinductive_lfinite @ A @ Xs4 )
% 2.91/1.57 => ( B4 = B5 ) )
% 2.91/1.57 => ( ( tLList1672613558_llist @ B @ A @ B4 @ Xs )
% 2.91/1.57 = ( tLList1672613558_llist @ B @ A @ B5 @ Xs4 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_175_llist__of__tllist_Osimps_I3_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( ( coinductive_lhd @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 = ( tLList200813139tllist @ B @ A @ A
% 2.91/1.57 @ ^ [X2: B] : ( undefined @ A )
% 2.91/1.57 @ ^ [X2: A,Xs5: tLList446370796tllist @ A @ B] : X2
% 2.91/1.57 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_176_llist__of__tllist_Octr_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( ( tLList798109904tllist @ A @ B @ Xs )
% 2.91/1.57 = ( coinductive_LCons @ A
% 2.91/1.57 @ ( tLList200813139tllist @ B @ A @ A
% 2.91/1.57 @ ^ [X2: B] : ( undefined @ A )
% 2.91/1.57 @ ^ [X2: A,Xs5: tLList446370796tllist @ A @ B] : X2
% 2.91/1.57 @ Xs )
% 2.91/1.57 @ ( tLList200813139tllist @ B @ ( coinductive_llist @ A ) @ A
% 2.91/1.57 @ ^ [X2: B] : ( undefined @ ( coinductive_llist @ A ) )
% 2.91/1.57 @ ^ [X2: A] : ( tLList798109904tllist @ A @ B )
% 2.91/1.57 @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_177_thd__TNil,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B] :
% 2.91/1.57 ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 2.91/1.57 = ( undefined @ A ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_178_thd__def,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList_Mirabelle_thd @ A @ B )
% 2.91/1.57 = ( tLList200813139tllist @ B @ A @ A
% 2.91/1.57 @ ^ [X_dummy: B] : ( undefined @ A )
% 2.91/1.57 @ ^ [X213: A,X223: tLList446370796tllist @ A @ B] : X213 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_179_terminal0_Oraw__induct,axiom,
% 2.91/1.57 ! [C: $tType,D: $tType,P: ( tLList446370796tllist @ C @ D ) > D > $o,Xs: tLList446370796tllist @ C @ D,Y: D] :
% 2.91/1.57 ( ! [Terminal0: ( tLList446370796tllist @ C @ D ) > D] :
% 2.91/1.57 ( ! [X6: tLList446370796tllist @ C @ D] :
% 2.91/1.57 ( ( ( Terminal0 @ X6 )
% 2.91/1.57 != ( undefined @ D ) )
% 2.91/1.57 => ( P @ X6 @ ( Terminal0 @ X6 ) ) )
% 2.91/1.57 => ! [Xs3: tLList446370796tllist @ C @ D,Xsa: D] :
% 2.91/1.57 ( ( ( ( tLList1968894004s_TNil @ C @ D @ Xs3 )
% 2.91/1.57 => ( ( tLList200813139tllist @ D @ D @ C @ ( id @ D ) @ ( undefined @ ( C > ( tLList446370796tllist @ C @ D ) > D ) ) @ Xs3 )
% 2.91/1.57 = Xsa ) )
% 2.91/1.57 & ( ~ ( tLList1968894004s_TNil @ C @ D @ Xs3 )
% 2.91/1.57 => ( ( Terminal0 @ ( tLList_Mirabelle_ttl @ C @ D @ Xs3 ) )
% 2.91/1.57 = Xsa ) ) )
% 2.91/1.57 => ( ( Xsa
% 2.91/1.57 != ( undefined @ D ) )
% 2.91/1.57 => ( P @ Xs3 @ Xsa ) ) ) )
% 2.91/1.57 => ( ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) @ Xs )
% 2.91/1.57 = Y )
% 2.91/1.57 => ( ( Y
% 2.91/1.57 != ( undefined @ D ) )
% 2.91/1.57 => ( P @ Xs @ Y ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_180_terminal0_Osimps,axiom,
% 2.91/1.57 ! [D: $tType,C: $tType] :
% 2.91/1.57 ( ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) )
% 2.91/1.57 = ( ^ [Xs6: tLList446370796tllist @ C @ D] : ( if @ D @ ( tLList1968894004s_TNil @ C @ D @ Xs6 ) @ ( tLList200813139tllist @ D @ D @ C @ ( id @ D ) @ ( undefined @ ( C > ( tLList446370796tllist @ C @ D ) > D ) ) @ Xs6 ) @ ( tLList1825092077minal0 @ ( ( tLList446370796tllist @ C @ D ) > D ) @ ( tLList_Mirabelle_ttl @ C @ D @ Xs6 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_181_tllist__of__llist_Ocode,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType] :
% 2.91/1.57 ( ( tLList1672613558_llist @ B @ A )
% 2.91/1.57 = ( ^ [B6: B] :
% 2.91/1.57 ( coindu1381640503_llist @ ( tLList446370796tllist @ A @ B ) @ A @ ( tLList57907754e_TNil @ B @ A @ B6 )
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( tLList1992840728_TCons @ A @ B @ X2 @ ( tLList1672613558_llist @ B @ A @ B6 @ Xs5 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_182_tllist_Omap__id,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,T2: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1669959861e_tmap @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) @ T2 )
% 2.91/1.57 = T2 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_183_tllist_Omap__id0,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList1669959861e_tmap @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 2.91/1.57 = ( id @ ( tLList446370796tllist @ A @ B ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_184_lhd__def,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( coinductive_lhd @ A )
% 2.91/1.57 = ( coindu1381640503_llist @ A @ A @ ( undefined @ A )
% 2.91/1.57 @ ^ [X213: A,X223: coinductive_llist @ A] : X213 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_185_tllist__of__llist_Octr_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ~ ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 => ( ( tLList1672613558_llist @ B @ A @ B4 @ Xs )
% 2.91/1.57 = ( tLList1992840728_TCons @ A @ B
% 2.91/1.57 @ ( coindu1381640503_llist @ A @ A @ ( undefined @ A )
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : X2
% 2.91/1.57 @ Xs )
% 2.91/1.57 @ ( coindu1381640503_llist @ ( tLList446370796tllist @ A @ B ) @ A @ ( undefined @ ( tLList446370796tllist @ A @ B ) )
% 2.91/1.57 @ ^ [X2: A] : ( tLList1672613558_llist @ B @ A @ B4 )
% 2.91/1.57 @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_186_llist__of__tllist_Osimps_I4_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( ( coinductive_ltl @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 = ( tLList200813139tllist @ B @ ( coinductive_llist @ A ) @ A
% 2.91/1.57 @ ^ [X2: B] : ( undefined @ ( coinductive_llist @ A ) )
% 2.91/1.57 @ ^ [X2: A] : ( tLList798109904tllist @ A @ B )
% 2.91/1.57 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_187_tllist__of__llist_Odisc__iff_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) ) )
% 2.91/1.57 = ( ~ ( coinductive_lnull @ A @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_188_tllist__of__llist_Odisc__iff_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = ( coinductive_lnull @ A @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_189_llist__of__tllist_Odisc__iff_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( ~ ( coinductive_lnull @ A @ ( tLList798109904tllist @ A @ B @ Xs ) ) )
% 2.91/1.57 = ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_190_llist__of__tllist_Odisc__iff_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( coinductive_lnull @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 = ( tLList1968894004s_TNil @ A @ B @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_191_terminal__tllist__of__llist__lnull,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = B4 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_192_ttl__tllist__of__llist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = ( tLList1672613558_llist @ B @ A @ B4 @ ( coinductive_ltl @ A @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_193_ltl__llist__of__tllist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( coinductive_ltl @ A @ ( tLList798109904tllist @ A @ B @ Xs ) )
% 2.91/1.57 = ( tLList798109904tllist @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_194_llist_Odisc__eq__case_I2_J,axiom,
% 2.91/1.57 ! [A: $tType,Llist: coinductive_llist @ A] :
% 2.91/1.57 ( ( ~ ( coinductive_lnull @ A @ Llist ) )
% 2.91/1.57 = ( coindu1381640503_llist @ $o @ A @ $false
% 2.91/1.57 @ ^ [Uu: A,Uv: coinductive_llist @ A] : $true
% 2.91/1.57 @ Llist ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_195_llist_Odisc__eq__case_I1_J,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( coinductive_lnull @ A )
% 2.91/1.57 = ( coindu1381640503_llist @ $o @ A @ $true
