%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT178^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n022.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 08:45:02 AM UTC 2026
% Result : Theorem 2.99s 1.68s
% Output : Refutation 2.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT178^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.33 % Computer : n022.cluster.edu
% 0.18/0.33 % Model : x86_64 x86_64
% 0.18/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.33 % Memory : 8042.1875MB
% 0.18/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Tue Feb 24 06:10:51 EST 2026
% 0.18/0.33 % CPUTime :
% 0.18/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : DAT178^1 : TPTP v9.2.1. Released v7.0.0.
% 0.31/0.45 % Domain : Data Structures
% 0.31/0.45 % Problem : Lazy lists II 507
% 0.31/0.45 % Version : [Bla16] axioms : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Fri04] Friedrich (2004), Lazy Lists II
% 0.31/0.45 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.31/0.45 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Bla16]
% 0.31/0.45 % Names : llist2__507.p [Bla16]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.31/0.45 % Syntax : Number of formulae : 321 ( 131 unt; 48 typ; 0 def)
% 0.31/0.45 % Number of atoms : 665 ( 253 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.31/0.45 % Number of connectives : 3892 ( 92 ~; 30 |; 64 &;3425 @)
% 0.31/0.45 % ( 0 <=>; 281 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 19 ( 7 avg)
% 0.31/0.45 % Number of types : 2 ( 1 usr)
% 0.31/0.45 % Number of type conns : 191 ( 191 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 48 ( 47 usr; 4 con; 0-5 aty)
% 0.31/0.45 % Number of variables : 970 ( 33 ^; 859 !; 38 ?; 970 :)
% 0.31/0.45 % ( 40 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.45 % SPC : TH1_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.31/0.45 % 2016-07-13 14:46:49.184
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 %----Could-be-implicit typings (4)
% 0.31/0.45 thf(ty_t_Coinductive__List_Ollist,type,
% 0.31/0.45 coinductive_llist: $tType > $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_t_Set_Oset,type,
% 0.31/0.45 set: $tType > $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_t_itself,type,
% 0.31/0.45 itself: $tType > $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_tf_a,type,
% 0.31/0.45 a: $tType ).
% 0.31/0.45
% 0.31/0.45 %----Explicit typings (44)
% 0.31/0.45 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.31/0.45 bounded_lattice:
% 0.31/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_cl_HOL_Otype,type,
% 0.31/0.45 type:
% 0.31/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_cl_Groups_Ominus,type,
% 0.31/0.45 minus:
% 0.31/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_cl_Orderings_Otop,type,
% 0.31/0.45 top:
% 0.31/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_cl_Lattices_Olattice,type,
% 0.31/0.45 lattice:
% 0.31/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.31/0.45 semilattice_sup:
% 0.31/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.31/0.45 bounded_lattice_top:
% 0.31/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.31/0.45 coindu328551480prefix:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Ogen__lset,type,
% 0.31/0.45 coinductive_gen_lset:
% 0.31/0.45 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Olappend,type,
% 0.31/0.45 coinductive_lappend:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Oldistinct,type,
% 0.31/0.45 coindu351974385stinct:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Olfilter,type,
% 0.31/0.45 coinductive_lfilter:
% 0.31/0.45 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.31/0.45 coinductive_lfinite:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Ollast,type,
% 0.31/0.45 coinductive_llast:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Ollexord,type,
% 0.31/0.45 coinductive_llexord:
% 0.31/0.45 !>[A: $tType] : ( ( A > A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.31/0.45 coinductive_LCons:
% 0.31/0.45 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.31/0.45 coinductive_LNil:
% 0.31/0.45 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 0.31/0.45 coinductive_lnull:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 0.31/0.45 coinductive_lset:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Olmember,type,
% 0.31/0.45 coinductive_lmember:
% 0.31/0.45 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.31/0.45 coindu1478340336prefix:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.31/0.45 minus_minus:
% 0.31/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_HOL_Oundefined,type,
% 0.31/0.45 undefined:
% 0.31/0.45 !>[A: $tType] : A ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 0.31/0.45 lList2435255213lllsts:
% 0.31/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp,type,
% 0.31/0.45 lList21511617539llstsp:
% 0.31/0.45 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.31/0.45 lList2236698231inlsts:
% 0.31/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.31/0.45 lList21916056377ts_rec:
% 0.31/0.45 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp,type,
% 0.31/0.45 lList2860480441nlstsp:
% 0.31/0.45 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.31/0.45 lList22096119349pslsts:
% 0.31/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 0.31/0.45 lList21612149805nflsts:
% 0.31/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 0.31/0.45 lList2370560421utlast:
% 0.31/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 0.31/0.46 lList2170638824_llast:
% 0.31/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 0.31/0.46 lList2281150353e_lrev:
% 0.31/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.31/0.46 lList21148268032oslsts:
% 0.31/0.46 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.31/0.46 sup_sup:
% 0.31/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.31/0.46 top_top:
% 0.31/0.46 !>[A: $tType] : A ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Pure_Otype,type,
% 0.31/0.46 type2:
% 0.31/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect,type,
% 0.31/0.46 collect:
% 0.31/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member,type,
% 0.31/0.46 member:
% 0.31/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_A,type,
% 0.31/0.46 a2: set @ a ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_P,type,
% 0.31/0.46 p: ( coinductive_llist @ a ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_l____,type,
% 0.31/0.46 l: coinductive_llist @ a ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_la______,type,
% 0.31/0.46 la: coinductive_llist @ a ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_xs,type,
% 0.31/0.46 xs: coinductive_llist @ a ).
% 0.31/0.46
% 0.31/0.46 %----Relevant facts (254)
% 0.31/0.46 thf(fact_0_init,axiom,
% 0.31/0.46 p @ ( coinductive_LNil @ a ) ).
% 0.31/0.46
% 0.31/0.46 % init
% 0.31/0.46 thf(fact_1_LNil__fin_Ohyps,axiom,
% 0.31/0.46 ( la
% 0.31/0.46 = ( coinductive_LNil @ a ) ) ).
% 0.31/0.46
% 0.31/0.46 % LNil_fin.hyps
% 0.31/0.46 thf(fact_2_l__def,axiom,
% 0.31/0.46 ( l
% 0.31/0.46 = ( lList2281150353e_lrev @ a @ xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % l_def
% 0.31/0.46 thf(fact_3_lrev__LNil,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lrev_LNil
% 0.31/0.46 thf(fact_4_lrevT,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lrevT
% 0.31/0.46 thf(fact_5_local_Ostep,axiom,
% 0.31/0.46 ! [Xs: coinductive_llist @ a,X: a] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ a ) @ Xs @ ( lList2236698231inlsts @ a @ a2 ) )
% 0.31/0.46 => ( ( p @ Xs )
% 0.31/0.46 => ( ( member @ a @ X @ a2 )
% 0.31/0.46 => ( p @ ( coinductive_lappend @ a @ Xs @ ( coinductive_LCons @ a @ X @ ( coinductive_LNil @ a ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.step
% 0.31/0.46 thf(fact_6_lrev__lrev__ident,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 0.31/0.46 = Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lrev_lrev_ident
% 0.31/0.46 thf(fact_7_lrev__is__lrev__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.31/0.46 = ( lList2281150353e_lrev @ A @ Ys ) )
% 0.31/0.46 = ( Xs = Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lrev_is_lrev_conv
% 0.31/0.46 thf(fact_8_LNil__is__lrev__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( ( ( coinductive_LNil @ A )
% 0.31/0.46 = ( lList2281150353e_lrev @ A @ Xs ) )
% 0.31/0.46 = ( Xs
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LNil_is_lrev_conv
% 0.31/0.46 thf(fact_9_lrev__is__LNil__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( Xs
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lrev_is_LNil_conv
% 0.31/0.46 thf(fact_10_lbutlast__LNil,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lbutlast_LNil
% 0.31/0.46 thf(fact_11_lrev__lappend,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lrev_lappend
% 0.31/0.46 thf(fact_12_fin,axiom,
% 0.31/0.46 member @ ( coinductive_llist @ a ) @ xs @ ( lList2236698231inlsts @ a @ a2 ) ).
% 0.31/0.46
% 0.31/0.46 % fin
% 0.31/0.46 thf(fact_13__092_060open_062l_A_092_060in_062_AA_092_060_094sup_062_092_060star_062_092_060close_062,axiom,
% 0.31/0.46 member @ ( coinductive_llist @ a ) @ l @ ( lList2236698231inlsts @ a @ a2 ) ).
% 0.31/0.46
% 0.31/0.46 % \<open>l \<in> A\<^sup>\<star>\<close>
% 0.31/0.46 thf(fact_14_LNil__is__lappend__conv,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_LNil @ A )
% 0.31/0.46 = ( coinductive_lappend @ A @ S @ T ) )
% 0.31/0.46 = ( ( S
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 & ( T
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LNil_is_lappend_conv
% 0.31/0.46 thf(fact_15_lappend__is__LNil__conv,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lappend @ A @ S @ T )
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( ( S
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 & ( T
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_is_LNil_conv
% 0.31/0.46 thf(fact_16_same__lappend__eq,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( ( coinductive_lappend @ A @ R @ S )
% 0.31/0.46 = ( coinductive_lappend @ A @ R @ T ) )
% 0.31/0.46 = ( S = T ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % same_lappend_eq
% 0.31/0.46 thf(fact_17_lapp__fin__fin__iff,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lapp_fin_fin_iff
% 0.31/0.46 thf(fact_18_lbutlast__LCons,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( ( R
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.31/0.46 = ( coinductive_LNil @ A ) ) )
% 0.31/0.46 & ( ( R
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.31/0.46 = ( coinductive_LCons @ A @ A3 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lbutlast_LCons
% 0.31/0.46 thf(fact_19_lrev__LCons,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.31/0.46 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A3 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lrev_LCons
% 0.31/0.46 thf(fact_20_llistE,axiom,
% 0.31/0.46 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.31/0.46 ( ( Y
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 => ~ ! [X21: A,X22: coinductive_llist @ A] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llistE
% 0.31/0.46 thf(fact_21_finT__simp,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finT_simp
% 0.31/0.46 thf(fact_22_fin__finite,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fin_finite
% 0.31/0.46 thf(fact_23_lappfin__finT,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappfin_finT
% 0.31/0.46 thf(fact_24_finlsts_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( A3
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 0.31/0.46 ( ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ A4 @ L ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ~ ( member @ A @ A4 @ A2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts.cases
% 0.31/0.46 thf(fact_25_finlsts_Osimps,axiom,
% 0.31/0.46 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 = ( ( A3
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [L2: coinductive_llist @ A,A5: A] :
% 0.31/0.46 ( ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.31/0.46 & ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts.simps
% 0.31/0.46 thf(fact_26_finlsts__induct,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ! [L: coinductive_llist @ A] :
% 0.31/0.46 ( ( L
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( P @ L ) )
% 0.31/0.46 => ( ! [A4: A,L: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( P @ L )
% 0.31/0.46 => ( ( member @ A @ A4 @ A2 )
% 0.31/0.46 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 0.31/0.46 => ( P @ X ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts_induct
% 0.31/0.46 thf(fact_27_finlsts_Oinducts,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( ! [L: coinductive_llist @ A,A4: A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( P @ L )
% 0.31/0.46 => ( ( member @ A @ A4 @ A2 )
% 0.31/0.46 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 0.31/0.46 => ( P @ X ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts.inducts
% 0.31/0.46 thf(fact_28_finlsts_OLNil__fin,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts.LNil_fin
% 0.31/0.46 thf(fact_29_finlsts_OLCons__fin,axiom,
% 0.31/0.46 ! [A: $tType,L3: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( member @ A @ A3 @ A2 )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L3 ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts.LCons_fin
% 0.31/0.46 thf(fact_30_lapp__fin__fin__lemma,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lapp_fin_fin_lemma
% 0.31/0.46 thf(fact_31_lappend__code_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.31/0.46 = Ys ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_code(1)
% 0.31/0.46 thf(fact_32_lappend__LNil2,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = Xs ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_LNil2
% 0.31/0.46 thf(fact_33_LNil__eq__lappend__iff,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_LNil @ A )
% 0.31/0.46 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( ( Xs
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 & ( Ys
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LNil_eq_lappend_iff
% 0.31/0.46 thf(fact_34_lappend__eq__LNil__iff,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( ( Xs
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 & ( Ys
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_eq_LNil_iff
% 0.31/0.46 thf(fact_35_lappend__code_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 0.31/0.46 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_code(2)
% 0.31/0.46 thf(fact_36_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 0.31/0.46 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A3: B] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 0.31/0.46 => ( ( ( R
% 0.31/0.46 = ( coinductive_LNil @ B ) )
% 0.31/0.46 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A3 @ R ) )
% 0.31/0.46 = A3 ) )
% 0.31/0.46 & ( ( R
% 0.31/0.46 != ( coinductive_LNil @ B ) )
% 0.31/0.46 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A3 @ R ) )
% 0.31/0.46 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LList2_Mirabelle_hamjzmohle.llast_LCons
% 0.31/0.46 thf(fact_37_lappend__snocL1__conv__LCons2,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.31/0.46 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_snocL1_conv_LCons2
% 0.31/0.46 thf(fact_38_llist_Oinject,axiom,
% 0.31/0.46 ! [A: $tType,X212: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_LCons @ A @ X212 @ X222 )
% 0.31/0.46 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.31/0.46 = ( ( X212 = Y21 )
% 0.31/0.46 & ( X222 = Y22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.inject
% 0.31/0.46 thf(fact_39_UNIV__I,axiom,
% 0.31/0.46 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % UNIV_I
% 0.31/0.46 thf(fact_40_iso__tuple__UNIV__I,axiom,
% 0.31/0.46 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % iso_tuple_UNIV_I
% 0.31/0.46 thf(fact_41_top__apply,axiom,
% 0.31/0.46 ! [C: $tType,D: $tType] :
% 0.31/0.46 ( ( top @ C @ ( type2 @ C ) )
% 0.31/0.46 => ( ( top_top @ ( D > C ) )
% 0.31/0.46 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % top_apply
% 0.31/0.46 thf(fact_42_top__set__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( top_top @ ( set @ A ) )
% 0.31/0.46 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % top_set_def
% 0.31/0.46 thf(fact_43_UNIV__witness,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % UNIV_witness
% 0.31/0.46 thf(fact_44_UNIV__eq__I,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.31/0.46 => ( ( top_top @ ( set @ A ) )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % UNIV_eq_I
% 0.31/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,P: A > $o] :
% 0.31/0.46 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.31/0.46 = ( P @ A3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( collect @ A
% 0.31/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_47_Collect__cong,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.46 ( ! [X3: A] :
% 0.31/0.46 ( ( P @ X3 )
% 0.31/0.46 = ( Q @ X3 ) )
% 0.31/0.46 => ( ( collect @ A @ P )
% 0.31/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_48_ext,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/0.46 ( ! [X3: A] :
% 0.31/0.46 ( ( F @ X3 )
% 0.31/0.46 = ( G @ X3 ) )
% 0.31/0.46 => ( F = G ) ) ).