% 2.91/1.57 @ ^ [Uu: A,Uv: coinductive_llist @ A] : $false ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_196_tllist__of__llist_Odisc_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ~ ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 => ~ ( tLList1968894004s_TNil @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_197_tllist__of__llist_Odisc_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 => ( tLList1968894004s_TNil @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_198_llist__of__tllist_Odisc_I2_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ~ ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ~ ( coinductive_lnull @ A @ ( tLList798109904tllist @ A @ B @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_199_llist__of__tllist_Odisc_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( coinductive_lnull @ A @ ( tLList798109904tllist @ A @ B @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_200_tllist__of__llist_Osimps_I5_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ~ ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 => ( ( tLList_Mirabelle_ttl @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = ( coindu1381640503_llist @ ( tLList446370796tllist @ A @ B ) @ A @ ( undefined @ ( tLList446370796tllist @ A @ B ) )
% 2.91/1.57 @ ^ [X2: A] : ( tLList1672613558_llist @ B @ A @ B4 )
% 2.91/1.57 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_201_tllist__of__llist_Octr_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 => ( ( tLList1672613558_llist @ B @ A @ B4 @ Xs )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A
% 2.91/1.57 @ ( coindu1381640503_llist @ B @ A @ B4
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( undefined @ B )
% 2.91/1.57 @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_202_tllist__of__llist_Osimps_I3_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 => ( ( tLList2110128105rminal @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = ( coindu1381640503_llist @ B @ A @ B4
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( undefined @ B )
% 2.91/1.57 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_203_tllist__of__llist_Osimps_I4_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ~ ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 => ( ( tLList_Mirabelle_thd @ A @ B @ ( tLList1672613558_llist @ B @ A @ B4 @ Xs ) )
% 2.91/1.57 = ( coindu1381640503_llist @ A @ A @ ( undefined @ A )
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : X2
% 2.91/1.57 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_204_llist_Ocase__distrib,axiom,
% 2.91/1.57 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: B,F2: A > ( coinductive_llist @ A ) > B,Llist: coinductive_llist @ A] :
% 2.91/1.57 ( ( H @ ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 2.91/1.57 = ( coindu1381640503_llist @ C @ A @ ( H @ F1 )
% 2.91/1.57 @ ^ [X13: A,X24: coinductive_llist @ A] : ( H @ ( F2 @ X13 @ X24 ) )
% 2.91/1.57 @ Llist ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_205_lappend_Octr_I2_J,axiom,
% 2.91/1.57 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.91/1.57 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 | ~ ( coinductive_lnull @ A @ Ys ) )
% 2.91/1.57 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.91/1.57 = ( coinductive_LCons @ A
% 2.91/1.57 @ ( coindu1381640503_llist @ A @ A @ ( coinductive_lhd @ A @ Ys )
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : X2
% 2.91/1.57 @ Xs )
% 2.91/1.57 @ ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A
% 2.91/1.57 @ ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ ( undefined @ ( coinductive_llist @ A ) )
% 2.91/1.57 @ ^ [Uu2: A,Uv2: coinductive_llist @ A] : Uv2
% 2.91/1.57 @ Ys )
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( coinductive_lappend @ A @ Xs5 @ Ys )
% 2.91/1.57 @ Xs ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_206_llist__of__tllist_Ocode,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType] :
% 2.91/1.57 ( ( tLList798109904tllist @ A @ B )
% 2.91/1.57 = ( tLList200813139tllist @ B @ ( coinductive_llist @ A ) @ A
% 2.91/1.57 @ ^ [X2: B] : ( coinductive_LNil @ A )
% 2.91/1.57 @ ^ [X2: A,Xs5: tLList446370796tllist @ A @ B] : ( coinductive_LCons @ A @ X2 @ ( tLList798109904tllist @ A @ B @ Xs5 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_207_lappendt__LNil,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Tr: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList98099029ppendt @ A @ B @ ( coinductive_LNil @ A ) @ Tr )
% 2.91/1.57 = Tr ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_208_TNil__eq__tllist__of__llist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B4: B,B5: B,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( ( tLList57907754e_TNil @ B @ A @ B4 )
% 2.91/1.57 = ( tLList1672613558_llist @ B @ A @ B5 @ Xs ) )
% 2.91/1.57 = ( ( B4 = B5 )
% 2.91/1.57 & ( Xs
% 2.91/1.57 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_209_tllist__of__llist__LNil,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,B4: B] :
% 2.91/1.57 ( ( tLList1672613558_llist @ B @ A @ B4 @ ( coinductive_LNil @ A ) )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ B4 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_210_tllist__of__llist__eq,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,B5: B,Xs: coinductive_llist @ A,B4: B] :
% 2.91/1.57 ( ( ( tLList1672613558_llist @ B @ A @ B5 @ Xs )
% 2.91/1.57 = ( tLList57907754e_TNil @ B @ A @ B4 ) )
% 2.91/1.57 = ( ( B4 = B5 )
% 2.91/1.57 & ( Xs
% 2.91/1.57 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_211_llist__of__tllist__TNil,axiom,
% 2.91/1.57 ! [A: $tType,Aa: $tType,X: A] :
% 2.91/1.57 ( ( tLList798109904tllist @ Aa @ A @ ( tLList57907754e_TNil @ A @ Aa @ X ) )
% 2.91/1.57 = ( coinductive_LNil @ Aa ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_212_lappend_Ocode,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( coinductive_lappend @ A )
% 2.91/1.57 = ( ^ [Xs6: coinductive_llist @ A,Ys4: coinductive_llist @ A] :
% 2.91/1.57 ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ Ys4
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( coinductive_LCons @ A @ X2 @ ( coinductive_lappend @ A @ Xs5 @ Ys4 ) )
% 2.91/1.57 @ Xs6 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_213_ltl__def,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( coinductive_ltl @ A )
% 2.91/1.57 = ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ ( coinductive_LNil @ A )
% 2.91/1.57 @ ^ [X213: A,X223: coinductive_llist @ A] : X223 ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_214_lhd__LNil,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( coinductive_lhd @ A @ ( coinductive_LNil @ A ) )
% 2.91/1.57 = ( undefined @ A ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_215_llist__of__tllist__eq__LNil,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( ( tLList798109904tllist @ A @ B @ Xs )
% 2.91/1.57 = ( coinductive_LNil @ A ) )
% 2.91/1.57 = ( tLList1968894004s_TNil @ A @ B @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_216_llist__of__tllist_Octr_I1_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1968894004s_TNil @ A @ B @ Xs )
% 2.91/1.57 => ( ( tLList798109904tllist @ A @ B @ Xs )
% 2.91/1.57 = ( coinductive_LNil @ A ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_217_tllist__of__llist__eq__lappendt__conv,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,A2: B,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( ( tLList1672613558_llist @ B @ A @ A2 @ Xs )
% 2.91/1.57 = ( tLList98099029ppendt @ A @ B @ Ys @ Zs2 ) )
% 2.91/1.57 = ( ? [Xs5: coinductive_llist @ A,A6: B] :
% 2.91/1.57 ( ( Xs
% 2.91/1.57 = ( coinductive_lappend @ A @ Ys @ Xs5 ) )
% 2.91/1.57 & ( Zs2
% 2.91/1.57 = ( tLList1672613558_llist @ B @ A @ A6 @ Xs5 ) )
% 2.91/1.57 & ( ( coinductive_lfinite @ A @ Ys )
% 2.91/1.57 => ( A2 = A6 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_218_lappend_Osimps_I3_J,axiom,
% 2.91/1.57 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.91/1.57 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 | ~ ( coinductive_lnull @ A @ Ys ) )
% 2.91/1.57 => ( ( coinductive_lhd @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.91/1.57 = ( coindu1381640503_llist @ A @ A @ ( coinductive_lhd @ A @ Ys )
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : X2