% 0.31/0.46
% 0.31/0.46 % ext
% 0.31/0.46 thf(fact_49_lappend__assoc,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.31/0.46 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_assoc
% 0.31/0.46 thf(fact_50_neq__LNil__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( Xs
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.31/0.46 ( Xs
% 0.31/0.46 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % neq_LNil_conv
% 0.31/0.46 thf(fact_51_llist_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_LNil @ A )
% 0.31/0.46 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.distinct(1)
% 0.31/0.46 thf(fact_52_lappend__LNil__LNil,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_LNil_LNil
% 0.31/0.46 thf(fact_53_fpslsts__iff,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.31/0.46 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 & ( S
% 0.31/0.46 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fpslsts_iff
% 0.31/0.46 thf(fact_54_poslsts__UNIV,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 = ( S
% 0.31/0.46 != ( coinductive_LNil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % poslsts_UNIV
% 0.31/0.46 thf(fact_55_fpslsts__cases,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.31/0.46 => ~ ! [A4: A,Rs: coinductive_llist @ A] :
% 0.31/0.46 ( ( R
% 0.31/0.46 = ( coinductive_LCons @ A @ A4 @ Rs ) )
% 0.31/0.46 => ( ( member @ A @ A4 @ A2 )
% 0.31/0.46 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fpslsts_cases
% 0.31/0.46 thf(fact_56_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.31/0.46 = ( ( Xs
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [Xs2: coinductive_llist @ A] :
% 0.31/0.46 ( ( Xs
% 0.31/0.46 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 0.31/0.46 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.31/0.46 thf(fact_57_lstrict__prefix__code_I2_J,axiom,
% 0.31/0.46 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.31/0.46
% 0.31/0.46 % lstrict_prefix_code(2)
% 0.31/0.46 thf(fact_58_lstrict__prefix__code_I3_J,axiom,
% 0.31/0.46 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.31/0.46 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 % lstrict_prefix_code(3)
% 0.31/0.46 thf(fact_59_finlsts__rec__LCons__def,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.31/0.46 ( ( F
% 0.31/0.46 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( F @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.31/0.46 = ( D2 @ A3 @ R @ ( F @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts_rec_LCons_def
% 0.31/0.46 thf(fact_60_finlsts__rec__LCons,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,A3: A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.31/0.46 = ( D2 @ A3 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts_rec_LCons
% 0.31/0.46 thf(fact_61_top1I,axiom,
% 0.31/0.46 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.31/0.46
% 0.31/0.46 % top1I
% 0.31/0.46 thf(fact_62_lstrict__prefix__code_I4_J,axiom,
% 0.31/0.46 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.31/0.46 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.31/0.46 = ( ( X = Y )
% 0.31/0.46 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lstrict_prefix_code(4)
% 0.31/0.46 thf(fact_63_lstrict__prefix__code_I1_J,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lstrict_prefix_code(1)
% 0.31/0.46 thf(fact_64_llist__less__induct,axiom,
% 0.31/0.46 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ! [Xs3: coinductive_llist @ A] :
% 0.31/0.46 ( ! [Ys2: coinductive_llist @ A] :
% 0.31/0.46 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.31/0.46 => ( P @ Ys2 ) )
% 0.31/0.46 => ( P @ Xs3 ) )
% 0.31/0.46 => ( P @ Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist_less_induct
% 0.31/0.46 thf(fact_65_finlsts__rec__LNil,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,C2: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 0.31/0.46 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D2 @ ( coinductive_LNil @ B ) )
% 0.31/0.46 = C2 ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts_rec_LNil
% 0.31/0.46 thf(fact_66_finlsts__rec__LNil__def,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 0.31/0.46 ( ( F
% 0.31/0.46 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.31/0.46 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = C2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlsts_rec_LNil_def
% 0.31/0.46 thf(fact_67_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.31/0.46
% 0.31/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.31/0.46 thf(fact_68_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( Xs
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.31/0.46 thf(fact_69_top__empty__eq,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( top_top @ ( A > $o ) )
% 0.31/0.46 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % top_empty_eq
% 0.31/0.46 thf(fact_70_top__conj_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,P: $o,X: A] :
% 0.31/0.46 ( ( P
% 0.31/0.46 & ( top_top @ ( A > $o ) @ X ) )
% 0.31/0.46 = P ) ).
% 0.31/0.46
% 0.31/0.46 % top_conj(2)
% 0.31/0.46 thf(fact_71_top__conj_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X: A,P: $o] :
% 0.31/0.46 ( ( ( top_top @ ( A > $o ) @ X )
% 0.31/0.46 & P )
% 0.31/0.46 = P ) ).
% 0.31/0.46
% 0.31/0.46 % top_conj(1)
% 0.31/0.46 thf(fact_72_poslsts__iff,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.31/0.46 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 & ( S
% 0.31/0.46 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % poslsts_iff
% 0.31/0.46 thf(fact_73_llast__singleton,axiom,
% 0.31/0.46 ! [A: $tType,X: A] :
% 0.31/0.46 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 0.31/0.46 = X ) ).
% 0.31/0.46
% 0.31/0.46 % llast_singleton
% 0.31/0.46 thf(fact_74_notfin__inf,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A] :
% 0.31/0.46 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.31/0.46 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % notfin_inf
% 0.31/0.46 thf(fact_75_notinf__fin,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A] :
% 0.31/0.46 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.31/0.46 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % notinf_fin
% 0.31/0.46 thf(fact_76_alllsts__UNIV,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllsts_UNIV
% 0.31/0.46 thf(fact_77_LConsE,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 = ( ( member @ A @ X @ A2 )
% 0.31/0.46 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LConsE
% 0.31/0.46 thf(fact_78_lapp__inf,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ( ( coinductive_lappend @ A @ S @ T )
% 0.31/0.46 = S ) ) ).
% 0.31/0.46
% 0.31/0.46 % lapp_inf
% 0.31/0.46 thf(fact_79_llast__LCons2,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Y: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 0.31/0.46 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llast_LCons2
% 0.31/0.46 thf(fact_80_inflstsI,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inflstsI
% 0.31/0.46 thf(fact_81_alllstsE,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllstsE
% 0.31/0.46 thf(fact_82_infsubsetall,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % infsubsetall
% 0.31/0.46 thf(fact_83_inflstsE,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inflstsE
% 0.31/0.46 thf(fact_84_lapp__allT__iff,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.31/0.46 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lapp_allT_iff
% 0.31/0.46 thf(fact_85_infT__simp,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % infT_simp
% 0.31/0.46 thf(fact_86_alllsts_OLCons__all,axiom,
% 0.31/0.46 ! [A: $tType,L3: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ( ( member @ A @ A3 @ A2 )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L3 ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllsts.LCons_all
% 0.31/0.46 thf(fact_87_alllsts_OLNil__all,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllsts.LNil_all
% 0.31/0.46 thf(fact_88_inflsts__cases,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ~ ! [A4: A,L: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ( ( member @ A @ A4 @ A2 )
% 0.31/0.46 => ( S
% 0.31/0.46 != ( coinductive_LCons @ A @ A4 @ L ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inflsts_cases
% 0.31/0.46 thf(fact_89_inflstsI2,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,A2: set @ A,T: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ A3 @ A2 )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inflstsI2
% 0.31/0.46 thf(fact_90_lapp__all__invT,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lapp_all_invT
% 0.31/0.46 thf(fact_91_lappT,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappT
% 0.31/0.46 thf(fact_92_finsubsetall,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finsubsetall
% 0.31/0.46 thf(fact_93_finite__lemma,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finite_lemma
% 0.31/0.46 thf(fact_94_alllsts_Ocoinduct,axiom,
% 0.31/0.46 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( X4 @ X )
% 0.31/0.46 => ( ! [X3: coinductive_llist @ A] :
% 0.31/0.46 ( ( X4 @ X3 )
% 0.31/0.46 => ( ( X3
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [L4: coinductive_llist @ A,A6: A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( coinductive_LCons @ A @ A6 @ L4 ) )
% 0.31/0.46 & ( ( X4 @ L4 )
% 0.31/0.46 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.31/0.46 & ( member @ A @ A6 @ A2 ) ) ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllsts.coinduct
% 0.31/0.46 thf(fact_95_alllsts_Osimps,axiom,
% 0.31/0.46 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 = ( ( A3
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [L2: coinductive_llist @ A,A5: A] :
% 0.31/0.46 ( ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.31/0.46 & ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllsts.simps
% 0.31/0.46 thf(fact_96_alllsts_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ( ( A3
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 0.31/0.46 ( ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ A4 @ L ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.31/0.46 => ~ ( member @ A @ A4 @ A2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllsts.cases
% 0.31/0.46 thf(fact_97_fin__inf__cases,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A] :
% 0.31/0.46 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fin_inf_cases
% 0.31/0.46 thf(fact_98_lapp__fin__infT,axiom,
% 0.31/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lapp_fin_infT
% 0.31/0.46 thf(fact_99_lapp__inv2T,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 0.31/0.46 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lapp_inv2T
% 0.31/0.46 thf(fact_100_lapp__infT,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 0.31/0.46 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lapp_infT
% 0.31/0.46 thf(fact_101_app__invT,axiom,
% 0.31/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.31/0.46 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % app_invT
% 0.31/0.46 thf(fact_102_inflsts__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lList21612149805nflsts @ A )
% 0.31/0.46 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A7 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inflsts_def
% 0.31/0.46 thf(fact_103_llast__lappend__LCons,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 0.31/0.46 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llast_lappend_LCons
% 0.31/0.46 thf(fact_104_fin__Un__inf,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.31/0.46 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % fin_Un_inf
% 0.31/0.46 thf(fact_105_alllstsp_Ocoinduct,axiom,
% 0.31/0.46 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: A > $o] :
% 0.31/0.46 ( ( X4 @ X )
% 0.31/0.46 => ( ! [X3: coinductive_llist @ A] :
% 0.31/0.46 ( ( X4 @ X3 )
% 0.31/0.46 => ( ( X3
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [L4: coinductive_llist @ A,A6: A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( coinductive_LCons @ A @ A6 @ L4 ) )
% 0.31/0.46 & ( ( X4 @ L4 )
% 0.31/0.46 | ( lList21511617539llstsp @ A @ A2 @ L4 ) )
% 0.31/0.46 & ( A2 @ A6 ) ) ) )
% 0.31/0.46 => ( lList21511617539llstsp @ A @ A2 @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllstsp.coinduct
% 0.31/0.46 thf(fact_106_finlstsp_Oinducts,axiom,
% 0.31/0.46 ! [A: $tType,A2: A > $o,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.31/0.46 ( ( lList2860480441nlstsp @ A @ A2 @ X )
% 0.31/0.46 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( ! [L: coinductive_llist @ A,A4: A] :
% 0.31/0.46 ( ( lList2860480441nlstsp @ A @ A2 @ L )
% 0.31/0.46 => ( ( P @ L )
% 0.31/0.46 => ( ( A2 @ A4 )
% 0.31/0.46 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 0.31/0.46 => ( P @ X ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlstsp.inducts
% 0.31/0.46 thf(fact_107_finlstsp_Osimps,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lList2860480441nlstsp @ A )
% 0.31/0.46 = ( ^ [A7: A > $o,A5: coinductive_llist @ A] :
% 0.31/0.46 ( ( A5
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [L2: coinductive_llist @ A,B3: A] :
% 0.31/0.46 ( ( A5
% 0.31/0.46 = ( coinductive_LCons @ A @ B3 @ L2 ) )
% 0.31/0.46 & ( lList2860480441nlstsp @ A @ A7 @ L2 )
% 0.31/0.46 & ( A7 @ B3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlstsp.simps
% 0.31/0.46 thf(fact_108_Un__iff,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 = ( ( member @ A @ C2 @ A2 )
% 0.31/0.46 | ( member @ A @ C2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_iff
% 0.31/0.46 thf(fact_109_UnCI,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.31/0.46 ( ( ~ ( member @ A @ C2 @ B2 )
% 0.31/0.46 => ( member @ A @ C2 @ A2 ) )
% 0.31/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % UnCI
% 0.31/0.46 thf(fact_110_Diff__idemp,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 0.31/0.46 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Diff_idemp
% 0.31/0.46 thf(fact_111_Diff__iff,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 = ( ( member @ A @ C2 @ A2 )
% 0.31/0.46 & ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Diff_iff
% 0.31/0.46 thf(fact_112_DiffI,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ A2 )
% 0.31/0.46 => ( ~ ( member @ A @ C2 @ B2 )
% 0.31/0.46 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % DiffI
% 0.31/0.46 thf(fact_113_Un__Diff__cancel2,axiom,
% 0.31/0.46 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) @ A2 )
% 0.31/0.46 = ( sup_sup @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_Diff_cancel2
% 0.31/0.46 thf(fact_114_Un__Diff__cancel,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_Diff_cancel
% 0.31/0.46 thf(fact_115_lfinite__code_I2_J,axiom,
% 0.31/0.46 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.31/0.46 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 0.31/0.46 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite_code(2)
% 0.31/0.46 thf(fact_116_lfinite__LCons,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.31/0.46 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite_LCons
% 0.31/0.46 thf(fact_117_lfinite__code_I1_J,axiom,
% 0.31/0.46 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite_code(1)
% 0.31/0.46 thf(fact_118_lfinite__lappend,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite_lappend
% 0.31/0.46 thf(fact_119_Un__left__commute,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_left_commute
% 0.31/0.46 thf(fact_120_Un__left__absorb,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_left_absorb