% 2.91/1.57 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_219_lappend_Osimps_I4_J,axiom,
% 2.91/1.57 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.91/1.57 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 2.91/1.57 | ~ ( coinductive_lnull @ A @ Ys ) )
% 2.91/1.57 => ( ( coinductive_ltl @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.91/1.57 = ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A
% 2.91/1.57 @ ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ ( undefined @ ( coinductive_llist @ A ) )
% 2.91/1.57 @ ^ [Uu2: A,Uv2: coinductive_llist @ A] : Uv2
% 2.91/1.57 @ Ys )
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( coinductive_lappend @ A @ Xs5 @ Ys )
% 2.91/1.57 @ Xs ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_220_lfilter_Osimps,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( coinductive_lfilter @ A )
% 2.91/1.57 = ( ^ [P5: A > $o] :
% 2.91/1.57 ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ A @ ( coinductive_LNil @ A )
% 2.91/1.57 @ ^ [X2: A,Xs5: coinductive_llist @ A] : ( if @ ( coinductive_llist @ A ) @ ( P5 @ X2 ) @ ( coinductive_LCons @ A @ X2 @ ( coinductive_lfilter @ A @ P5 @ Xs5 ) ) @ ( coinductive_lfilter @ A @ P5 @ Xs5 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_221_tllist_Osimps_I21_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X21: A,X22: tLList446370796tllist @ A @ B] :
% 2.91/1.57 ( ( tLList1719791291e_tset @ A @ B @ ( tLList1992840728_TCons @ A @ B @ X21 @ X22 ) )
% 2.91/1.57 = ( insert @ A @ X21 @ ( tLList1719791291e_tset @ A @ B @ X22 ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_222_lfilter__K__True,axiom,
% 2.91/1.57 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( coinductive_lfilter @ A
% 2.91/1.57 @ ^ [Uu: A] : $true
% 2.91/1.57 @ Xs )
% 2.91/1.57 = Xs ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_223_lfitler__K__False,axiom,
% 2.91/1.57 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( coinductive_lfilter @ A
% 2.91/1.57 @ ^ [Uu: A] : $false
% 2.91/1.57 @ Xs )
% 2.91/1.57 = ( coinductive_LNil @ A ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_224_lset__lfilter,axiom,
% 2.91/1.57 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( coinductive_lset @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 2.91/1.57 = ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs ) )
% 2.91/1.57 & ( P @ X2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_225_insert__def,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( insert @ A )
% 2.91/1.57 = ( ^ [A4: A] :
% 2.91/1.57 ( sup_sup @ ( set @ A )
% 2.91/1.57 @ ( collect @ A
% 2.91/1.57 @ ^ [X2: A] : ( X2 = A4 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_226_insert__compr,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( insert @ A )
% 2.91/1.57 = ( ^ [A4: A,B8: set @ A] :
% 2.91/1.57 ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( X2 = A4 )
% 2.91/1.57 | ( member @ A @ X2 @ B8 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_227_insert__Collect,axiom,
% 2.91/1.57 ! [A: $tType,A2: A,P: A > $o] :
% 2.91/1.57 ( ( insert @ A @ A2 @ ( collect @ A @ P ) )
% 2.91/1.57 = ( collect @ A
% 2.91/1.57 @ ^ [U: A] :
% 2.91/1.57 ( ( U != A2 )
% 2.91/1.57 => ( P @ U ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_228_lfilter__lfilter,axiom,
% 2.91/1.57 ! [A: $tType,P: A > $o,Q: A > $o,Xs: coinductive_llist @ A] :
% 2.91/1.57 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ Q @ Xs ) )
% 2.91/1.57 = ( coinductive_lfilter @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( P @ X2 )
% 2.91/1.57 & ( Q @ X2 ) )
% 2.91/1.57 @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_229_set2__tllist__tllist__of__llist,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: coinductive_llist @ B,B4: A] :
% 2.91/1.57 ( ( ( coinductive_lfinite @ B @ Xs )
% 2.91/1.57 => ( ( tLList457864275tllist @ B @ A @ ( tLList1672613558_llist @ A @ B @ B4 @ Xs ) )
% 2.91/1.57 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.91/1.57 & ( ~ ( coinductive_lfinite @ B @ Xs )
% 2.91/1.57 => ( ( tLList457864275tllist @ B @ A @ ( tLList1672613558_llist @ A @ B @ B4 @ Xs ) )
% 2.91/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_230_lfilter__repeat,axiom,
% 2.91/1.57 ! [A: $tType,P: A > $o,X: A] :
% 2.91/1.57 ( ( ( P @ X )
% 2.91/1.57 => ( ( coinductive_lfilter @ A @ P
% 2.91/1.57 @ ( coinductive_iterates @ A
% 2.91/1.57 @ ^ [X2: A] : X2
% 2.91/1.57 @ X ) )
% 2.91/1.57 = ( coinductive_iterates @ A
% 2.91/1.57 @ ^ [X2: A] : X2
% 2.91/1.57 @ X ) ) )
% 2.91/1.57 & ( ~ ( P @ X )
% 2.91/1.57 => ( ( coinductive_lfilter @ A @ P
% 2.91/1.57 @ ( coinductive_iterates @ A
% 2.91/1.57 @ ^ [X2: A] : X2
% 2.91/1.57 @ X ) )
% 2.91/1.57 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_231_singleton__conv,axiom,
% 2.91/1.57 ! [A: $tType,A2: A] :
% 2.91/1.57 ( ( collect @ A
% 2.91/1.57 @ ^ [X2: A] : ( X2 = A2 ) )
% 2.91/1.57 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_232_singleton__conv2,axiom,
% 2.91/1.57 ! [A: $tType,A2: A] :
% 2.91/1.57 ( ( collect @ A
% 2.91/1.57 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 2.91/1.57 @ A2 ) )
% 2.91/1.57 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_233_lset__repeat,axiom,
% 2.91/1.57 ! [A: $tType,X: A] :
% 2.91/1.57 ( ( coinductive_lset @ A
% 2.91/1.57 @ ( coinductive_iterates @ A
% 2.91/1.57 @ ^ [X2: A] : X2
% 2.91/1.57 @ X ) )
% 2.91/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_234_Collect__conv__if,axiom,
% 2.91/1.57 ! [A: $tType,P: A > $o,A2: A] :
% 2.91/1.57 ( ( ( P @ A2 )
% 2.91/1.57 => ( ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( X2 = A2 )
% 2.91/1.57 & ( P @ X2 ) ) )
% 2.91/1.57 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.91/1.57 & ( ~ ( P @ A2 )
% 2.91/1.57 => ( ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( X2 = A2 )
% 2.91/1.57 & ( P @ X2 ) ) )
% 2.91/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_235_Collect__conv__if2,axiom,
% 2.91/1.57 ! [A: $tType,P: A > $o,A2: A] :
% 2.91/1.57 ( ( ( P @ A2 )
% 2.91/1.57 => ( ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( A2 = X2 )
% 2.91/1.57 & ( P @ X2 ) ) )
% 2.91/1.57 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.91/1.57 & ( ~ ( P @ A2 )
% 2.91/1.57 => ( ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( A2 = X2 )
% 2.91/1.57 & ( P @ X2 ) ) )
% 2.91/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_236_empty__def,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( bot_bot @ ( set @ A ) )
% 2.91/1.57 = ( collect @ A
% 2.91/1.57 @ ^ [X2: A] : $false ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_237_tllist_Osimps_I20_J,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,X1: B] :
% 2.91/1.57 ( ( tLList1719791291e_tset @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.91/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_238_tllist_Osimps_I22_J,axiom,
% 2.91/1.57 ! [A: $tType,B: $tType,X1: B] :
% 2.91/1.57 ( ( tLList457864275tllist @ A @ B @ ( tLList57907754e_TNil @ B @ A @ X1 ) )
% 2.91/1.57 = ( insert @ B @ X1 @ ( bot_bot @ ( set @ B ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_239_lfinite__lconcat,axiom,
% 2.91/1.57 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 2.91/1.57 ( ( coinductive_lfinite @ A @ ( coinductive_lconcat @ A @ Xss ) )
% 2.91/1.57 = ( ( coinductive_lfinite @ ( coinductive_llist @ A )
% 2.91/1.57 @ ( coinductive_lfilter @ ( coinductive_llist @ A )
% 2.91/1.57 @ ^ [Xs6: coinductive_llist @ A] :
% 2.91/1.57 ~ ( coinductive_lnull @ A @ Xs6 )
% 2.91/1.57 @ Xss ) )
% 2.91/1.57 & ! [X2: coinductive_llist @ A] :
% 2.91/1.57 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( coinductive_lset @ ( coinductive_llist @ A ) @ Xss ) )
% 2.91/1.57 => ( coinductive_lfinite @ A @ X2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_240_lconcat__repeat__LNil,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( coinductive_lconcat @ A
% 2.91/1.57 @ ( coinductive_iterates @ ( coinductive_llist @ A )
% 2.91/1.57 @ ^ [X2: coinductive_llist @ A] : X2
% 2.91/1.57 @ ( coinductive_LNil @ A ) ) )
% 2.91/1.57 = ( coinductive_LNil @ A ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_241_lconcat_Osimps,axiom,
% 2.91/1.57 ! [A: $tType] :
% 2.91/1.57 ( ( coinductive_lconcat @ A )
% 2.91/1.57 = ( coindu1381640503_llist @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A )
% 2.91/1.57 @ ^ [Xs6: coinductive_llist @ A,Xss2: coinductive_llist @ ( coinductive_llist @ A )] : ( coinductive_lappend @ A @ Xs6 @ ( coinductive_lconcat @ A @ Xss2 ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_242_lconcat__lfilter__neq__LNil,axiom,
% 2.91/1.57 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 2.91/1.57 ( ( coinductive_lconcat @ A
% 2.91/1.57 @ ( coinductive_lfilter @ ( coinductive_llist @ A )
% 2.91/1.57 @ ^ [Xs6: coinductive_llist @ A] :
% 2.91/1.57 ~ ( coinductive_lnull @ A @ Xs6 )
% 2.91/1.57 @ Xss ) )
% 2.91/1.57 = ( coinductive_lconcat @ A @ Xss ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_243_lnull__lconcat,axiom,
% 2.91/1.57 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 2.91/1.57 ( ( coinductive_lnull @ A @ ( coinductive_lconcat @ A @ Xss ) )
% 2.91/1.57 = ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( coinductive_lset @ ( coinductive_llist @ A ) @ Xss ) @ ( collect @ ( coinductive_llist @ A ) @ ( coinductive_lnull @ A ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_244_tset__ttl,axiom,
% 2.91/1.57 ! [B: $tType,A: $tType,Xs: tLList446370796tllist @ A @ B] : ( ord_less_eq @ ( set @ A ) @ ( tLList1719791291e_tset @ A @ B @ ( tLList_Mirabelle_ttl @ A @ B @ Xs ) ) @ ( tLList1719791291e_tset @ A @ B @ Xs ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_245_conj__subset__def,axiom,
% 2.91/1.57 ! [A: $tType,A3: set @ A,P: A > $o,Q: A > $o] :
% 2.91/1.57 ( ( ord_less_eq @ ( set @ A ) @ A3
% 2.91/1.57 @ ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( P @ X2 )
% 2.91/1.57 & ( Q @ X2 ) ) ) )
% 2.91/1.57 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( collect @ A @ P ) )
% 2.91/1.57 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( collect @ A @ Q ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_246_prop__restrict,axiom,
% 2.91/1.57 ! [A: $tType,X: A,Z5: set @ A,X5: set @ A,P: A > $o] :
% 2.91/1.57 ( ( member @ A @ X @ Z5 )
% 2.91/1.57 => ( ( ord_less_eq @ ( set @ A ) @ Z5
% 2.91/1.57 @ ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ X5 )
% 2.91/1.57 & ( P @ X2 ) ) ) )
% 2.91/1.57 => ( P @ X ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_247_Collect__restrict,axiom,
% 2.91/1.57 ! [A: $tType,X5: set @ A,P: A > $o] :
% 2.91/1.57 ( ord_less_eq @ ( set @ A )
% 2.91/1.57 @ ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ X5 )
% 2.91/1.57 & ( P @ X2 ) ) )
% 2.91/1.57 @ X5 ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_248_subset__Collect__iff,axiom,
% 2.91/1.57 ! [A: $tType,B9: set @ A,A3: set @ A,P: A > $o] :
% 2.91/1.57 ( ( ord_less_eq @ ( set @ A ) @ B9 @ A3 )
% 2.91/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B9
% 2.91/1.57 @ ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ A3 )
% 2.91/1.57 & ( P @ X2 ) ) ) )
% 2.91/1.57 = ( ! [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ B9 )
% 2.91/1.57 => ( P @ X2 ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(fact_249_subset__CollectI,axiom,
% 2.91/1.57 ! [A: $tType,B9: set @ A,A3: set @ A,Q: A > $o,P: A > $o] :
% 2.91/1.57 ( ( ord_less_eq @ ( set @ A ) @ B9 @ A3 )
% 2.91/1.57 => ( ! [X3: A] :
% 2.91/1.57 ( ( member @ A @ X3 @ B9 )
% 2.91/1.57 => ( ( Q @ X3 )
% 2.91/1.57 => ( P @ X3 ) ) )
% 2.91/1.57 => ( ord_less_eq @ ( set @ A )
% 2.91/1.57 @ ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ B9 )
% 2.91/1.57 & ( Q @ X2 ) ) )
% 2.91/1.57 @ ( collect @ A
% 2.91/1.57 @ ^ [X2: A] :
% 2.91/1.57 ( ( member @ A @ X2 @ A3 )
% 2.91/1.57 & ( P @ X2 ) ) ) ) ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(help_If_3_1_T,axiom,
% 2.91/1.57 ! [P: $o] :
% 2.91/1.57 ( ( P = $true )
% 2.91/1.57 | ( P = $false ) ) ).
% 2.91/1.57
% 2.91/1.57 thf(help_If_2_1_T,axiom,
% 2.91/1.57 ! [A: $tType,X: A,Y: A] :
% 2.91/1.57 ( ( if @ A @ $false @ X @ Y )
% 2.91/1.57 = Y ) ).
% 2.91/1.57
% 2.91/1.57 thf(help_If_1_1_T,axiom,
% 2.91/1.57 ! [A: $tType,X: A,Y: A] :
% 2.91/1.57 ( ( if @ A @ $true @ X @ Y )
% 2.91/1.57 = X ) ).
% 2.91/1.57
% 2.91/1.57 thf(conj_0,conjecture,
% 2.91/1.57 ( ( tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ ( tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs ) @ ys )
% 2.91/1.57 = ( tLList1380991092t_all2 @ e @ b @ f @ d
% 2.91/1.57 @ ^ [X2: e] : ( p @ ( f2 @ X2 ) )
% 2.91/1.57 @ ^ [X2: f] : ( q @ ( g @ X2 ) )
% 2.91/1.57 @ xs
% 2.91/1.57 @ ys ) ) ).
% 2.91/1.57 ------------------------
% 2.91/1.59 % (25851)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_25576 for (2999ds/27Mi)
% 2.91/1.59 % (25849)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/183Mi)
% 2.91/1.59 % (25855)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/18Mi)
% 3.00/1.60 % (25855)Instruction limit reached!
% 3.00/1.60 % (25855)------------------------------
% 3.00/1.60 % (25855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (25855)Termination reason: Unknown
% 3.00/1.60 % (25855)Termination phase: shuffling
% 3.00/1.60
% 3.00/1.60 % (25855)Memory used [KB]: 1918
% 3.00/1.60 % (25855)Time elapsed: 0.008 s
% 3.00/1.60 % (25855)Instructions burned: 19 (million)
% 3.00/1.60 % (25855)------------------------------
% 3.00/1.60 % (25855)------------------------------
% 3.00/1.60 % (25852)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/2Mi)
% 3.00/1.60 % (25853)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_25576 for (2999ds/2Mi)
% 3.00/1.60 % (25854)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_25576 for (2999ds/275Mi)
% 3.00/1.60 % (25850)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_25576 for (2999ds/4Mi)
% 3.00/1.60 % (25851)Instruction limit reached!
% 3.00/1.60 % (25851)------------------------------
% 3.00/1.60 % (25851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (25851)Termination reason: Unknown
% 3.00/1.60 % (25851)Termination phase: shuffling
% 3.00/1.60
% 3.00/1.60 % (25851)Memory used [KB]: 2046
% 3.00/1.60 % (25851)Time elapsed: 0.011 s
% 3.00/1.60 % (25851)Instructions burned: 29 (million)
% 3.00/1.60 % (25851)------------------------------
% 3.00/1.60 % (25851)------------------------------
% 3.00/1.60 % (25852)Instruction limit reached!
% 3.00/1.60 % (25852)------------------------------
% 3.00/1.60 % (25852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (25852)Termination reason: Unknown
% 3.00/1.60 % (25852)Termination phase: shuffling
% 3.00/1.60
% 3.00/1.60 % (25852)Memory used [KB]: 1407
% 3.00/1.60 % (25852)Time elapsed: 0.004 s
% 3.00/1.60 % (25852)Instructions burned: 3 (million)
% 3.00/1.60 % (25852)------------------------------
% 3.00/1.60 % (25852)------------------------------
% 3.00/1.60 % (25853)Instruction limit reached!
% 3.00/1.60 % (25853)------------------------------
% 3.00/1.60 % (25853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (25853)Termination reason: Unknown
% 3.00/1.60 % (25853)Termination phase: shuffling
% 3.00/1.60
% 3.00/1.60 % (25853)Memory used [KB]: 1407
% 3.00/1.60 % (25853)Time elapsed: 0.004 s
% 3.00/1.60 % (25853)Instructions burned: 3 (million)
% 3.00/1.60 % (25853)------------------------------
% 3.00/1.60 % (25853)------------------------------
% 3.00/1.60 % (25850)Instruction limit reached!
% 3.00/1.60 % (25850)------------------------------
% 3.00/1.60 % (25850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (25850)Termination reason: Unknown
% 3.00/1.60 % (25850)Termination phase: shuffling
% 3.00/1.60
% 3.00/1.60 % (25850)Memory used [KB]: 1535
% 3.00/1.60 % (25850)Time elapsed: 0.004 s
% 3.00/1.60 % (25850)Instructions burned: 4 (million)
% 3.00/1.60 % (25850)------------------------------
% 3.00/1.60 % (25850)------------------------------
% 3.00/1.61 % (25856)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/3Mi)
% 3.00/1.61 % (25856)Instruction limit reached!