% 0.31/0.46 thf(fact_121_Un__commute,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) )
% 0.31/0.46 = ( ^ [A7: set @ A,B4: set @ A] : ( sup_sup @ ( set @ A ) @ B4 @ A7 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_commute
% 0.31/0.46 thf(fact_122_Un__absorb,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % Un_absorb
% 0.31/0.46 thf(fact_123_Un__assoc,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.31/0.46 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_assoc
% 0.31/0.46 thf(fact_124_ball__Un,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.31/0.46 ( ( ! [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 => ( P @ X2 ) ) )
% 0.31/0.46 = ( ! [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ A2 )
% 0.31/0.46 => ( P @ X2 ) )
% 0.31/0.46 & ! [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ B2 )
% 0.31/0.46 => ( P @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ball_Un
% 0.31/0.46 thf(fact_125_Un__Diff,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/0.46 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.31/0.46 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_Diff
% 0.31/0.46 thf(fact_126_bex__Un,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.31/0.46 ( ( ? [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 & ( P @ X2 ) ) )
% 0.31/0.46 = ( ? [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ A2 )
% 0.31/0.46 & ( P @ X2 ) )
% 0.31/0.46 | ? [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ B2 )
% 0.31/0.46 & ( P @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bex_Un
% 0.31/0.46 thf(fact_127_DiffD2,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 => ~ ( member @ A @ C2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % DiffD2
% 0.31/0.46 thf(fact_128_DiffD1,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 => ( member @ A @ C2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % DiffD1
% 0.31/0.46 thf(fact_129_DiffE,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 => ~ ( ( member @ A @ C2 @ A2 )
% 0.31/0.46 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % DiffE
% 0.31/0.46 thf(fact_130_UnI2,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ B2 )
% 0.31/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % UnI2
% 0.31/0.46 thf(fact_131_UnI1,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ A2 )
% 0.31/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % UnI1
% 0.31/0.46 thf(fact_132_UnE,axiom,
% 0.31/0.46 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.46 => ( ~ ( member @ A @ C2 @ A2 )
% 0.31/0.46 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % UnE
% 0.31/0.46 thf(fact_133_lfinite__LConsI,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite_LConsI
% 0.31/0.46 thf(fact_134_lfinite__LNil,axiom,
% 0.31/0.46 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite_LNil
% 0.31/0.46 thf(fact_135_lappend__inf,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.31/0.46 = Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_inf
% 0.31/0.46 thf(fact_136_Un__UNIV__left,axiom,
% 0.31/0.46 ! [A: $tType,B2: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.31/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_UNIV_left
% 0.31/0.46 thf(fact_137_Un__UNIV__right,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.31/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Un_UNIV_right
% 0.31/0.46 thf(fact_138_lstrict__prefix__lfinite1,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 0.31/0.46 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lstrict_prefix_lfinite1
% 0.31/0.46 thf(fact_139_alllstsp_OLCons__all,axiom,
% 0.31/0.46 ! [A: $tType,A2: A > $o,L3: coinductive_llist @ A,A3: A] :
% 0.31/0.46 ( ( lList21511617539llstsp @ A @ A2 @ L3 )
% 0.31/0.46 => ( ( A2 @ A3 )
% 0.31/0.46 => ( lList21511617539llstsp @ A @ A2 @ ( coinductive_LCons @ A @ A3 @ L3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllstsp.LCons_all
% 0.31/0.46 thf(fact_140_finlstsp_OLCons__fin,axiom,
% 0.31/0.46 ! [A: $tType,A2: A > $o,L3: coinductive_llist @ A,A3: A] :
% 0.31/0.46 ( ( lList2860480441nlstsp @ A @ A2 @ L3 )
% 0.31/0.46 => ( ( A2 @ A3 )
% 0.31/0.46 => ( lList2860480441nlstsp @ A @ A2 @ ( coinductive_LCons @ A @ A3 @ L3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlstsp.LCons_fin
% 0.31/0.46 thf(fact_141_alllstsp_OLNil__all,axiom,
% 0.31/0.46 ! [A: $tType,A2: A > $o] : ( lList21511617539llstsp @ A @ A2 @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllstsp.LNil_all
% 0.31/0.46 thf(fact_142_finlstsp_OLNil__fin,axiom,
% 0.31/0.46 ! [A: $tType,A2: A > $o] : ( lList2860480441nlstsp @ A @ A2 @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlstsp.LNil_fin
% 0.31/0.46 thf(fact_143_lfinite_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,A3: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ A3 )
% 0.31/0.46 => ( ( A3
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 => ~ ! [Xs3: coinductive_llist @ A] :
% 0.31/0.46 ( ? [X3: A] :
% 0.31/0.46 ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 0.31/0.46 => ~ ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite.cases
% 0.31/0.46 thf(fact_144_lfinite_Osimps,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( coinductive_lfinite @ A )
% 0.31/0.46 = ( ^ [A5: coinductive_llist @ A] :
% 0.31/0.46 ( ( A5
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [Xs4: coinductive_llist @ A,X2: A] :
% 0.31/0.46 ( ( A5
% 0.31/0.46 = ( coinductive_LCons @ A @ X2 @ Xs4 ) )
% 0.31/0.46 & ( coinductive_lfinite @ A @ Xs4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite.simps
% 0.31/0.46 thf(fact_145_lfinite_Oinducts,axiom,
% 0.31/0.46 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ X )
% 0.31/0.46 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( ! [Xs3: coinductive_llist @ A,X3: A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.31/0.46 => ( ( P @ Xs3 )
% 0.31/0.46 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) )
% 0.31/0.46 => ( P @ X ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite.inducts
% 0.31/0.46 thf(fact_146_lfinite__rev__induct,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.31/0.46 => ( ( P @ Xs3 )
% 0.31/0.46 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 0.31/0.46 => ( P @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite_rev_induct
% 0.31/0.46 thf(fact_147_llimit__induct,axiom,
% 0.31/0.46 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( P @ ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.31/0.46 => ( ( P @ Xs3 )
% 0.31/0.46 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) )
% 0.31/0.46 => ( ( ! [Ys2: coinductive_llist @ A] :
% 0.31/0.46 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs )
% 0.31/0.46 => ( P @ Ys2 ) )
% 0.31/0.46 => ( P @ Xs ) )
% 0.31/0.46 => ( P @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llimit_induct
% 0.31/0.46 thf(fact_148_alllstsp_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,A2: A > $o,A3: coinductive_llist @ A] :
% 0.31/0.46 ( ( lList21511617539llstsp @ A @ A2 @ A3 )
% 0.31/0.46 => ( ( A3
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 0.31/0.46 ( ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ A4 @ L ) )
% 0.31/0.46 => ( ( lList21511617539llstsp @ A @ A2 @ L )
% 0.31/0.46 => ~ ( A2 @ A4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllstsp.cases
% 0.31/0.46 thf(fact_149_alllstsp_Osimps,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lList21511617539llstsp @ A )
% 0.31/0.46 = ( ^ [A7: A > $o,A5: coinductive_llist @ A] :
% 0.31/0.46 ( ( A5
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [L2: coinductive_llist @ A,B3: A] :
% 0.31/0.46 ( ( A5
% 0.31/0.46 = ( coinductive_LCons @ A @ B3 @ L2 ) )
% 0.31/0.46 & ( lList21511617539llstsp @ A @ A7 @ L2 )
% 0.31/0.46 & ( A7 @ B3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % alllstsp.simps
% 0.31/0.46 thf(fact_150_finlstsp_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,A2: A > $o,A3: coinductive_llist @ A] :
% 0.31/0.46 ( ( lList2860480441nlstsp @ A @ A2 @ A3 )
% 0.31/0.46 => ( ( A3
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 0.31/0.46 ( ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ A4 @ L ) )
% 0.31/0.46 => ( ( lList2860480441nlstsp @ A @ A2 @ L )
% 0.31/0.46 => ~ ( A2 @ A4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % finlstsp.cases
% 0.31/0.46 thf(fact_151_sup__top__left,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A] :
% 0.31/0.46 ( ( sup_sup @ A @ ( top_top @ A ) @ X )
% 0.31/0.46 = ( top_top @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_top_left
% 0.31/0.46 thf(fact_152_sup__top__right,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A] :
% 0.31/0.46 ( ( sup_sup @ A @ X @ ( top_top @ A ) )
% 0.31/0.46 = ( top_top @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_top_right
% 0.31/0.46 thf(fact_153_sup__apply,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.31/0.46 => ( ( sup_sup @ ( A > B ) )
% 0.31/0.46 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_apply
% 0.31/0.46 thf(fact_154_sup_Oidem,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [A3: A] :
% 0.31/0.46 ( ( sup_sup @ A @ A3 @ A3 )
% 0.31/0.46 = A3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup.idem
% 0.31/0.46 thf(fact_155_sup__idem,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A] :
% 0.31/0.46 ( ( sup_sup @ A @ X @ X )
% 0.31/0.46 = X ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_idem
% 0.31/0.46 thf(fact_156_minus__apply,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( minus @ B @ ( type2 @ B ) )
% 0.31/0.46 => ( ( minus_minus @ ( A > B ) )
% 0.31/0.46 = ( ^ [A7: A > B,B4: A > B,X2: A] : ( minus_minus @ B @ ( A7 @ X2 ) @ ( B4 @ X2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % minus_apply
% 0.31/0.46 thf(fact_157_sup_Oright__idem,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [A3: A,B5: A] :
% 0.31/0.46 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B5 ) @ B5 )
% 0.31/0.46 = ( sup_sup @ A @ A3 @ B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup.right_idem
% 0.31/0.46 thf(fact_158_sup__left__idem,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A,Y: A] :
% 0.31/0.46 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.31/0.46 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_left_idem
% 0.31/0.46 thf(fact_159_sup_Oleft__idem,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [A3: A,B5: A] :
% 0.31/0.46 ( ( sup_sup @ A @ A3 @ ( sup_sup @ A @ A3 @ B5 ) )
% 0.31/0.46 = ( sup_sup @ A @ A3 @ B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup.left_idem
% 0.31/0.46 thf(fact_160_fun__diff__def,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( minus @ B @ ( type2 @ B ) )
% 0.31/0.46 => ( ( minus_minus @ ( A > B ) )
% 0.31/0.46 = ( ^ [A7: A > B,B4: A > B,X2: A] : ( minus_minus @ B @ ( A7 @ X2 ) @ ( B4 @ X2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fun_diff_def
% 0.31/0.46 thf(fact_161_sup__left__commute,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A,Y: A,Z: A] :
% 0.31/0.46 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.31/0.46 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_left_commute
% 0.31/0.46 thf(fact_162_sup_Oleft__commute,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [B5: A,A3: A,C2: A] :
% 0.31/0.46 ( ( sup_sup @ A @ B5 @ ( sup_sup @ A @ A3 @ C2 ) )
% 0.31/0.46 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B5 @ C2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup.left_commute
% 0.31/0.46 thf(fact_163_sup__commute,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ( ( sup_sup @ A )
% 0.31/0.46 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_commute
% 0.31/0.46 thf(fact_164_sup_Ocommute,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ( ( sup_sup @ A )
% 0.31/0.46 = ( ^ [A5: A,B3: A] : ( sup_sup @ A @ B3 @ A5 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup.commute
% 0.31/0.46 thf(fact_165_sup__assoc,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A,Y: A,Z: A] :
% 0.31/0.46 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.31/0.46 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_assoc
% 0.31/0.46 thf(fact_166_sup_Oassoc,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [A3: A,B5: A,C2: A] :
% 0.31/0.46 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B5 ) @ C2 )
% 0.31/0.46 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B5 @ C2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup.assoc
% 0.31/0.46 thf(fact_167_sup__fun__def,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.31/0.46 => ( ( sup_sup @ ( A > B ) )
% 0.31/0.46 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sup_fun_def
% 0.31/0.46 thf(fact_168_inf__sup__aci_I5_J,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.31/0.46 => ( ( sup_sup @ A )
% 0.31/0.46 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inf_sup_aci(5)
% 0.31/0.46 thf(fact_169_inf__sup__aci_I6_J,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A,Y: A,Z: A] :
% 0.31/0.46 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.31/0.46 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inf_sup_aci(6)
% 0.31/0.46 thf(fact_170_inf__sup__aci_I7_J,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A,Y: A,Z: A] :
% 0.31/0.46 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.31/0.46 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inf_sup_aci(7)
% 0.31/0.46 thf(fact_171_inf__sup__aci_I8_J,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.31/0.46 => ! [X: A,Y: A] :
% 0.31/0.46 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.31/0.46 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inf_sup_aci(8)
% 0.31/0.46 thf(fact_172_lset__lappend__lfinite,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( coinductive_lset @ A @ Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lset_lappend_lfinite
% 0.31/0.46 thf(fact_173_lstrict__prefix__lappend__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coindu1478340336prefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lstrict_prefix_lappend_conv
% 0.31/0.46 thf(fact_174_lmember__code_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X: A] :
% 0.31/0.46 ~ ( coinductive_lmember @ A @ X @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lmember_code(1)
% 0.31/0.46 thf(fact_175_lnull__lappend,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lnull_lappend
% 0.31/0.46 thf(fact_176_lappend_Odisc__iff_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 0.31/0.46 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend.disc_iff(2)
% 0.31/0.46 thf(fact_177_lappend_Oexhaust,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ~ ( coinductive_lnull @ A @ Ys ) )
% 0.31/0.46 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend.exhaust
% 0.31/0.46 thf(fact_178_lzip_Oexhaust,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.31/0.46 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 | ( coinductive_lnull @ B @ Ys ) )
% 0.31/0.46 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ( coinductive_lnull @ B @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lzip.exhaust
% 0.31/0.46 thf(fact_179_lset__lmember,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 = ( coinductive_lmember @ A @ X @ Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lset_lmember
% 0.31/0.46 thf(fact_180_lappend__lnull2,axiom,
% 0.31/0.46 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ Ys )
% 0.31/0.46 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.31/0.46 = Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_lnull2