% 3.00/1.61 % (25856)------------------------------
% 3.00/1.61 % (25856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.61 % (25856)Termination reason: Unknown
% 3.00/1.61 % (25856)Termination phase: shuffling
% 3.00/1.61
% 3.00/1.61 % (25856)Memory used [KB]: 1407
% 3.00/1.61 % (25856)Time elapsed: 0.003 s
% 3.00/1.61 % (25856)Instructions burned: 3 (million)
% 3.00/1.61 % (25856)------------------------------
% 3.00/1.61 % (25856)------------------------------
% 3.00/1.61 % (25857)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_25576 for (2999ds/37Mi)
% 3.00/1.62 % (25858)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_25576 for (2999ds/15Mi)
% 3.00/1.62 % (25859)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_25576 for (2999ds/3Mi)
% 3.00/1.62 % (25860)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_25576 for (2999ds/1041Mi)
% 3.00/1.62 % (25859)Instruction limit reached!
% 3.00/1.62 % (25859)------------------------------
% 3.00/1.62 % (25859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.62 % (25859)Termination reason: Unknown
% 3.00/1.62 % (25859)Termination phase: shuffling
% 3.00/1.62
% 3.00/1.62 % (25859)Memory used [KB]: 1407
% 3.00/1.62 % (25859)Time elapsed: 0.004 s
% 3.00/1.62 % (25859)Instructions burned: 3 (million)
% 3.00/1.62 % (25859)------------------------------
% 3.00/1.62 % (25859)------------------------------
% 3.00/1.62 % (25861)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/7Mi)
% 3.00/1.62 % (25857)Instruction limit reached!
% 3.00/1.62 % (25857)------------------------------
% 3.00/1.62 % (25857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.62 % (25857)Termination reason: Unknown
% 3.00/1.62 % (25857)Termination phase: shuffling
% 3.00/1.62
% 3.00/1.62 % (25857)Memory used [KB]: 2174
% 3.00/1.62 % (25857)Time elapsed: 0.012 s
% 3.00/1.62 % (25857)Instructions burned: 38 (million)
% 3.00/1.62 % (25857)------------------------------
% 3.00/1.62 % (25857)------------------------------
% 3.00/1.63 % (25861)Instruction limit reached!
% 3.00/1.63 % (25861)------------------------------
% 3.00/1.63 % (25861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.63 % (25861)Termination reason: Unknown
% 3.00/1.63 % (25861)Termination phase: shuffling
% 3.00/1.63
% 3.00/1.63 % (25861)Memory used [KB]: 1663
% 3.00/1.63 % (25861)Time elapsed: 0.005 s
% 3.00/1.63 % (25861)Instructions burned: 9 (million)
% 3.00/1.63 % (25861)------------------------------
% 3.00/1.63 % (25861)------------------------------
% 3.00/1.63 % (25858)Instruction limit reached!
% 3.00/1.63 % (25858)------------------------------
% 3.00/1.63 % (25858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.63 % (25858)Termination reason: Unknown
% 3.00/1.63 % (25858)Termination phase: shuffling
% 3.00/1.63
% 3.00/1.63 % (25858)Memory used [KB]: 1791
% 3.00/1.63 % (25858)Time elapsed: 0.012 s
% 3.00/1.63 % (25858)Instructions burned: 16 (million)
% 3.00/1.63 % (25858)------------------------------
% 3.00/1.63 % (25858)------------------------------
% 3.00/1.63 % (25863)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_25576 for (2999ds/3Mi)
% 3.00/1.63 % (25863)Instruction limit reached!
% 3.00/1.63 % (25863)------------------------------
% 3.00/1.63 % (25863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.63 % (25863)Termination reason: Unknown
% 3.00/1.63 % (25863)Termination phase: shuffling
% 3.00/1.63
% 3.00/1.63 % (25863)Memory used [KB]: 1407
% 3.00/1.63 % (25863)Time elapsed: 0.002 s
% 3.00/1.63 % (25863)Instructions burned: 3 (million)
% 3.00/1.63 % (25863)------------------------------
% 3.00/1.63 % (25863)------------------------------
% 3.00/1.64 % (25864)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_25576 for (2999ds/3Mi)
% 3.00/1.64 % (25864)Instruction limit reached!
% 3.00/1.64 % (25864)------------------------------
% 3.00/1.64 % (25864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.64 % (25864)Termination reason: Unknown
% 3.00/1.64 % (25864)Termination phase: shuffling
% 3.00/1.64
% 3.00/1.64 % (25864)Memory used [KB]: 1535
% 3.00/1.64 % (25864)Time elapsed: 0.003 s
% 3.00/1.64 % (25864)Instructions burned: 4 (million)
% 3.00/1.64 % (25864)------------------------------
% 3.00/1.64 % (25864)------------------------------
% 3.00/1.64 % (25862)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/16Mi)
% 3.00/1.64 % (25866)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/3Mi)
% 3.00/1.64 % (25866)Instruction limit reached!
% 3.00/1.64 % (25866)------------------------------
% 3.00/1.64 % (25866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.64 % (25866)Termination reason: Unknown
% 3.00/1.64 % (25866)Termination phase: shuffling
% 3.00/1.64
% 3.00/1.64 % (25866)Memory used [KB]: 1407
% 3.00/1.64 % (25866)Time elapsed: 0.002 s
% 3.00/1.64 % (25866)Instructions burned: 3 (million)
% 3.00/1.64 % (25866)------------------------------
% 3.00/1.64 % (25866)------------------------------
% 3.00/1.65 % (25849)Instruction limit reached!
% 3.00/1.65 % (25849)------------------------------
% 3.00/1.65 % (25849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.65 % (25849)Termination reason: Unknown
% 3.00/1.65 % (25849)Termination phase: Saturation
% 3.00/1.65
% 3.00/1.65 % (25849)Memory used [KB]: 7547
% 3.00/1.65 % (25849)Time elapsed: 0.055 s
% 3.00/1.65 % (25849)Instructions burned: 184 (million)
% 3.00/1.65 % (25849)------------------------------
% 3.00/1.65 % (25849)------------------------------
% 3.00/1.65 % (25865)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/7Mi)
% 3.00/1.65 % (25867)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/4Mi)
% 3.00/1.65 % (25867)Instruction limit reached!
% 3.00/1.65 % (25867)------------------------------
% 3.00/1.65 % (25867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.65 % (25867)Termination reason: Unknown
% 3.00/1.65 % (25867)Termination phase: shuffling
% 3.00/1.65
% 3.00/1.65 % (25867)Memory used [KB]: 1535
% 3.00/1.65 % (25867)Time elapsed: 0.004 s
% 3.00/1.65 % (25867)Instructions burned: 6 (million)
% 3.00/1.65 % (25867)------------------------------
% 3.00/1.65 % (25867)------------------------------
% 3.00/1.65 % (25862)Instruction limit reached!
% 3.00/1.65 % (25862)------------------------------
% 3.00/1.65 % (25862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.65 % (25862)Termination reason: Unknown
% 3.00/1.65 % (25862)Termination phase: shuffling
% 3.00/1.65
% 3.00/1.65 % (25862)Memory used [KB]: 1791
% 3.00/1.65 % (25862)Time elapsed: 0.012 s
% 3.00/1.65 % (25862)Instructions burned: 16 (million)
% 3.00/1.65 % (25862)------------------------------
% 3.00/1.65 % (25862)------------------------------
% 3.00/1.65 % (25865)Instruction limit reached!
% 3.00/1.65 % (25865)------------------------------
% 3.00/1.65 % (25865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.65 % (25865)Termination reason: Unknown
% 3.00/1.65 % (25865)Termination phase: shuffling
% 3.00/1.65
% 3.00/1.65 % (25865)Memory used [KB]: 1663
% 3.00/1.65 % (25865)Time elapsed: 0.005 s
% 3.00/1.65 % (25865)Instructions burned: 8 (million)
% 3.00/1.65 % (25865)------------------------------
% 3.00/1.65 % (25865)------------------------------
% 3.00/1.65 % (25868)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/18Mi)
% 3.00/1.66 % (25869)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/710Mi)
% 3.00/1.66 % (25870)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/6Mi)
% 3.00/1.66 % (25868)Instruction limit reached!
% 3.00/1.66 % (25868)------------------------------
% 3.00/1.66 % (25868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.66 % (25868)Termination reason: Unknown
% 3.00/1.66 % (25868)Termination phase: shuffling
% 3.00/1.66
% 3.00/1.66 % (25868)Memory used [KB]: 1918
% 3.00/1.66 % (25868)Time elapsed: 0.008 s
% 3.00/1.66 % (25868)Instructions burned: 20 (million)
% 3.00/1.66 % (25868)------------------------------
% 3.00/1.66 % (25868)------------------------------
% 3.00/1.66 % (25870)Instruction limit reached!