% 0.31/0.46 thf(fact_181_lappend__lnull1,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.31/0.46 = Ys ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend_lnull1
% 0.31/0.46 thf(fact_182_lappend_Odisc_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_lnull @ A @ Ys )
% 0.31/0.46 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend.disc(1)
% 0.31/0.46 thf(fact_183_lappend_Odisc_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 | ~ ( coinductive_lnull @ A @ Ys ) )
% 0.31/0.46 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend.disc(2)
% 0.31/0.46 thf(fact_184_lnull__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( coinductive_lnull @ A )
% 0.31/0.46 = ( ^ [Llist: coinductive_llist @ A] :
% 0.31/0.46 ( Llist
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lnull_def
% 0.31/0.46 thf(fact_185_llist_Ocollapse_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Llist2: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ Llist2 )
% 0.31/0.46 => ( Llist2
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.collapse(1)
% 0.31/0.46 thf(fact_186_llist_OdiscI_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Llist2: coinductive_llist @ A] :
% 0.31/0.46 ( ( Llist2
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 => ( coinductive_lnull @ A @ Llist2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.discI(1)
% 0.31/0.46 thf(fact_187_llist_Odisc_I1_J,axiom,
% 0.31/0.46 ! [A: $tType] : ( coinductive_lnull @ A @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.disc(1)
% 0.31/0.46 thf(fact_188_not__lnull__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( ~ ( coinductive_lnull @ A @ Xs ) )
% 0.31/0.46 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.31/0.46 ( Xs
% 0.31/0.46 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_lnull_conv
% 0.31/0.46 thf(fact_189_llist_OdiscI_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,Llist2: coinductive_llist @ A,X212: A,X222: coinductive_llist @ A] :
% 0.31/0.46 ( ( Llist2
% 0.31/0.46 = ( coinductive_LCons @ A @ X212 @ X222 ) )
% 0.31/0.46 => ~ ( coinductive_lnull @ A @ Llist2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.discI(2)
% 0.31/0.46 thf(fact_190_llist_Odisc_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 0.31/0.46 ~ ( coinductive_lnull @ A @ ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.disc(2)
% 0.31/0.46 thf(fact_191_llist_Oset__induct,axiom,
% 0.31/0.46 ! [A: $tType,X: A,A3: coinductive_llist @ A,P: A > ( coinductive_llist @ A ) > $o] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ A3 ) )
% 0.31/0.46 => ( ! [Z1: A,Z2: coinductive_llist @ A] : ( P @ Z1 @ ( coinductive_LCons @ A @ Z1 @ Z2 ) )
% 0.31/0.46 => ( ! [Z1: A,Z2: coinductive_llist @ A,Xa2: A] :
% 0.31/0.46 ( ( member @ A @ Xa2 @ ( coinductive_lset @ A @ Z2 ) )
% 0.31/0.46 => ( ( P @ Xa2 @ Z2 )
% 0.31/0.46 => ( P @ Xa2 @ ( coinductive_LCons @ A @ Z1 @ Z2 ) ) ) )
% 0.31/0.46 => ( P @ X @ A3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.set_induct
% 0.31/0.46 thf(fact_192_llist_Oset__cases,axiom,
% 0.31/0.46 ! [A: $tType,E: A,A3: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ E @ ( coinductive_lset @ A @ A3 ) )
% 0.31/0.46 => ( ! [Z2: coinductive_llist @ A] :
% 0.31/0.46 ( A3
% 0.31/0.46 != ( coinductive_LCons @ A @ E @ Z2 ) )
% 0.31/0.46 => ~ ! [Z1: A,Z2: coinductive_llist @ A] :
% 0.31/0.46 ( ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ Z1 @ Z2 ) )
% 0.31/0.46 => ~ ( member @ A @ E @ ( coinductive_lset @ A @ Z2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.set_cases
% 0.31/0.46 thf(fact_193_lset__induct_H,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ( ! [Xs3: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.31/0.46 => ( ! [X5: A,Xs3: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.31/0.46 => ( ( P @ Xs3 )
% 0.31/0.46 => ( P @ ( coinductive_LCons @ A @ X5 @ Xs3 ) ) ) )
% 0.31/0.46 => ( P @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lset_induct'
% 0.31/0.46 thf(fact_194_lset__induct,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ( ! [Xs3: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.31/0.46 => ( ! [X5: A,Xs3: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.31/0.46 => ( ( X != X5 )
% 0.31/0.46 => ( ( P @ Xs3 )
% 0.31/0.46 => ( P @ ( coinductive_LCons @ A @ X5 @ Xs3 ) ) ) ) )
% 0.31/0.46 => ( P @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lset_induct
% 0.31/0.46 thf(fact_195_lset__cases,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ( ! [Xs5: coinductive_llist @ A] :
% 0.31/0.46 ( Xs
% 0.31/0.46 != ( coinductive_LCons @ A @ X @ Xs5 ) )
% 0.31/0.46 => ~ ! [X5: A,Xs5: coinductive_llist @ A] :
% 0.31/0.46 ( ( Xs
% 0.31/0.46 = ( coinductive_LCons @ A @ X5 @ Xs5 ) )
% 0.31/0.46 => ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs5 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lset_cases
% 0.31/0.46 thf(fact_196_llist_Oset__intros_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,A1: A,A22: coinductive_llist @ A] : ( member @ A @ A1 @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.set_intros(1)
% 0.31/0.46 thf(fact_197_llist_Oset__intros_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X: A,A22: coinductive_llist @ A,A1: A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ A22 ) )
% 0.31/0.46 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llist.set_intros(2)
% 0.31/0.46 thf(fact_198_lset__intros_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] : ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lset_intros(1)
% 0.31/0.46 thf(fact_199_lset__intros_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,X6: A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X6 @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lset_intros(2)
% 0.31/0.46 thf(fact_200_lnull__imp__lfinite,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lnull_imp_lfinite
% 0.31/0.46 thf(fact_201_in__lset__lappend__iff,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 0.31/0.46 = ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 | ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 & ( member @ A @ X @ ( coinductive_lset @ A @ Ys ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_lset_lappend_iff
% 0.31/0.46 thf(fact_202_lappend_Octr_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_lnull @ A @ Ys )
% 0.31/0.46 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lappend.ctr(1)
% 0.31/0.46 thf(fact_203_Coinductive__List_Ollast__LCons,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.31/0.46 ( ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.31/0.46 = X ) )
% 0.31/0.46 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.31/0.46 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Coinductive_List.llast_LCons
% 0.31/0.46 thf(fact_204_lset__lappend__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( coinductive_lset @ A @ Ys ) ) ) )
% 0.31/0.46 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( coinductive_lset @ A @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lset_lappend_conv
% 0.31/0.46 thf(fact_205_split__llist,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ? [Ys3: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 0.31/0.46 ( ( Xs
% 0.31/0.46 = ( coinductive_lappend @ A @ Ys3 @ ( coinductive_LCons @ A @ X @ Zs2 ) ) )
% 0.31/0.46 & ( coinductive_lfinite @ A @ Ys3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_llist
% 0.31/0.46 thf(fact_206_split__llist__first,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ? [Ys3: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 0.31/0.46 ( ( Xs
% 0.31/0.46 = ( coinductive_lappend @ A @ Ys3 @ ( coinductive_LCons @ A @ X @ Zs2 ) ) )
% 0.31/0.46 & ( coinductive_lfinite @ A @ Ys3 )
% 0.31/0.46 & ~ ( member @ A @ X @ ( coinductive_lset @ A @ Ys3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_llist_first
% 0.31/0.46 thf(fact_207_lmember__code_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Y: A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lmember @ A @ X @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.31/0.46 = ( ( X = Y )
% 0.31/0.46 | ( coinductive_lmember @ A @ X @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lmember_code(2)
% 0.31/0.46 thf(fact_208_gen__lset__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( coinductive_gen_lset @ A )
% 0.31/0.46 = ( ^ [A7: set @ A,Xs4: coinductive_llist @ A] : ( sup_sup @ ( set @ A ) @ A7 @ ( coinductive_lset @ A @ Xs4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % gen_lset_def
% 0.31/0.46 thf(fact_209_llast__lappend,axiom,
% 0.31/0.46 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lnull @ A @ Ys )
% 0.31/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( coinductive_llast @ A @ Xs ) ) )
% 0.31/0.46 & ( ~ ( coinductive_lnull @ A @ Ys )
% 0.31/0.46 => ( ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( coinductive_llast @ A @ Ys ) ) )
% 0.31/0.46 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( undefined @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llast_lappend
% 0.31/0.46 thf(fact_210_lfilter__eq__LConsD,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Ys: coinductive_llist @ A,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lfilter @ A @ P @ Ys )
% 0.31/0.46 = ( coinductive_LCons @ A @ X @ Xs ) )
% 0.31/0.46 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 0.31/0.46 ( ( Ys
% 0.31/0.46 = ( coinductive_lappend @ A @ Us @ ( coinductive_LCons @ A @ X @ Vs ) ) )
% 0.31/0.46 & ( coinductive_lfinite @ A @ Us )
% 0.31/0.46 & ! [X7: A] :
% 0.31/0.46 ( ( member @ A @ X7 @ ( coinductive_lset @ A @ Us ) )
% 0.31/0.46 => ~ ( P @ X7 ) )
% 0.31/0.46 & ( P @ X )
% 0.31/0.46 & ( Xs
% 0.31/0.46 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_eq_LConsD
% 0.31/0.46 thf(fact_211_lfilter__idem,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 0.31/0.46 = ( coinductive_lfilter @ A @ P @ Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_idem
% 0.31/0.46 thf(fact_212_lfilter__LCons,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( P @ X )
% 0.31/0.46 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.31/0.46 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) )
% 0.31/0.46 & ( ~ ( P @ X )
% 0.31/0.46 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.31/0.46 = ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_LCons
% 0.31/0.46 thf(fact_213_lfilter__LNil,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o] :
% 0.31/0.46 ( ( coinductive_lfilter @ A @ P @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_LNil
% 0.31/0.46 thf(fact_214_diverge__lfilter__LNil,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.31/0.46 ( ! [X3: A] :
% 0.31/0.46 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ~ ( P @ X3 ) )
% 0.31/0.46 => ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.31/0.46 = ( coinductive_LNil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % diverge_lfilter_LNil
% 0.31/0.46 thf(fact_215_lnull__lfilter,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 0.31/0.46 = ( ! [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ~ ( P @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lnull_lfilter
% 0.31/0.46 thf(fact_216_lfilter__lappend__lfinite,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.31/0.46 = ( coinductive_lappend @ A @ ( coinductive_lfilter @ A @ P @ Xs ) @ ( coinductive_lfilter @ A @ P @ Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_lappend_lfinite
% 0.31/0.46 thf(fact_217_LList2__Mirabelle__hamjzmohle_Ollast__LNil,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( lList2170638824_llast @ B @ ( coinductive_LNil @ B ) )
% 0.31/0.46 = ( undefined @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 % LList2_Mirabelle_hamjzmohle.llast_LNil
% 0.31/0.46 thf(fact_218_lfilter__id__conv,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.31/0.46 = Xs )
% 0.31/0.46 = ( ! [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ( P @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_id_conv
% 0.31/0.46 thf(fact_219_lfilter__cong,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,P: A > $o,Q: A > $o] :
% 0.31/0.46 ( ( Xs = Ys )
% 0.31/0.46 => ( ! [X3: A] :
% 0.31/0.46 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Ys ) )
% 0.31/0.46 => ( ( P @ X3 )
% 0.31/0.46 = ( Q @ X3 ) ) )
% 0.31/0.46 => ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.31/0.46 = ( coinductive_lfilter @ A @ Q @ Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_cong
% 0.31/0.46 thf(fact_220_lfinite__lfilterI,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( coinductive_lfinite @ A @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfinite_lfilterI
% 0.31/0.46 thf(fact_221_lfilter__LCons__seek,axiom,
% 0.31/0.46 ! [A: $tType,P2: A > $o,X: A,L3: coinductive_llist @ A] :
% 0.31/0.46 ( ~ ( P2 @ X )
% 0.31/0.46 => ( ( coinductive_lfilter @ A @ P2 @ ( coinductive_LCons @ A @ X @ L3 ) )
% 0.31/0.46 = ( coinductive_lfilter @ A @ P2 @ L3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_LCons_seek
% 0.31/0.46 thf(fact_222_lfilter__LCons__found,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( P @ X )
% 0.31/0.46 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.31/0.46 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_LCons_found
% 0.31/0.46 thf(fact_223_lfilter__empty__conv,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( ! [X2: A] :
% 0.31/0.46 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ~ ( P @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_empty_conv
% 0.31/0.46 thf(fact_224_lfilter__eq__lappend__lfiniteD,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.31/0.46 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.31/0.46 = ( coinductive_lappend @ A @ Ys @ Zs ) )
% 0.31/0.46 => ( ( coinductive_lfinite @ A @ Ys )
% 0.31/0.46 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 0.31/0.46 ( ( Xs
% 0.31/0.46 = ( coinductive_lappend @ A @ Us @ Vs ) )
% 0.31/0.46 & ( coinductive_lfinite @ A @ Us )
% 0.31/0.46 & ( Ys
% 0.31/0.46 = ( coinductive_lfilter @ A @ P @ Us ) )
% 0.31/0.46 & ( Zs
% 0.31/0.46 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lfilter_eq_lappend_lfiniteD
% 0.31/0.46 thf(fact_225_Coinductive__List_Ollast__LNil,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = ( undefined @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % Coinductive_List.llast_LNil
% 0.31/0.46 thf(fact_226_llast__linfinite,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ( coinductive_llast @ A @ Xs )
% 0.31/0.46 = ( undefined @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llast_linfinite
% 0.31/0.46 thf(fact_227_gen__lset__code_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( coinductive_gen_lset @ A @ A2 @ ( coinductive_LNil @ A ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % gen_lset_code(1)
% 0.31/0.46 thf(fact_228_ldistinct_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,A3: coinductive_llist @ A] :
% 0.31/0.46 ( ( coindu351974385stinct @ A @ A3 )
% 0.31/0.46 => ( ( A3
% 0.31/0.46 != ( coinductive_LNil @ A ) )
% 0.31/0.46 => ~ ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.31/0.46 ( ( A3
% 0.31/0.46 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 0.31/0.46 => ( ~ ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs3 ) )
% 0.31/0.46 => ~ ( coindu351974385stinct @ A @ Xs3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ldistinct.cases
% 0.31/0.46 thf(fact_229_ldistinct_Osimps,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( coindu351974385stinct @ A )
% 0.31/0.46 = ( ^ [A5: coinductive_llist @ A] :
% 0.31/0.46 ( ( A5
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [X2: A,Xs4: coinductive_llist @ A] :
% 0.31/0.46 ( ( A5
% 0.31/0.46 = ( coinductive_LCons @ A @ X2 @ Xs4 ) )
% 0.31/0.46 & ~ ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs4 ) )
% 0.31/0.46 & ( coindu351974385stinct @ A @ Xs4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ldistinct.simps
% 0.31/0.46 thf(fact_230_ldistinct__LNil__code,axiom,
% 0.31/0.46 ! [A: $tType] : ( coindu351974385stinct @ A @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % ldistinct_LNil_code
% 0.31/0.46 thf(fact_231_ldistinct__LCons,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coindu351974385stinct @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.31/0.46 = ( ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 & ( coindu351974385stinct @ A @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ldistinct_LCons
% 0.31/0.46 thf(fact_232_ldistinct__lfilterI,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.31/0.46 ( ( coindu351974385stinct @ A @ Xs )
% 0.31/0.46 => ( coindu351974385stinct @ A @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ldistinct_lfilterI
% 0.31/0.46 thf(fact_233_ldistinct_OLCons,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ( ( coindu351974385stinct @ A @ Xs )
% 0.31/0.46 => ( coindu351974385stinct @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ldistinct.LCons
% 0.31/0.46 thf(fact_234_ldistinct_OLNil,axiom,
% 0.31/0.46 ! [A: $tType] : ( coindu351974385stinct @ A @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % ldistinct.LNil
% 0.31/0.46 thf(fact_235_ldistinct_Ocoinduct,axiom,
% 0.31/0.46 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A] :
% 0.31/0.46 ( ( X4 @ X )
% 0.31/0.46 => ( ! [X3: coinductive_llist @ A] :
% 0.31/0.46 ( ( X4 @ X3 )
% 0.31/0.46 => ( ( X3
% 0.31/0.46 = ( coinductive_LNil @ A ) )
% 0.31/0.46 | ? [Xa3: A,Xs6: coinductive_llist @ A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( coinductive_LCons @ A @ Xa3 @ Xs6 ) )
% 0.31/0.46 & ~ ( member @ A @ Xa3 @ ( coinductive_lset @ A @ Xs6 ) )
% 0.31/0.46 & ( ( X4 @ Xs6 )
% 0.31/0.46 | ( coindu351974385stinct @ A @ Xs6 ) ) ) ) )
% 0.31/0.46 => ( coindu351974385stinct @ A @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ldistinct.coinduct
% 0.31/0.46 thf(fact_236_llexord__lappend__leftD,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 0.31/0.46 => ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ! [X3: A] :
% 0.31/0.46 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ~ ( R @ X3 @ X3 ) )
% 0.31/0.46 => ( coinductive_llexord @ A @ R @ Ys @ Zs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_lappend_leftD
% 0.31/0.46 thf(fact_237_llexord__lappend__left,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,R: A > A > $o,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.31/0.46 => ( ! [X3: A] :
% 0.31/0.46 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.31/0.46 => ~ ( R @ X3 @ X3 ) )
% 0.31/0.46 => ( ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 0.31/0.46 = ( coinductive_llexord @ A @ R @ Ys @ Zs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_lappend_left
% 0.31/0.46 thf(fact_238_llexord__refl,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ Xs @ Xs ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_refl
% 0.31/0.46 thf(fact_239_llexord__LCons__LCons,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.31/0.46 = ( ( ( X = Y )
% 0.31/0.46 & ( coinductive_llexord @ A @ R @ Xs @ Ys ) )
% 0.31/0.46 | ( R @ X @ Y ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_LCons_LCons
% 0.31/0.46 thf(fact_240_llexord__code_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ ( coinductive_LNil @ A ) @ Ys ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_code(1)
% 0.31/0.46 thf(fact_241_llexord__LNil__right,axiom,
% 0.31/0.46 ! [A: $tType,Ys: coinductive_llist @ A,R: A > A > $o,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ Ys )
% 0.31/0.46 => ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 0.31/0.46 = ( coinductive_lnull @ A @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_LNil_right
% 0.31/0.46 thf(fact_242_lnull__llexord,axiom,
% 0.31/0.46 ! [A: $tType,Xs: coinductive_llist @ A,R: A > A > $o,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_lnull @ A @ Xs )
% 0.31/0.46 => ( coinductive_llexord @ A @ R @ Xs @ Ys ) ) ).
% 0.31/0.46
% 0.31/0.46 % lnull_llexord
% 0.31/0.46 thf(fact_243_llexord__trans,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 0.31/0.46 => ( ( coinductive_llexord @ A @ R @ Ys @ Zs )
% 0.31/0.46 => ( ! [A4: A,B6: A,C4: A] :
% 0.31/0.46 ( ( R @ A4 @ B6 )
% 0.31/0.46 => ( ( R @ B6 @ C4 )
% 0.31/0.46 => ( R @ A4 @ C4 ) ) )
% 0.31/0.46 => ( coinductive_llexord @ A @ R @ Xs @ Zs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_trans
% 0.31/0.46 thf(fact_244_llexord__linear,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ! [X3: A,Y3: A] :
% 0.31/0.46 ( ( R @ X3 @ Y3 )
% 0.31/0.46 | ( X3 = Y3 )
% 0.31/0.46 | ( R @ Y3 @ X3 ) )
% 0.31/0.46 => ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 0.31/0.46 | ( coinductive_llexord @ A @ R @ Ys @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_linear
% 0.31/0.46 thf(fact_245_llexord__antisym,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 0.31/0.46 => ( ( coinductive_llexord @ A @ R @ Ys @ Xs )
% 0.31/0.46 => ( ! [A4: A,B6: A] :
% 0.31/0.46 ( ( R @ A4 @ B6 )
% 0.31/0.46 => ~ ( R @ B6 @ A4 ) )
% 0.31/0.46 => ( Xs = Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_antisym
% 0.31/0.46 thf(fact_246_llexord__append__right,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_append_right
% 0.31/0.46 thf(fact_247_llexord__lappend__leftI,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_llexord @ A @ R @ Ys @ Zs )
% 0.31/0.46 => ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_lappend_leftI
% 0.31/0.46 thf(fact_248_llexord__LNil,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ ( coinductive_LNil @ A ) @ Ys ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_LNil
% 0.31/0.46 thf(fact_249_llexord__code_I3_J,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.31/0.46 = ( ( R @ X @ Y )
% 0.31/0.46 | ( ( X = Y )
% 0.31/0.46 & ( coinductive_llexord @ A @ R @ Xs @ Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_code(3)
% 0.31/0.46 thf(fact_250_llexord__LCons__left,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 0.31/0.46 = ( ? [Y2: A,Ys4: coinductive_llist @ A] :
% 0.31/0.46 ( ( Ys
% 0.31/0.46 = ( coinductive_LCons @ A @ Y2 @ Ys4 ) )
% 0.31/0.46 & ( ( ( X = Y2 )
% 0.31/0.46 & ( coinductive_llexord @ A @ R @ Xs @ Ys4 ) )
% 0.31/0.46 | ( R @ X @ Y2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_LCons_left
% 0.31/0.46 thf(fact_251_llexord__LCons__eq,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 0.31/0.46 ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 0.31/0.46 => ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_LCons_eq
% 0.31/0.46 thf(fact_252_llexord__LCons__less,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,X: A,Y: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.31/0.46 ( ( R @ X @ Y )
% 0.31/0.46 => ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_LCons_less
% 0.31/0.46 thf(fact_253_llexord__code_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,R: A > A > $o,X: A,Xs: coinductive_llist @ A] :
% 0.31/0.46 ~ ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LNil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % llexord_code(2)
% 0.31/0.46
% 0.31/0.46 %----Type constructors (18)
% 0.31/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.31/0.46 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.31/0.46 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.31/0.46 ! [A8: $tType,A9: $tType] :
% 0.31/0.46 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.31/0.46 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.31/0.46 ! [A8: $tType,A9: $tType] :
% 0.31/0.46 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.31/0.46 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.31/0.46 ! [A8: $tType,A9: $tType] :
% 0.31/0.46 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 0.31/0.46 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.31/0.46 ! [A8: $tType,A9: $tType] :
% 0.31/0.46 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 0.31/0.46 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_fun___Orderings_Otop,axiom,
% 0.31/0.46 ! [A8: $tType,A9: $tType] :
% 0.31/0.46 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.31/0.46 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_fun___Groups_Ominus,axiom,
% 0.31/0.46 ! [A8: $tType,A9: $tType] :
% 0.31/0.46 ( ( minus @ A9 @ ( type2 @ A9 ) )
% 0.31/0.46 => ( minus @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_3,axiom,
% 0.31/0.46 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_4,axiom,
% 0.31/0.46 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Set_Oset___Lattices_Olattice_5,axiom,
% 0.31/0.46 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Set_Oset___Orderings_Otop_6,axiom,
% 0.31/0.46 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Set_Oset___Groups_Ominus_7,axiom,
% 0.31/0.46 ! [A8: $tType] : ( minus @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_8,axiom,
% 0.31/0.46 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_9,axiom,
% 0.31/0.46 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Lattices_Olattice_10,axiom,
% 0.31/0.46 lattice @ $o @ ( type2 @ $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Orderings_Otop_11,axiom,
% 0.31/0.46 top @ $o @ ( type2 @ $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Groups_Ominus_12,axiom,
% 0.31/0.46 minus @ $o @ ( type2 @ $o ) ).
% 0.31/0.46
% 0.31/0.46 %----Conjectures (1)
% 0.31/0.46 thf(conj_0,conjecture,
% 0.31/0.46 p @ ( lList2281150353e_lrev @ a @ la ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 2.75/1.59 ---- Embedded in THF ---
% 2.75/1.59 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.75/1.59 %%% Generated on Tue Feb 24 06:10:52 EST 2026
% 2.75/1.59 %%% using '$$dhol' embedding, version 1.3.0.
% 2.75/1.59 %%% Logic specification used:
% 2.75/1.59 %%% thf(spec, logic, $$dhol).
% 2.75/1.59
% 2.75/1.59 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OwTl828x0i/DTF2DTF25099.p
% 2.75/1.59 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.75/1.59 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.75/1.59 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.75/1.59 thf(ty_tf_a, type, a: $tType).
% 2.75/1.59 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.59 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.59 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.59 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.59 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.59 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.59 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Ogen__lset, type, coinductive_gen_lset: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ A)))))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Oldistinct, type, coindu351974385stinct: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Olfilter, type, coinductive_lfilter: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Ollexord, type, coinductive_llexord: (!> [A:$tType]: (((A > (A > $o)) > ((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)))))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Ollist_Olnull, type, coinductive_lnull: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Ollist_Olset, type, coinductive_lset: (!> [A:$tType]: (((coinductive_llist @ A) > (set @ A))))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Olmember, type, coinductive_lmember: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > $o))))).
% 2.75/1.59 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.75/1.59 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.75/1.59 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts, type, lList2435255213lllsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp, type, lList21511617539llstsp: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > $o))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts, type, lList2236698231inlsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec, type, lList21916056377ts_rec: (!> [B:$tType,A:$tType]: ((B > ((A > ((coinductive_llist @ A) > (B > B))) > ((coinductive_llist @ A) > B)))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp, type, lList2860480441nlstsp: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > $o))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts, type, lList22096119349pslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts, type, lList21612149805nflsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast, type, lList2370560421utlast: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast, type, lList2170638824_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev, type, lList2281150353e_lrev: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.75/1.59 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts, type, lList21148268032oslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.75/1.59 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.75/1.59 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.75/1.59 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.75/1.59 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.75/1.59 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.75/1.59 thf(sy_v_A, type, a2: (set @ a)).
% 2.75/1.59 thf(sy_v_P, type, p: ((coinductive_llist @ a) > $o)).
% 2.75/1.59 thf(sy_v_l____, type, l: (coinductive_llist @ a)).
% 2.75/1.59 thf(sy_v_la______, type, la: (coinductive_llist @ a)).
% 2.75/1.59 thf(sy_v_xs, type, xs: (coinductive_llist @ a)).
% 2.75/1.59 thf(fact_0_init, axiom, (p @ (coinductive_LNil @ a))).
% 2.75/1.59 thf(fact_1_LNil__fin_Ohyps, axiom, (la = (coinductive_LNil @ a))).
% 2.75/1.59 thf(fact_2_l__def, axiom, (l = ((lList2281150353e_lrev @ a) @ xs))).
% 2.75/1.59 thf(fact_3_lrev__LNil, axiom, (! [A:$tType]: ((((lList2281150353e_lrev @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_4_lrevT, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ ((lList2281150353e_lrev @ A) @ Xs)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.75/1.59 thf(fact_5_local_Ostep, axiom, (! [Xs:(coinductive_llist @ a),X:a]: (((((member @ (coinductive_llist @ a)) @ Xs) @ ((lList2236698231inlsts @ a) @ a2)) => ((p @ Xs) => ((((member @ a) @ X) @ a2) => (p @ (((coinductive_lappend @ a) @ Xs) @ (((coinductive_LCons @ a) @ X) @ (coinductive_LNil @ a)))))))))).
% 2.75/1.59 thf(fact_6_lrev__lrev__ident, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ ((lList2281150353e_lrev @ A) @ Xs)) = Xs))))).
% 2.75/1.59 thf(fact_7_lrev__is__lrev__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Ys) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = ((lList2281150353e_lrev @ A) @ Ys)) = (Xs = Ys))))))).
% 2.75/1.59 thf(fact_8_LNil__is__lrev__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((coinductive_LNil @ A) = ((lList2281150353e_lrev @ A) @ Xs)) = (Xs = (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_9_lrev__is__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_10_lbutlast__LNil, axiom, (! [A:$tType]: ((((lList2370560421utlast @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_11_lrev__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Ys) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ Ys)) @ ((lList2281150353e_lrev @ A) @ Xs)))))))).
% 2.75/1.59 thf(fact_12_fin, axiom, (((member @ (coinductive_llist @ a)) @ xs) @ ((lList2236698231inlsts @ a) @ a2))).