% 3.00/1.66 % (25870)------------------------------
% 3.00/1.66 % (25870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.66 % (25870)Termination reason: Unknown
% 3.00/1.66 % (25870)Termination phase: shuffling
% 3.00/1.66
% 3.00/1.66 % (25870)Memory used [KB]: 1535
% 3.00/1.66 % (25870)Time elapsed: 0.004 s
% 3.00/1.66 % (25870)Instructions burned: 7 (million)
% 3.00/1.66 % (25870)------------------------------
% 3.00/1.66 % (25870)------------------------------
% 3.00/1.66 % (25872)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/21Mi)
% 3.00/1.67 % (25854)First to succeed.
% 3.00/1.67 % (25871)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_25576 for (2999ds/902Mi)
% 3.00/1.67 % (25854)Refutation found. Thanks to Tanya!
% 3.00/1.67 % SZS status Theorem for DTF2THF_25576
% 3.00/1.67 % SZS output start Proof for DTF2THF_25576
% 3.00/1.67 thf(type_def_6, type, coinductive_llist: ($tType) > $tType).
% 3.00/1.67 thf(type_def_7, type, set: ($tType) > $tType).
% 3.00/1.67 thf(type_def_8, type, product_unit: $tType).
% 3.00/1.67 thf(type_def_9, type, itself: ($tType) > $tType).
% 3.00/1.67 thf(type_def_10, type, tLList446370796tllist: ($tType * $tType) > $tType).
% 3.00/1.67 thf(type_def_11, type, a: $tType).
% 3.00/1.67 thf(type_def_12, type, b: $tType).
% 3.00/1.67 thf(type_def_13, type, c: $tType).
% 3.00/1.67 thf(type_def_14, type, d: $tType).
% 3.00/1.67 thf(type_def_15, type, e: $tType).
% 3.00/1.67 thf(type_def_16, type, f: $tType).
% 3.00/1.67 thf(func_def_0, type, tLList446370796tllist: ($tType * $tType) > $tType).
% 3.00/1.67 thf(func_def_1, type, coinductive_llist: ($tType) > $tType).
% 3.00/1.67 thf(func_def_2, type, product_unit: $tType).
% 3.00/1.67 thf(func_def_3, type, set: ($tType) > $tType).
% 3.00/1.67 thf(func_def_4, type, itself: ($tType) > $tType).
% 3.00/1.67 thf(func_def_5, type, f: $tType).
% 3.00/1.67 thf(func_def_6, type, e: $tType).
% 3.00/1.67 thf(func_def_7, type, d: $tType).
% 3.00/1.67 thf(func_def_8, type, c: $tType).
% 3.00/1.67 thf(func_def_9, type, b: $tType).
% 3.00/1.67 thf(func_def_10, type, a: $tType).
% 3.00/1.67 thf(func_def_11, type, coinductive_iterates: !>[X0: $tType]:((X0 > X0) > X0 > coinductive_llist @ X0)).
% 3.00/1.67 thf(func_def_12, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.00/1.67 thf(func_def_13, type, coinductive_lconcat: !>[X0: $tType]:(coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.00/1.67 thf(func_def_14, type, coinductive_lfilter: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.00/1.67 thf(func_def_15, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 3.00/1.67 thf(func_def_16, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.00/1.67 thf(func_def_17, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 3.00/1.67 thf(func_def_18, type, coindu1381640503_llist: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0) > coinductive_llist @ X1 > X0)).
% 3.00/1.67 thf(func_def_19, type, coinductive_lhd: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 3.00/1.67 thf(func_def_20, type, coinductive_lnull: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 3.00/1.67 thf(func_def_21, type, coinductive_lset: !>[X0: $tType]:(coinductive_llist @ X0 > set @ X0)).
% 3.00/1.67 thf(func_def_22, type, coinductive_ltl: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.00/1.67 thf(func_def_23, type, id: !>[X0: $tType]:(X0 > X0)).
% 3.00/1.67 thf(func_def_24, type, default_default: !>[X0: $tType]:(X0)).
% 3.00/1.67 thf(func_def_25, type, undefined: !>[X0: $tType]:(X0)).
% 3.00/1.67 thf(func_def_26, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.00/1.67 thf(func_def_27, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.00/1.67 thf(func_def_28, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.00/1.67 thf(func_def_29, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.00/1.67 thf(func_def_30, type, product_Unity: product_unit).
% 3.00/1.67 thf(func_def_31, type, product_rec_unit: !>[X0: $tType]:(X0 > product_unit > X0)).
% 3.00/1.67 thf(func_def_32, type, product_case_unit: !>[X0: $tType]:(X0 > product_unit > X0)).
% 3.00/1.67 thf(func_def_33, type, type: !>[X0: $tType]:(itself @ X0)).
% 3.00/1.67 thf(func_def_34, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.00/1.67 thf(func_def_35, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 3.00/1.67 thf(func_def_36, type, tLList98099029ppendt: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X0 > tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X0 @ X1)).
% 3.00/1.67 thf(func_def_37, type, tLList798109904tllist: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > coinductive_llist @ X0)).
% 3.00/1.67 thf(func_def_38, type, tLList192138471append: !>[X0: $tType, X1: $tType, X2: $tType]:(tLList446370796tllist @ X0 @ X1 > (X1 > tLList446370796tllist @ X0 @ X2) > tLList446370796tllist @ X0 @ X2)).
% 3.00/1.67 thf(func_def_39, type, tLList222516140_tcast: !>[X0: $tType, X1: $tType, X2: $tType]:(tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X0 @ X2)).
% 3.00/1.67 thf(func_def_40, type, tLList365522113concat: !>[X0: $tType, X1: $tType]:(X0 > tLList446370796tllist @ coinductive_llist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0)).
% 3.00/1.67 thf(func_def_41, type, tLList1329345514concat: !>[X0: $tType, X1: $tType]:((product_unit > X0) > tLList446370796tllist @ coinductive_llist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0)).
% 3.00/1.67 thf(func_def_42, type, tLList1825092077minal0: !>[X0: $tType]:(X0)).
% 3.00/1.67 thf(func_def_43, type, tLList1813626245filter: !>[X0: $tType, X1: $tType]:(X0 > (X1 > $o) > tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0)).
% 3.00/1.67 thf(func_def_44, type, tLList1122525870filter: !>[X0: $tType, X1: $tType]:((product_unit > X0) > (X1 > $o) > tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0)).
% 3.00/1.67 thf(func_def_45, type, tLList1992840728_TCons: !>[X0: $tType, X1: $tType]:(X0 > tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X0 @ X1)).
% 3.00/1.67 thf(func_def_46, type, tLList57907754e_TNil: !>[X0: $tType, X1: $tType]:(X0 > tLList446370796tllist @ X1 @ X0)).
% 3.00/1.67 thf(func_def_47, type, tLList200813139tllist: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > tLList446370796tllist @ X2 @ X0 > X1) > tLList446370796tllist @ X2 @ X0 > X1)).
% 3.00/1.67 thf(func_def_48, 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)).
% 3.00/1.67 thf(func_def_49, type, tLList1968894004s_TNil: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > $o)).
% 3.00/1.67 thf(func_def_50, type, tLList11265572tllist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > tLList446370796tllist @ X0 @ X1 > $o)).
% 3.00/1.67 thf(func_def_51, type, tLList457864275tllist: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > set @ X1)).
% 3.00/1.67 thf(func_def_52, type, tLList2110128105rminal: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > X1)).
% 3.00/1.67 thf(func_def_53, type, tLList_Mirabelle_thd: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > X0)).
% 3.00/1.67 thf(func_def_54, type, tLList1380991092t_all2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > tLList446370796tllist @ X0 @ X2 > tLList446370796tllist @ X1 @ X3 > $o)).
% 3.00/1.67 thf(func_def_55, type, tLList1669959861e_tmap: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > tLList446370796tllist @ X0 @ X2 > tLList446370796tllist @ X1 @ X3)).
% 3.00/1.67 thf(func_def_56, type, tLList1719791291e_tset: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > set @ X0)).
% 3.00/1.67 thf(func_def_57, type, tLList_Mirabelle_ttl: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X0 @ X1)).
% 3.00/1.67 thf(func_def_58, type, tLList1672613558_llist: !>[X0: $tType, X1: $tType]:(X0 > coinductive_llist @ X1 > tLList446370796tllist @ X1 @ X0)).
% 3.00/1.67 thf(func_def_59, type, tLList636831159tllist: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X2) > (X0 > X0) > X0 > tLList446370796tllist @ X2 @ X1)).
% 3.00/1.67 thf(func_def_60, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.00/1.67 thf(func_def_61, type, p: a > b > $o).
% 3.00/1.67 thf(func_def_62, type, q: c > d > $o).
% 3.00/1.67 thf(func_def_63, type, f2: e > a).
% 3.00/1.67 thf(func_def_64, type, g: f > c).
% 3.00/1.67 thf(func_def_65, type, xs: tLList446370796tllist @ e @ f).
% 3.00/1.67 thf(func_def_66, type, ys: tLList446370796tllist @ b @ d).