% 2.75/1.59 thf(fact_13__092_060open_062l_A_092_060in_062_AA_092_060_094sup_062_092_060star_062_092_060close_062, axiom, (((member @ (coinductive_llist @ a)) @ l) @ ((lList2236698231inlsts @ a) @ a2))).
% 2.75/1.59 thf(fact_14_LNil__is__lappend__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ S) @ T)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_15_lappend__is__LNil__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ S) @ T) = (coinductive_LNil @ A)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_16_same__lappend__eq, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((((coinductive_lappend @ A) @ R) @ S) = (((coinductive_lappend @ A) @ R) @ T)) = (S = T)))))).
% 2.75/1.59 thf(fact_17_lapp__fin__fin__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_18_lbutlast__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((R = (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A3) @ R)) = (coinductive_LNil @ A))) & ((R != (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A3) @ R)) = (((coinductive_LCons @ A) @ A3) @ ((lList2370560421utlast @ A) @ R))))))))).
% 2.75/1.59 thf(fact_19_lrev__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2281150353e_lrev @ A) @ (((coinductive_LCons @ A) @ A3) @ R)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ R)) @ (((coinductive_LCons @ A) @ A3) @ (coinductive_LNil @ A)))))))).
% 2.75/1.59 thf(fact_20_llistE, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X21:A,X22:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X21) @ X22)))))))))).
% 2.75/1.59 thf(fact_21_finT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.75/1.59 thf(fact_22_fin__finite, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.75/1.59 thf(fact_23_lappfin__finT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_24_finlsts_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2236698231inlsts @ A) @ A2)) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [L:(coinductive_llist @ A),A4:A]: (((A3 = (((coinductive_LCons @ A) @ A4) @ L)) => ((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => (~ ((((member @ A) @ A4) @ A2)))))))))))))).
% 2.75/1.59 thf(fact_25_finlsts_Osimps, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2236698231inlsts @ A) @ A2)) = ((A3 = (coinductive_LNil @ A)) | (? [L2:(coinductive_llist @ A),A5:A]: (((A3 = (((coinductive_LCons @ A) @ A5) @ L2)) & ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ A) @ A5) @ A2)))))))))).
% 2.75/1.59 thf(fact_26_finlsts__induct, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((! [L:(coinductive_llist @ A)]: (((L = (coinductive_LNil @ A)) => (P @ L)))) => ((! [A4:A,L:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L) => ((((member @ A) @ A4) @ A2) => (P @ (((coinductive_LCons @ A) @ A4) @ L))))))) => (P @ X))))))).
% 2.75/1.59 thf(fact_27_finlsts_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [L:(coinductive_llist @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L) => ((((member @ A) @ A4) @ A2) => (P @ (((coinductive_LCons @ A) @ A4) @ L))))))) => (P @ X))))))).
% 2.75/1.59 thf(fact_28_finlsts_OLNil__fin, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2236698231inlsts @ A) @ A2))))).
% 2.75/1.59 thf(fact_29_finlsts_OLCons__fin, axiom, (! [A:$tType,L3:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A3) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ L3)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_30_lapp__fin__fin__lemma, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.75/1.59 thf(fact_31_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.75/1.59 thf(fact_32_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 2.75/1.59 thf(fact_33_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_34_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_35_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_LCons @ A) @ Xa) @ X)) @ Ys) = (((coinductive_LCons @ A) @ Xa) @ (((coinductive_lappend @ A) @ X) @ Ys)))))).
% 2.75/1.59 thf(fact_36_LList2__Mirabelle__hamjzmohle_Ollast__LCons, axiom, (! [B:$tType,R:(coinductive_llist @ B),A2:(set @ B),A3:B]: (((((member @ (coinductive_llist @ B)) @ R) @ ((lList2236698231inlsts @ B) @ A2)) => (((R = (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A3) @ R)) = A3)) & ((R != (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A3) @ R)) = ((lList2170638824_llast @ B) @ R)))))))).
% 2.75/1.59 thf(fact_37_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 2.75/1.59 thf(fact_38_llist_Oinject, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X212) @ X222) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X212 = Y21) & (X222 = Y22)))))).
% 2.75/1.59 thf(fact_39_UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.75/1.59 thf(fact_40_iso__tuple__UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.75/1.59 thf(fact_41_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X2:D]: ((top_top @ C)))))))).
% 2.75/1.59 thf(fact_42_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.75/1.59 thf(fact_43_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 2.75/1.59 thf(fact_44_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.75/1.59 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.75/1.59 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 2.75/1.59 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.75/1.59 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.75/1.59 thf(fact_49_lappend__assoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ Zs) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_lappend @ A) @ Ys) @ Zs)))))).
% 2.75/1.59 thf(fact_50_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X2:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs2)))))))).
% 2.75/1.59 thf(fact_51_llist_Odistinct_I1_J, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X212) @ X222))))).
% 2.75/1.59 thf(fact_52_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_53_fpslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList22096119349pslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) & (S != (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_54_poslsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ (top_top @ (set @ A)))) = (S != (coinductive_LNil @ A)))))).
% 2.75/1.59 thf(fact_55_fpslsts__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList22096119349pslsts @ A) @ A2)) => (~ ((! [A4:A,Rs:(coinductive_llist @ A)]: (((R = (((coinductive_LCons @ A) @ A4) @ Rs)) => ((((member @ A) @ A4) @ A2) => (~ ((((member @ (coinductive_llist @ A)) @ Rs) @ ((lList2236698231inlsts @ A) @ A2)))))))))))))).
% 2.75/1.59 thf(fact_56_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Xs2)) & (((coindu328551480prefix @ A) @ Xs2) @ Ys))))))))).
% 2.75/1.59 thf(fact_57_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y) @ Ys))))).
% 2.75/1.59 thf(fact_58_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (coinductive_LNil @ B))))))).
% 2.75/1.59 thf(fact_59_finlsts__rec__LCons__def, axiom, (! [B:$tType,A:$tType,F:((coinductive_llist @ A) > B),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B))),R:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((F @ (((coinductive_LCons @ A) @ A3) @ R)) = (((D2 @ A3) @ R) @ (F @ R)))))))).
% 2.75/1.59 thf(fact_60_finlsts__rec__LCons, axiom, (! [B:$tType,A:$tType,R:(coinductive_llist @ A),A2:(set @ A),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B))),A3:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2) @ (((coinductive_LCons @ A) @ A3) @ R)) = (((D2 @ A3) @ R) @ (((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2) @ R))))))).
% 2.75/1.59 thf(fact_61_top1I, axiom, (! [A:$tType,X:A]: (((top_top @ (A > $o)) @ X)))).
% 2.75/1.59 thf(fact_62_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B),Y:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (((coinductive_LCons @ B) @ Y) @ Ys)) = ((X = Y) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 2.75/1.59 thf(fact_63_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_64_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs3:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs3) => (P @ Ys2)))) => (P @ Xs3)))) => (P @ Xs))))).
% 2.75/1.59 thf(fact_65_finlsts__rec__LNil, axiom, (! [B:$tType,A:$tType,C2:A,D2:(B > ((coinductive_llist @ B) > (A > A)))]: (((((((lList21916056377ts_rec @ A) @ B) @ C2) @ D2) @ (coinductive_LNil @ B)) = C2)))).
% 2.75/1.59 thf(fact_66_finlsts__rec__LNil__def, axiom, (! [A:$tType,B:$tType,F:((coinductive_llist @ A) > B),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B)))]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2)) => ((F @ (coinductive_LNil @ A)) = C2))))).
% 2.75/1.59 thf(fact_67_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.75/1.59 thf(fact_68_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 2.75/1.59 thf(fact_69_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A))))))))).
% 2.75/1.59 thf(fact_70_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X:A]: (((P & ((top_top @ (A > $o)) @ X)) = P)))).
% 2.75/1.59 thf(fact_71_top__conj_I1_J, axiom, (! [A:$tType,X:A,P:$o]: (((((top_top @ (A > $o)) @ X) & P) = P)))).
% 2.75/1.59 thf(fact_72_poslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2)) & (S != (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_73_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) = X)))).
% 2.75/1.59 thf(fact_74_notfin__inf, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.75/1.59 thf(fact_75_notinf__fin, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.75/1.59 thf(fact_76_alllsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ (top_top @ (set @ A))))))).
% 2.75/1.59 thf(fact_77_LConsE, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ ((lList2435255213lllsts @ A) @ A2)) = ((((member @ A) @ X) @ A2) & (((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_78_lapp__inf, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => ((((coinductive_lappend @ A) @ S) @ T) = S))))).
% 2.75/1.59 thf(fact_79_llast__LCons2, axiom, (! [A:$tType,X:A,Y:A,Xs:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Xs)))))).
% 2.75/1.59 thf(fact_80_inflstsI, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_81_alllstsE, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_82_infsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.75/1.59 thf(fact_83_inflstsE, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => (~ (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))))))).
% 2.75/1.59 thf(fact_84_lapp__allT__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A2)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_85_infT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.75/1.59 thf(fact_86_alllsts_OLCons__all, axiom, (! [A:$tType,L3:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ A) @ A3) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ L3)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_87_alllsts_OLNil__all, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2435255213lllsts @ A) @ A2))))).
% 2.75/1.59 thf(fact_88_inflsts__cases, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => (~ ((! [A4:A,L:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ A) @ A4) @ A2) => (S != (((coinductive_LCons @ A) @ A4) @ L)))))))))))).
% 2.75/1.59 thf(fact_89_inflstsI2, axiom, (! [A:$tType,A3:A,A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ A) @ A3) @ A2) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_90_lapp__all__invT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.75/1.59 thf(fact_91_lappT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_92_finsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.75/1.59 thf(fact_93_finite__lemma, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),B2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ B2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ B2))))))).
% 2.75/1.59 thf(fact_94_alllsts_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A),A2:(set @ A)]: (((X4 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X4 @ X3) => ((X3 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A6:A]: (((X3 = (((coinductive_LCons @ A) @ A6) @ L4)) & (((X4 @ L4) | (((member @ (coinductive_llist @ A)) @ L4) @ ((lList2435255213lllsts @ A) @ A2))) & (((member @ A) @ A6) @ A2))))))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_95_alllsts_Osimps, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2435255213lllsts @ A) @ A2)) = ((A3 = (coinductive_LNil @ A)) | (? [L2:(coinductive_llist @ A),A5:A]: (((A3 = (((coinductive_LCons @ A) @ A5) @ L2)) & ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ A) @ A5) @ A2)))))))))).
% 2.75/1.59 thf(fact_96_alllsts_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2435255213lllsts @ A) @ A2)) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [L:(coinductive_llist @ A),A4:A]: (((A3 = (((coinductive_LCons @ A) @ A4) @ L)) => ((((member @ (coinductive_llist @ A)) @ L) @ ((lList2435255213lllsts @ A) @ A2)) => (~ ((((member @ A) @ A4) @ A2)))))))))))))).
% 2.75/1.59 thf(fact_97_fin__inf__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.75/1.59 thf(fact_98_lapp__fin__infT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_99_lapp__inv2T, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A2)) => (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_100_lapp__infT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A2)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_101_app__invT, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.75/1.59 thf(fact_102_inflsts__def, axiom, (! [A:$tType]: (((lList21612149805nflsts @ A) = (^ [A7:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A7)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))))).
% 2.75/1.59 thf(fact_103_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Ys))))))).
% 2.75/1.59 thf(fact_104_fin__Un__inf, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A2)) @ ((lList21612149805nflsts @ A) @ A2)) = ((lList2435255213lllsts @ A) @ A2))))).
% 2.75/1.59 thf(fact_105_alllstsp_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A),A2:(A > $o)]: (((X4 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X4 @ X3) => ((X3 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A6:A]: (((X3 = (((coinductive_LCons @ A) @ A6) @ L4)) & (((X4 @ L4) | (((lList21511617539llstsp @ A) @ A2) @ L4)) & (A2 @ A6))))))))) => (((lList21511617539llstsp @ A) @ A2) @ X)))))).
% 2.75/1.59 thf(fact_106_finlstsp_Oinducts, axiom, (! [A:$tType,A2:(A > $o),X:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((lList2860480441nlstsp @ A) @ A2) @ X) => ((P @ (coinductive_LNil @ A)) => ((! [L:(coinductive_llist @ A),A4:A]: (((((lList2860480441nlstsp @ A) @ A2) @ L) => ((P @ L) => ((A2 @ A4) => (P @ (((coinductive_LCons @ A) @ A4) @ L))))))) => (P @ X))))))).
% 2.75/1.59 thf(fact_107_finlstsp_Osimps, axiom, (! [A:$tType]: (((lList2860480441nlstsp @ A) = (^ [A7:(A > $o),A5:(coinductive_llist @ A)]: (((A5 = (coinductive_LNil @ A)) | (? [L2:(coinductive_llist @ A),B3:A]: (((A5 = (((coinductive_LCons @ A) @ B3) @ L2)) & ((((lList2860480441nlstsp @ A) @ A7) @ L2) & (A7 @ B3)))))))))))).
% 2.75/1.59 thf(fact_108_Un__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C2) @ A2) | (((member @ A) @ C2) @ B2)))))).
% 2.75/1.59 thf(fact_109_UnCI, axiom, (! [A:$tType,C2:A,B2:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ A2)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.75/1.59 thf(fact_110_Diff__idemp, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ B2) = (((minus_minus @ (set @ A)) @ A2) @ B2))))).
% 2.75/1.59 thf(fact_111_Diff__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C2) @ A2) & (~ ((((member @ A) @ C2) @ B2)))))))).
% 2.75/1.59 thf(fact_112_DiffI, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A2) => ((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2))))))).
% 2.75/1.59 thf(fact_113_Un__Diff__cancel2, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) @ A2) = (((sup_sup @ (set @ A)) @ B2) @ A2))))).
% 2.75/1.59 thf(fact_114_Un__Diff__cancel, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.75/1.59 thf(fact_115_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((((coinductive_lfinite @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) = ((coinductive_lfinite @ B) @ Xs))))).
% 2.75/1.59 thf(fact_116_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 2.75/1.59 thf(fact_117_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_118_lfinite__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & ((coinductive_lfinite @ A) @ Ys)))))).
% 2.75/1.59 thf(fact_119_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C3)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A2) @ C3)))))).
% 2.75/1.59 thf(fact_120_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.75/1.59 thf(fact_121_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A7:(set @ A),B4:(set @ A)]: ((((sup_sup @ (set @ A)) @ B4) @ A7))))))).
% 2.75/1.59 thf(fact_122_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 2.75/1.59 thf(fact_123_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C3) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C3)))))).
% 2.75/1.59 thf(fact_124_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A2) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B2) => (P @ X2))))))))).
% 2.75/1.59 thf(fact_125_Un__Diff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C3) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ C3)) @ (((minus_minus @ (set @ A)) @ B2) @ C3)))))).
% 2.75/1.59 thf(fact_126_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B2) & (P @ X2))))))))).
% 2.75/1.59 thf(fact_127_DiffD2, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ ((((member @ A) @ C2) @ B2))))))).
% 2.75/1.59 thf(fact_128_DiffD1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C2) @ A2))))).
% 2.75/1.59 thf(fact_129_DiffE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B2)))))))).
% 2.75/1.59 thf(fact_130_UnI2, axiom, (! [A:$tType,C2:A,B2:(set @ A),A2:(set @ A)]: (((((member @ A) @ C2) @ B2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.75/1.59 thf(fact_131_UnI1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.75/1.59 thf(fact_132_UnE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => ((~ ((((member @ A) @ C2) @ A2))) => (((member @ A) @ C2) @ B2)))))).
% 2.75/1.59 thf(fact_133_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 2.75/1.59 thf(fact_134_lfinite__LNil, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_135_lappend__inf, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.75/1.59 thf(fact_136_Un__UNIV__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (top_top @ (set @ A))) @ B2) = (top_top @ (set @ A)))))).
% 2.75/1.59 thf(fact_137_Un__UNIV__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.75/1.59 thf(fact_138_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ Ys) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.75/1.59 thf(fact_139_alllstsp_OLCons__all, axiom, (! [A:$tType,A2:(A > $o),L3:(coinductive_llist @ A),A3:A]: (((((lList21511617539llstsp @ A) @ A2) @ L3) => ((A2 @ A3) => (((lList21511617539llstsp @ A) @ A2) @ (((coinductive_LCons @ A) @ A3) @ L3))))))).
% 2.75/1.59 thf(fact_140_finlstsp_OLCons__fin, axiom, (! [A:$tType,A2:(A > $o),L3:(coinductive_llist @ A),A3:A]: (((((lList2860480441nlstsp @ A) @ A2) @ L3) => ((A2 @ A3) => (((lList2860480441nlstsp @ A) @ A2) @ (((coinductive_LCons @ A) @ A3) @ L3))))))).
% 2.75/1.59 thf(fact_141_alllstsp_OLNil__all, axiom, (! [A:$tType,A2:(A > $o)]: ((((lList21511617539llstsp @ A) @ A2) @ (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_142_finlstsp_OLNil__fin, axiom, (! [A:$tType,A2:(A > $o)]: ((((lList2860480441nlstsp @ A) @ A2) @ (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_143_lfinite_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ A3) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [Xs3:(coinductive_llist @ A)]: (((? [X3:A]: ((A3 = (((coinductive_LCons @ A) @ X3) @ Xs3)))) => (~ (((coinductive_lfinite @ A) @ Xs3))))))))))))).
% 2.75/1.59 thf(fact_144_lfinite_Osimps, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) = (^ [A5:(coinductive_llist @ A)]: (((A5 = (coinductive_LNil @ A)) | (? [Xs4:(coinductive_llist @ A),X2:A]: (((A5 = (((coinductive_LCons @ A) @ X2) @ Xs4)) & ((coinductive_lfinite @ A) @ Xs4))))))))))).
% 2.75/1.59 thf(fact_145_lfinite_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ X) => ((P @ (coinductive_LNil @ A)) => ((! [Xs3:(coinductive_llist @ A),X3:A]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_LCons @ A) @ X3) @ Xs3)))))) => (P @ X))))))).
% 2.75/1.59 thf(fact_146_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ Xs) => ((P @ (coinductive_LNil @ A)) => ((! [X3:A,Xs3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A)))))))) => (P @ Xs))))))).
% 2.75/1.59 thf(fact_147_llimit__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((P @ (coinductive_LNil @ A)) => ((! [X3:A,Xs3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_LCons @ A) @ X3) @ Xs3)))))) => (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs) => (P @ Ys2)))) => (P @ Xs)) => (P @ Xs))))))).
% 2.75/1.59 thf(fact_148_alllstsp_Ocases, axiom, (! [A:$tType,A2:(A > $o),A3:(coinductive_llist @ A)]: (((((lList21511617539llstsp @ A) @ A2) @ A3) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [L:(coinductive_llist @ A),A4:A]: (((A3 = (((coinductive_LCons @ A) @ A4) @ L)) => ((((lList21511617539llstsp @ A) @ A2) @ L) => (~ ((A2 @ A4)))))))))))))).
% 2.75/1.59 thf(fact_149_alllstsp_Osimps, axiom, (! [A:$tType]: (((lList21511617539llstsp @ A) = (^ [A7:(A > $o),A5:(coinductive_llist @ A)]: (((A5 = (coinductive_LNil @ A)) | (? [L2:(coinductive_llist @ A),B3:A]: (((A5 = (((coinductive_LCons @ A) @ B3) @ L2)) & ((((lList21511617539llstsp @ A) @ A7) @ L2) & (A7 @ B3)))))))))))).
% 2.75/1.59 thf(fact_150_finlstsp_Ocases, axiom, (! [A:$tType,A2:(A > $o),A3:(coinductive_llist @ A)]: (((((lList2860480441nlstsp @ A) @ A2) @ A3) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [L:(coinductive_llist @ A),A4:A]: (((A3 = (((coinductive_LCons @ A) @ A4) @ L)) => ((((lList2860480441nlstsp @ A) @ A2) @ L) => (~ ((A2 @ A4)))))))))))))).
% 2.75/1.59 thf(fact_151_sup__top__left, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (top_top @ A)) @ X) = (top_top @ A)))))))).
% 2.75/1.59 thf(fact_152_sup__top__right, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (top_top @ A)) = (top_top @ A)))))))).
% 2.75/1.59 thf(fact_153_sup__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.75/1.59 thf(fact_154_sup_Oidem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ A3) = A3))))))).
% 2.75/1.59 thf(fact_155_sup__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 2.75/1.59 thf(fact_156_minus__apply, axiom, (! [B:$tType,A:$tType]: ((((minus @ B) @ (type2 @ B)) => ((minus_minus @ (A > B)) = (^ [A7:(A > B),B4:(A > B),X2:A]: ((((minus_minus @ B) @ (A7 @ X2)) @ (B4 @ X2))))))))).
% 2.75/1.59 thf(fact_157_sup_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A3:A,B5:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A3) @ B5)) @ B5) = (((sup_sup @ A) @ A3) @ B5)))))))).
% 2.75/1.59 thf(fact_158_sup__left__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.75/1.59 thf(fact_159_sup_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A3:A,B5:A]: (((((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ A3) @ B5)) = (((sup_sup @ A) @ A3) @ B5)))))))).
% 2.75/1.59 thf(fact_160_fun__diff__def, axiom, (! [B:$tType,A:$tType]: ((((minus @ B) @ (type2 @ B)) => ((minus_minus @ (A > B)) = (^ [A7:(A > B),B4:(A > B),X2:A]: ((((minus_minus @ B) @ (A7 @ X2)) @ (B4 @ X2))))))))).
% 2.75/1.59 thf(fact_161_sup__left__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 2.75/1.59 thf(fact_162_sup_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B5:A,A3:A,C2:A]: (((((sup_sup @ A) @ B5) @ (((sup_sup @ A) @ A3) @ C2)) = (((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ B5) @ C2))))))))).
% 2.75/1.59 thf(fact_163_sup__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X2)))))))).
% 2.75/1.59 thf(fact_164_sup_Ocommute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [A5:A,B3:A]: ((((sup_sup @ A) @ B3) @ A5)))))))).
% 2.75/1.59 thf(fact_165_sup__assoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 2.75/1.59 thf(fact_166_sup_Oassoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A3:A,B5:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A3) @ B5)) @ C2) = (((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ B5) @ C2))))))))).
% 2.75/1.59 thf(fact_167_sup__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.75/1.59 thf(fact_168_inf__sup__aci_I5_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X2)))))))).
% 2.75/1.59 thf(fact_169_inf__sup__aci_I6_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 2.75/1.59 thf(fact_170_inf__sup__aci_I7_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 2.75/1.59 thf(fact_171_inf__sup__aci_I8_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.75/1.59 thf(fact_172_lset__lappend__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((sup_sup @ (set @ A)) @ ((coinductive_lset @ A) @ Xs)) @ ((coinductive_lset @ A) @ Ys))))))).
% 2.75/1.59 thf(fact_173_lstrict__prefix__lappend__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.75/1.59 thf(fact_174_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coinductive_lmember @ A) @ X) @ (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_175_lnull__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lnull @ A) @ Xs) & ((coinductive_lnull @ A) @ Ys)))))).
% 2.75/1.59 thf(fact_176_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))) = ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.75/1.59 thf(fact_177_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (~ (((coinductive_lnull @ A) @ Ys)))) => ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.75/1.59 thf(fact_178_lzip_Oexhaust, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((~ ((((coinductive_lnull @ A) @ Xs) | ((coinductive_lnull @ B) @ Ys)))) => (~ (((~ (((coinductive_lnull @ A) @ Xs))) => ((coinductive_lnull @ B) @ Ys)))))))).
% 2.75/1.59 thf(fact_179_lset__lmember, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) = (((coinductive_lmember @ A) @ X) @ Xs))))).
% 2.75/1.59 thf(fact_180_lappend__lnull2, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.75/1.59 thf(fact_181_lappend__lnull1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Ys))))).
% 2.75/1.59 thf(fact_182_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))))).
% 2.75/1.59 thf(fact_183_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))) => (~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))))))).
% 2.75/1.59 thf(fact_184_lnull__def, axiom, (! [A:$tType]: (((coinductive_lnull @ A) = (^ [Llist:(coinductive_llist @ A)]: ((Llist = (coinductive_LNil @ A)))))))).
% 2.75/1.59 thf(fact_185_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist2:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Llist2) => (Llist2 = (coinductive_LNil @ A)))))).
% 2.75/1.59 thf(fact_186_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist2:(coinductive_llist @ A)]: (((Llist2 = (coinductive_LNil @ A)) => ((coinductive_lnull @ A) @ Llist2))))).
% 2.75/1.59 thf(fact_187_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coinductive_lnull @ A) @ (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_188_not__lnull__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ Xs))) = (? [X2:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs2)))))))).
% 2.75/1.59 thf(fact_189_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist2:(coinductive_llist @ A),X212:A,X222:(coinductive_llist @ A)]: (((Llist2 = (((coinductive_LCons @ A) @ X212) @ X222)) => (~ (((coinductive_lnull @ A) @ Llist2))))))).
% 2.75/1.59 thf(fact_190_llist_Odisc_I2_J, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A)]: ((~ (((coinductive_lnull @ A) @ (((coinductive_LCons @ A) @ X212) @ X222))))))).
% 2.75/1.59 thf(fact_191_llist_Oset__induct, axiom, (! [A:$tType,X:A,A3:(coinductive_llist @ A),P:(A > ((coinductive_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ A3)) => ((! [Z1:A,Z2:(coinductive_llist @ A)]: (((P @ Z1) @ (((coinductive_LCons @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(coinductive_llist @ A),Xa2:A]: (((((member @ A) @ Xa2) @ ((coinductive_lset @ A) @ Z2)) => (((P @ Xa2) @ Z2) => ((P @ Xa2) @ (((coinductive_LCons @ A) @ Z1) @ Z2)))))) => ((P @ X) @ A3))))))).
% 2.75/1.59 thf(fact_192_llist_Oset__cases, axiom, (! [A:$tType,E:A,A3:(coinductive_llist @ A)]: (((((member @ A) @ E) @ ((coinductive_lset @ A) @ A3)) => ((! [Z2:(coinductive_llist @ A)]: ((A3 != (((coinductive_LCons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(coinductive_llist @ A)]: (((A3 = (((coinductive_LCons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((coinductive_lset @ A) @ Z2)))))))))))))).
% 2.75/1.59 thf(fact_193_lset__induct_H, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs3:(coinductive_llist @ A)]: ((P @ (((coinductive_LCons @ A) @ X) @ Xs3)))) => ((! [X5:A,Xs3:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => ((P @ Xs3) => (P @ (((coinductive_LCons @ A) @ X5) @ Xs3)))))) => (P @ Xs))))))).
% 2.75/1.59 thf(fact_194_lset__induct, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs3:(coinductive_llist @ A)]: ((P @ (((coinductive_LCons @ A) @ X) @ Xs3)))) => ((! [X5:A,Xs3:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => ((X != X5) => ((P @ Xs3) => (P @ (((coinductive_LCons @ A) @ X5) @ Xs3))))))) => (P @ Xs))))))).
% 2.75/1.59 thf(fact_195_lset__cases, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs5:(coinductive_llist @ A)]: ((Xs != (((coinductive_LCons @ A) @ X) @ Xs5)))) => (~ ((! [X5:A,Xs5:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ X5) @ Xs5)) => (~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs5)))))))))))))).
% 2.75/1.59 thf(fact_196_llist_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(coinductive_llist @ A)]: ((((member @ A) @ A1) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ A1) @ A22)))))).
% 2.75/1.59 thf(fact_197_llist_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(coinductive_llist @ A),A1:A]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ A22)) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ A1) @ A22))))))).
% 2.75/1.59 thf(fact_198_lset__intros_I1_J, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 2.75/1.59 thf(fact_199_lset__intros_I2_J, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),X6:A]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ X6) @ Xs))))))).
% 2.75/1.59 thf(fact_200_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.75/1.59 thf(fact_201_in__lset__lappend__iff, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))) = ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) | (((coinductive_lfinite @ A) @ Xs) & (((member @ A) @ X) @ ((coinductive_lset @ A) @ Ys)))))))).
% 2.75/1.59 thf(fact_202_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(fact_203_Coinductive__List_Ollast__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = X)) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_llast @ A) @ Xs))))))).