% 3.00/1.67 thf(func_def_85, type, sP0: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X1 @ X3 > (X3 > X2 > $o) > tLList446370796tllist @ X0 @ X2 > (X1 > X0 > $o) > $o)).
% 3.00/1.67 thf(func_def_86, type, sP1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X3 > (X3 > X0 > $o) > (X2 > X1 > $o) > tLList446370796tllist @ X1 @ X0 > $o)).
% 3.00/1.67 thf(func_def_87, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > tLList446370796tllist @ X1 @ X2 > (X2 > X0) > X2)).
% 3.00/1.67 thf(func_def_88, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X1 @ X3 > (X3 > X2 > $o) > tLList446370796tllist @ X0 @ X2 > (X1 > X0 > $o) > X1)).
% 3.00/1.67 thf(func_def_89, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X1 @ X3 > (X3 > X2 > $o) > tLList446370796tllist @ X0 @ X2 > (X1 > X0 > $o) > tLList446370796tllist @ X1 @ X3)).
% 3.00/1.67 thf(func_def_90, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X1 @ X3 > (X3 > X2 > $o) > tLList446370796tllist @ X0 @ X2 > (X1 > X0 > $o) > X0)).
% 3.00/1.67 thf(func_def_91, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X1 @ X3 > (X3 > X2 > $o) > tLList446370796tllist @ X0 @ X2 > (X1 > X0 > $o) > tLList446370796tllist @ X0 @ X2)).
% 3.00/1.67 thf(func_def_92, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X3 @ X2 > tLList446370796tllist @ X0 @ X1 > (X1 > X2 > $o) > X1)).
% 3.00/1.67 thf(func_def_93, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X3 @ X2 > tLList446370796tllist @ X0 @ X1 > (X1 > X2 > $o) > X2)).
% 3.00/1.67 thf(func_def_94, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.00/1.67 thf(func_def_95, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 3.00/1.67 thf(func_def_96, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:(tLList446370796tllist @ X1 @ X2 > (X2 > X0) > X0 > X2)).
% 3.00/1.67 thf(func_def_97, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X3 @ X0 > (X0 > X1) > (X3 > X2) > tLList446370796tllist @ X2 @ X1 > X2 > X3)).
% 3.00/1.67 thf(func_def_98, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X3 @ X0 > (X0 > X1) > (X3 > X2) > tLList446370796tllist @ X2 @ X1 > X2 > tLList446370796tllist @ X3 @ X0)).
% 3.00/1.67 thf(func_def_99, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X1 > X2 > tLList446370796tllist @ X3 @ X0 > (X0 > X1) > (X3 > X2) > X3)).
% 3.00/1.67 thf(func_def_100, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X1 > X2 > tLList446370796tllist @ X3 @ X0 > (X0 > X1) > (X3 > X2) > tLList446370796tllist @ X3 @ X0)).
% 3.00/1.67 thf(func_def_101, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X3 @ X0 > tLList446370796tllist @ X1 @ X2 > X1 > (X2 > X0 > $o) > (X1 > X3 > $o) > X3)).
% 3.00/1.67 thf(func_def_102, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X3 @ X0 > tLList446370796tllist @ X1 @ X2 > X1 > (X2 > X0 > $o) > (X1 > X3 > $o) > tLList446370796tllist @ X3 @ X0)).
% 3.00/1.67 thf(func_def_103, type, sK18: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > X1)).
% 3.00/1.67 thf(func_def_104, type, sK19: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0)).
% 3.00/1.67 thf(func_def_105, type, sK20: !>[X0: $tType, X1: $tType]:(tLList446370796tllist @ X1 @ X0 > X0)).
% 3.00/1.67 thf(func_def_106, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X1 > X2 > tLList446370796tllist @ X3 @ X0 > (X0 > X1 > $o) > (X3 > X2 > $o) > X3)).
% 3.00/1.67 thf(func_def_107, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X1 > X2 > tLList446370796tllist @ X3 @ X0 > (X0 > X1 > $o) > (X3 > X2 > $o) > tLList446370796tllist @ X3 @ X0)).
% 3.00/1.67 thf(func_def_108, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > tLList446370796tllist @ X1 @ X2 > (X2 > X0 > $o) > X2)).
% 3.00/1.67 thf(func_def_109, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType]:(tLList446370796tllist @ X1 @ X2 > X0 > (X0 > X2 > $o) > X2)).
% 3.00/1.67 thf(func_def_110, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X3 > (X3 > X0 > $o) > (X2 > X1 > $o) > tLList446370796tllist @ X1 @ X0 > X2)).
% 3.00/1.67 thf(func_def_111, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X3 > (X3 > X0 > $o) > (X2 > X1 > $o) > tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X2 @ X3)).
% 3.00/1.67 thf(func_def_112, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X3 > (X3 > X0 > $o) > (X2 > X1 > $o) > tLList446370796tllist @ X1 @ X0 > X1)).
% 3.00/1.67 thf(func_def_113, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X2 @ X3 > (X3 > X0 > $o) > (X2 > X1 > $o) > tLList446370796tllist @ X1 @ X0 > tLList446370796tllist @ X1 @ X0)).
% 3.00/1.67 thf(func_def_114, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X3 @ X2 > tLList446370796tllist @ X0 @ X1 > (X1 > X2 > $o) > X1)).
% 3.00/1.67 thf(func_def_115, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(tLList446370796tllist @ X3 @ X2 > tLList446370796tllist @ X0 @ X1 > (X1 > X2 > $o) > X2)).
% 3.00/1.67 thf(func_def_116, type, sK31: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.00/1.67 thf(func_def_118, type, ph33: !>[X0: $tType]:(X0)).
% 3.00/1.67 thf(f918,plain,(
% 3.00/1.67 $false),
% 3.00/1.67 inference(avatar_sat_refutation,[status(thm)],[f860,f869,f872,f897,f917])).
% 3.00/1.67 thf(f917,plain,(
% 3.00/1.67 spl32_3 | ~spl32_4),
% 3.00/1.67 inference(avatar_contradiction_clause,[status(thm)],[f916])).
% 3.00/1.67 thf(f916,plain,(
% 3.00/1.67 $false | (spl32_3 | ~spl32_4)),
% 3.00/1.67 inference(subsumption_resolution,[status(thm)],[f905,f863])).
% 3.00/1.67 thf(f863,plain,(
% 3.00/1.67 ($false != (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys)) | spl32_3),
% 3.00/1.67 inference(avatar_component_clause,[status(thm)],[f862])).
% 3.00/1.67 thf(f862,definition,(
% 3.00/1.67 spl32_3 <=> ($false = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys))),
% 3.00/1.67 introduced(definition,[new_symbols(naming,[spl32_3])],[avatar_definition])).
% 3.00/1.67 thf(f905,plain,(
% 3.00/1.67 ($false = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys)) | ~spl32_4),
% 3.00/1.67 inference(superposition,[status(thm)],[f758,f868])).
% 3.00/1.67 thf(f868,plain,(
% 3.00/1.67 ((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) = $false) | ~spl32_4),
% 3.00/1.67 inference(avatar_component_clause,[status(thm)],[f866])).
% 3.00/1.67 thf(f866,definition,(
% 3.00/1.67 spl32_4 <=> ((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) = $false)),
% 3.00/1.67 introduced(definition,[new_symbols(naming,[spl32_4])],[avatar_definition])).
% 3.00/1.67 thf(f758,plain,(
% 3.00/1.67 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X10 : tLList446370796tllist @ X0 @ X1,X11 : tLList446370796tllist @ X5 @ X4,X8 : X0 > X2,X6 : X2 > X5 > $o,X9 : X1 > X3,X7 : X3 > X4 > $o] : (((tLList1380991092t_all2 @ X2 @ X5 @ X3 @ X4 @ X6 @ X7 @ (tLList1669959861e_tmap @ X0 @ X2 @ X1 @ X3 @ X8 @ X9 @ X10) @ X11) = (tLList1380991092t_all2 @ X0 @ X5 @ X1 @ X4 @ (^[Y0 : X0]: (X6 @ (X8 @ Y0))) @ (^[Y0 : X1]: (X7 @ (X9 @ Y0))) @ X10 @ X11))) )),
% 3.00/1.67 inference(cnf_transformation,[status(thm)],[f560])).
% 3.00/1.67 thf(f560,plain,(
% 3.00/1.67 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : X2 > X5 > $o,X7 : X3 > X4 > $o,X8 : X0 > X2,X9 : X1 > X3,X10 : tLList446370796tllist @ X0 @ X1,X11 : tLList446370796tllist @ X5 @ X4] : ((tLList1380991092t_all2 @ X2 @ X5 @ X3 @ X4 @ X6 @ X7 @ (tLList1669959861e_tmap @ X0 @ X2 @ X1 @ X3 @ X8 @ X9 @ X10) @ X11) = (tLList1380991092t_all2 @ X0 @ X5 @ X1 @ X4 @ (^[Y0 : X0]: (X6 @ (X8 @ Y0))) @ (^[Y0 : X1]: (X7 @ (X9 @ Y0))) @ X10 @ X11))),
% 3.00/1.67 inference(fool_elimination,[status(thm)],[f559])).
% 3.00/1.67 thf(f559,plain,(
% 3.00/1.67 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : X2 > X5 > $o,X7 : X3 > X4 > $o,X8 : X0 > X2,X9 : X1 > X3,X10 : tLList446370796tllist @ X0 @ X1,X11 : tLList446370796tllist @ X5 @ X4] : ((tLList1380991092t_all2 @ X2 @ X5 @ X3 @ X4 @ X6 @ X7 @ (tLList1669959861e_tmap @ X0 @ X2 @ X1 @ X3 @ X8 @ X9 @ X10) @ X11) = (tLList1380991092t_all2 @ X0 @ X5 @ X1 @ X4 @ (^[X12 : X0] : (X6 @ (X8 @ X12))) @ (^[X13 : X1] : (X7 @ (X9 @ X13))) @ X10 @ X11))),
% 3.00/1.67 inference(rectify,[status(thm)],[f2])).
% 3.00/1.67 thf(f2,axiom,(
% 3.00/1.67 ! [X0 : $tType,X1 : $tType,X4 : $tType,X8 : $tType,X5 : $tType,X3 : $tType,X17 : X4 > X3 > $o,X18 : X8 > X5 > $o,X19 : X0 > X4,X20 : X1 > X8,X11 : tLList446370796tllist @ X0 @ X1,X14 : tLList446370796tllist @ X3 @ X5] : ((tLList1380991092t_all2 @ X4 @ X3 @ X8 @ X5 @ X17 @ X18 @ (tLList1669959861e_tmap @ X0 @ X4 @ X1 @ X8 @ X19 @ X20 @ X11) @ X14) = (tLList1380991092t_all2 @ X0 @ X3 @ X1 @ X5 @ (^[X15 : X0] : (X17 @ (X19 @ X15))) @ (^[X15 : X1] : (X18 @ (X20 @ X15))) @ X11 @ X14))),
% 3.00/1.67 file('/export/starexec/sandbox2/tmp/tmp.2EYh0nHoAB/DTF2THF_25576.p',fact_1_tllist_Orel__map_I1_J)).
% 3.00/1.67 thf(f897,plain,(
% 3.00/1.67 ~spl32_1 | ~spl32_3),
% 3.00/1.67 inference(avatar_contradiction_clause,[status(thm)],[f896])).
% 3.00/1.67 thf(f896,plain,(
% 3.00/1.67 $false | (~spl32_1 | ~spl32_3)),
% 3.00/1.67 inference(trivial_inequality_removal,[status(thm)],[f895])).
% 3.00/1.67 thf(f895,plain,(
% 3.00/1.67 ($false = $true) | (~spl32_1 | ~spl32_3)),
% 3.00/1.67 inference(forward_demodulation,[status(thm)],[f878,f864])).
% 3.00/1.67 thf(f864,plain,(
% 3.00/1.67 ($false = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys)) | ~spl32_3),
% 3.00/1.67 inference(avatar_component_clause,[status(thm)],[f862])).
% 3.00/1.67 thf(f878,plain,(
% 3.00/1.67 ($true = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys)) | ~spl32_1),
% 3.00/1.67 inference(superposition,[status(thm)],[f855,f758])).
% 3.00/1.67 thf(f855,plain,(
% 3.00/1.67 ((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) = $true) | ~spl32_1),
% 3.00/1.67 inference(avatar_component_clause,[status(thm)],[f853])).
% 3.00/1.67 thf(f853,definition,(
% 3.00/1.67 spl32_1 <=> ((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) = $true)),
% 3.00/1.67 introduced(definition,[new_symbols(naming,[spl32_1])],[avatar_definition])).
% 3.00/1.67 thf(f872,plain,(
% 3.00/1.67 ~spl32_2 | ~spl32_3),
% 3.00/1.67 inference(avatar_contradiction_clause,[status(thm)],[f871])).
% 3.00/1.67 thf(f871,plain,(
% 3.00/1.67 $false | (~spl32_2 | ~spl32_3)),
% 3.00/1.67 inference(trivial_inequality_removal,[status(thm)],[f870])).
% 3.00/1.67 thf(f870,plain,(
% 3.00/1.67 ($false = $true) | (~spl32_2 | ~spl32_3)),
% 3.00/1.67 inference(forward_demodulation,[status(thm)],[f859,f864])).
% 3.00/1.67 thf(f859,plain,(
% 3.00/1.67 ($true = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys)) | ~spl32_2),
% 3.00/1.67 inference(avatar_component_clause,[status(thm)],[f857])).
% 3.00/1.67 thf(f857,definition,(
% 3.00/1.67 spl32_2 <=> ($true = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys))),
% 3.00/1.67 introduced(definition,[new_symbols(naming,[spl32_2])],[avatar_definition])).
% 3.00/1.67 thf(f869,plain,(
% 3.00/1.67 spl32_3 | spl32_4),
% 3.00/1.67 inference(avatar_split_clause,[status(thm)],[f851,f866,f862])).
% 3.00/1.67 thf(f851,plain,(
% 3.00/1.67 ($false = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys)) | ((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) = $false)),
% 3.00/1.67 inference(binary_proxy_clausification,[status(thm)],[f826])).
% 3.00/1.67 thf(f826,plain,(
% 3.00/1.67 ((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) != (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys))),
% 3.00/1.67 inference(cnf_transformation,[status(thm)],[f641])).
% 3.00/1.67 thf(f641,plain,(
% 3.00/1.67 ((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) != (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys))),
% 3.00/1.67 inference(flattening,[status(thm)],[f638])).
% 3.00/1.67 thf(f638,plain,(
% 3.00/1.67 ~((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys))),
% 3.00/1.67 inference(fool_elimination,[status(thm)],[f637])).
% 3.00/1.67 thf(f637,plain,(
% 3.00/1.67 ~((tLList1380991092t_all2 @ e @ b @ f @ d @ (^[X0 : e] : (p @ (f2 @ X0))) @ (^[X1 : f] : (q @ (g @ X1))) @ xs @ ys) = (tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys))),
% 3.00/1.67 inference(rectify,[status(thm)],[f255])).
% 3.00/1.67 thf(f255,negated_conjecture,(
% 3.00/1.67 ~((tLList1380991092t_all2 @ e @ b @ f @ d @ (^[X15 : e] : (p @ (f2 @ X15))) @ (^[X15 : f] : (q @ (g @ X15))) @ xs @ ys) = (tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys))),
% 3.00/1.67 inference(negated_conjecture,[status(cth)],[f254])).
% 3.00/1.67 thf(f254,conjecture,(
% 3.00/1.67 ((tLList1380991092t_all2 @ e @ b @ f @ d @ (^[X15 : e] : (p @ (f2 @ X15))) @ (^[X15 : f] : (q @ (g @ X15))) @ xs @ ys) = (tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys))),
% 3.00/1.67 file('/export/starexec/sandbox2/tmp/tmp.2EYh0nHoAB/DTF2THF_25576.p',conj_0)).
% 3.00/1.67 thf(f860,plain,(
% 3.00/1.67 spl32_1 | spl32_2),
% 3.00/1.67 inference(avatar_split_clause,[status(thm)],[f850,f857,f853])).
% 3.00/1.67 thf(f850,plain,(
% 3.00/1.67 ($true = (tLList1380991092t_all2 @ e @ b @ f @ d @ (^[Y0 : e]: (p @ (f2 @ Y0))) @ (^[Y0 : f]: (q @ (g @ Y0))) @ xs @ ys)) | ((tLList1380991092t_all2 @ a @ b @ c @ d @ p @ q @ (tLList1669959861e_tmap @ e @ a @ f @ c @ f2 @ g @ xs) @ ys) = $true)),
% 3.00/1.67 inference(binary_proxy_clausification,[status(thm)],[f826])).
% 3.00/1.67 % SZS output end Proof for DTF2THF_25576
% 3.00/1.67 % (25854)------------------------------
% 3.00/1.67 % (25854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.67 % (25854)Termination reason: Refutation
% 3.00/1.67
% 3.00/1.67 % (25854)Memory used [KB]: 7419
% 3.00/1.67 % (25854)Time elapsed: 0.068 s
% 3.00/1.67 % (25854)Instructions burned: 120 (million)
% 3.00/1.67 % (25854)------------------------------
% 3.00/1.67 % (25854)------------------------------
% 3.00/1.67 % (25848)Success in time 0.088 s
%------------------------------------------------------------------------------