% 2.75/1.59 thf(fact_204_lset__lappend__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lfinite @ A) @ Xs) => (((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((sup_sup @ (set @ A)) @ ((coinductive_lset @ A) @ Xs)) @ ((coinductive_lset @ A) @ Ys)))) & ((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_lset @ A) @ Xs))))))).
% 2.75/1.59 thf(fact_205_split__llist, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (? [Ys3:(coinductive_llist @ A),Zs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_lappend @ A) @ Ys3) @ (((coinductive_LCons @ A) @ X) @ Zs2))) & ((coinductive_lfinite @ A) @ Ys3)))))))).
% 2.75/1.59 thf(fact_206_split__llist__first, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (? [Ys3:(coinductive_llist @ A),Zs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_lappend @ A) @ Ys3) @ (((coinductive_LCons @ A) @ X) @ Zs2))) & (((coinductive_lfinite @ A) @ Ys3) & (~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Ys3)))))))))))).
% 2.75/1.59 thf(fact_207_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lmember @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coinductive_lmember @ A) @ X) @ Ys)))))).
% 2.75/1.59 thf(fact_208_gen__lset__def, axiom, (! [A:$tType]: (((coinductive_gen_lset @ A) = (^ [A7:(set @ A),Xs4:(coinductive_llist @ A)]: ((((sup_sup @ (set @ A)) @ A7) @ ((coinductive_lset @ A) @ Xs4)))))))).
% 2.75/1.59 thf(fact_209_llast__lappend, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Ys) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Xs))) & ((~ (((coinductive_lnull @ A) @ Ys))) => ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Ys))) & ((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (undefined @ A))))))))).
% 2.75/1.59 thf(fact_210_lfilter__eq__LConsD, axiom, (! [A:$tType,P:(A > $o),Ys:(coinductive_llist @ A),X:A,Xs:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Ys) = (((coinductive_LCons @ A) @ X) @ Xs)) => (? [Us:(coinductive_llist @ A),Vs:(coinductive_llist @ A)]: (((Ys = (((coinductive_lappend @ A) @ Us) @ (((coinductive_LCons @ A) @ X) @ Vs))) & (((coinductive_lfinite @ A) @ Us) & ((! [X7:A]: (((((member @ A) @ X7) @ ((coinductive_lset @ A) @ Us)) => (~ ((P @ X7)))))) & ((P @ X) & (Xs = (((coinductive_lfilter @ A) @ P) @ Vs)))))))))))).
% 2.75/1.59 thf(fact_211_lfilter__idem, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ P) @ (((coinductive_lfilter @ A) @ P) @ Xs)) = (((coinductive_lfilter @ A) @ P) @ Xs))))).
% 2.75/1.59 thf(fact_212_lfilter__LCons, axiom, (! [A:$tType,P:(A > $o),X:A,Xs:(coinductive_llist @ A)]: ((((P @ X) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((coinductive_LCons @ A) @ X) @ (((coinductive_lfilter @ A) @ P) @ Xs)))) & ((~ ((P @ X))) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((coinductive_lfilter @ A) @ P) @ Xs))))))).
% 2.75/1.59 thf(fact_213_lfilter__LNil, axiom, (! [A:$tType,P:(A > $o)]: (((((coinductive_lfilter @ A) @ P) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_214_diverge__lfilter__LNil, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => (~ ((P @ X3)))))) => ((((coinductive_lfilter @ A) @ P) @ Xs) = (coinductive_LNil @ A)))))).
% 2.75/1.59 thf(fact_215_lnull__lfilter, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)) = (! [X2:A]: (((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs)) => (~ ((P @ X2)))))))))).
% 2.75/1.59 thf(fact_216_lfilter__lappend__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lappend @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)) @ (((coinductive_lfilter @ A) @ P) @ Ys))))))).
% 2.75/1.59 thf(fact_217_LList2__Mirabelle__hamjzmohle_Ollast__LNil, axiom, (! [B:$tType]: ((((lList2170638824_llast @ B) @ (coinductive_LNil @ B)) = (undefined @ B))))).
% 2.75/1.59 thf(fact_218_lfilter__id__conv, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs) = Xs) = (! [X2:A]: (((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs)) => (P @ X2)))))))).
% 2.75/1.59 thf(fact_219_lfilter__cong, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),P:(A > $o),Q:(A > $o)]: (((Xs = Ys) => ((! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Ys)) => ((P @ X3) = (Q @ X3))))) => ((((coinductive_lfilter @ A) @ P) @ Xs) = (((coinductive_lfilter @ A) @ Q) @ Ys))))))).
% 2.75/1.59 thf(fact_220_lfinite__lfilterI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)))))).
% 2.75/1.59 thf(fact_221_lfilter__LCons__seek, axiom, (! [A:$tType,P2:(A > $o),X:A,L3:(coinductive_llist @ A)]: (((~ ((P2 @ X))) => ((((coinductive_lfilter @ A) @ P2) @ (((coinductive_LCons @ A) @ X) @ L3)) = (((coinductive_lfilter @ A) @ P2) @ L3)))))).
% 2.75/1.59 thf(fact_222_lfilter__LCons__found, axiom, (! [A:$tType,P:(A > $o),X:A,Xs:(coinductive_llist @ A)]: (((P @ X) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((coinductive_LCons @ A) @ X) @ (((coinductive_lfilter @ A) @ P) @ Xs))))))).
% 2.75/1.59 thf(fact_223_lfilter__empty__conv, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs) = (coinductive_LNil @ A)) = (! [X2:A]: (((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs)) => (~ ((P @ X2)))))))))).
% 2.75/1.59 thf(fact_224_lfilter__eq__lappend__lfiniteD, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs) = (((coinductive_lappend @ A) @ Ys) @ Zs)) => (((coinductive_lfinite @ A) @ Ys) => (? [Us:(coinductive_llist @ A),Vs:(coinductive_llist @ A)]: (((Xs = (((coinductive_lappend @ A) @ Us) @ Vs)) & (((coinductive_lfinite @ A) @ Us) & ((Ys = (((coinductive_lfilter @ A) @ P) @ Us)) & (Zs = (((coinductive_lfilter @ A) @ P) @ Vs)))))))))))).
% 2.75/1.59 thf(fact_225_Coinductive__List_Ollast__LNil, axiom, (! [A:$tType]: ((((coinductive_llast @ A) @ (coinductive_LNil @ A)) = (undefined @ A))))).
% 2.75/1.59 thf(fact_226_llast__linfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ Xs) = (undefined @ A)))))).
% 2.75/1.59 thf(fact_227_gen__lset__code_I1_J, axiom, (! [A:$tType,A2:(set @ A)]: (((((coinductive_gen_lset @ A) @ A2) @ (coinductive_LNil @ A)) = A2)))).
% 2.75/1.59 thf(fact_228_ldistinct_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A)]: ((((coindu351974385stinct @ A) @ A3) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [X3:A,Xs3:(coinductive_llist @ A)]: (((A3 = (((coinductive_LCons @ A) @ X3) @ Xs3)) => ((~ ((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs3)))) => (~ (((coindu351974385stinct @ A) @ Xs3)))))))))))))).
% 2.75/1.59 thf(fact_229_ldistinct_Osimps, axiom, (! [A:$tType]: (((coindu351974385stinct @ A) = (^ [A5:(coinductive_llist @ A)]: (((A5 = (coinductive_LNil @ A)) | (? [X2:A,Xs4:(coinductive_llist @ A)]: (((A5 = (((coinductive_LCons @ A) @ X2) @ Xs4)) & ((~ ((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs4)))) & ((coindu351974385stinct @ A) @ Xs4)))))))))))).
% 2.75/1.59 thf(fact_230_ldistinct__LNil__code, axiom, (! [A:$tType]: (((coindu351974385stinct @ A) @ (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_231_ldistinct__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((coindu351974385stinct @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)))) & ((coindu351974385stinct @ A) @ Xs)))))).
% 2.75/1.59 thf(fact_232_ldistinct__lfilterI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: ((((coindu351974385stinct @ A) @ Xs) => ((coindu351974385stinct @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)))))).
% 2.75/1.59 thf(fact_233_ldistinct_OLCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)))) => (((coindu351974385stinct @ A) @ Xs) => ((coindu351974385stinct @ A) @ (((coinductive_LCons @ A) @ X) @ Xs))))))).
% 2.75/1.59 thf(fact_234_ldistinct_OLNil, axiom, (! [A:$tType]: (((coindu351974385stinct @ A) @ (coinductive_LNil @ A))))).
% 2.75/1.59 thf(fact_235_ldistinct_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A)]: (((X4 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X4 @ X3) => ((X3 = (coinductive_LNil @ A)) | (? [Xa3:A,Xs6:(coinductive_llist @ A)]: (((X3 = (((coinductive_LCons @ A) @ Xa3) @ Xs6)) & ((~ ((((member @ A) @ Xa3) @ ((coinductive_lset @ A) @ Xs6)))) & ((X4 @ Xs6) | ((coindu351974385stinct @ A) @ Xs6)))))))))) => ((coindu351974385stinct @ A) @ X)))))).
% 2.75/1.59 thf(fact_236_llexord__lappend__leftD, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ (((coinductive_lappend @ A) @ Xs) @ Zs)) => (((coinductive_lfinite @ A) @ Xs) => ((! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => (~ (((R @ X3) @ X3)))))) => ((((coinductive_llexord @ A) @ R) @ Ys) @ Zs))))))).
% 2.75/1.59 thf(fact_237_llexord__lappend__left, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),R:(A > (A > $o)),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => ((! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => (~ (((R @ X3) @ X3)))))) => (((((coinductive_llexord @ A) @ R) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ (((coinductive_lappend @ A) @ Xs) @ Zs)) = ((((coinductive_llexord @ A) @ R) @ Ys) @ Zs))))))).
% 2.75/1.59 thf(fact_238_llexord__refl, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R) @ Xs) @ Xs)))).
% 2.75/1.59 thf(fact_239_llexord__LCons__LCons, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = (((X = Y) & ((((coinductive_llexord @ A) @ R) @ Xs) @ Ys)) | ((R @ X) @ Y)))))).
% 2.75/1.59 thf(fact_240_llexord__code_I1_J, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R) @ (coinductive_LNil @ A)) @ Ys)))).
% 2.75/1.59 thf(fact_241_llexord__LNil__right, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),R:(A > (A > $o)),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => (((((coinductive_llexord @ A) @ R) @ Xs) @ Ys) = ((coinductive_lnull @ A) @ Xs)))))).
% 2.75/1.59 thf(fact_242_lnull__llexord, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),R:(A > (A > $o)),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((((coinductive_llexord @ A) @ R) @ Xs) @ Ys))))).
% 2.75/1.59 thf(fact_243_llexord__trans, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ Xs) @ Ys) => (((((coinductive_llexord @ A) @ R) @ Ys) @ Zs) => ((! [A4:A,B6:A,C4:A]: ((((R @ A4) @ B6) => (((R @ B6) @ C4) => ((R @ A4) @ C4))))) => ((((coinductive_llexord @ A) @ R) @ Xs) @ Zs))))))).
% 2.75/1.59 thf(fact_244_llexord__linear, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((! [X3:A,Y3:A]: ((((R @ X3) @ Y3) | ((X3 = Y3) | ((R @ Y3) @ X3))))) => (((((coinductive_llexord @ A) @ R) @ Xs) @ Ys) | ((((coinductive_llexord @ A) @ R) @ Ys) @ Xs)))))).
% 2.75/1.59 thf(fact_245_llexord__antisym, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ Xs) @ Ys) => (((((coinductive_llexord @ A) @ R) @ Ys) @ Xs) => ((! [A4:A,B6:A]: ((((R @ A4) @ B6) => (~ (((R @ B6) @ A4)))))) => (Xs = Ys))))))).
% 2.75/1.59 thf(fact_246_llexord__append__right, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R) @ Xs) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))).
% 2.75/1.59 thf(fact_247_llexord__lappend__leftI, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ Ys) @ Zs) => ((((coinductive_llexord @ A) @ R) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ (((coinductive_lappend @ A) @ Xs) @ Zs)))))).
% 2.75/1.59 thf(fact_248_llexord__LNil, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R) @ (coinductive_LNil @ A)) @ Ys)))).
% 2.75/1.59 thf(fact_249_llexord__code_I3_J, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = (((R @ X) @ Y) | ((X = Y) & ((((coinductive_llexord @ A) @ R) @ Xs) @ Ys))))))).
% 2.75/1.59 thf(fact_250_llexord__LCons__left, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Y2:A,Ys4:(coinductive_llist @ A)]: (((Ys = (((coinductive_LCons @ A) @ Y2) @ Ys4)) & (((X = Y2) & ((((coinductive_llexord @ A) @ R) @ Xs) @ Ys4)) | ((R @ X) @ Y2))))))))).
% 2.75/1.59 thf(fact_251_llexord__LCons__eq, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),X:A]: ((((((coinductive_llexord @ A) @ R) @ Xs) @ Ys) => ((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ X) @ Ys)))))).
% 2.75/1.59 thf(fact_252_llexord__LCons__less, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Y:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((R @ X) @ Y) => ((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 2.75/1.59 thf(fact_253_llexord__code_I2_J, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A)]: ((~ (((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (coinductive_LNil @ A))))))).
% 2.75/1.59 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.75/1.59 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: (((bounded_lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.75/1.59 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.75/1.59 thf(tcon_fun___Lattices_Obounded__lattice__top, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.75/1.59 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: ((((semilattice_sup @ A9) @ (type2 @ A9)) => ((semilattice_sup @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.75/1.59 thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: ((((lattice @ A9) @ (type2 @ A9)) => ((lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.75/1.59 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.75/1.59 thf(tcon_fun___Groups_Ominus, axiom, (! [A8:$tType,A9:$tType]: ((((minus @ A9) @ (type2 @ A9)) => ((minus @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.75/1.59 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_3, axiom, (! [A8:$tType]: (((bounded_lattice_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.75/1.59 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_4, axiom, (! [A8:$tType]: (((semilattice_sup @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.75/1.59 thf(tcon_Set_Oset___Lattices_Olattice_5, axiom, (! [A8:$tType]: (((lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.75/1.59 thf(tcon_Set_Oset___Orderings_Otop_6, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.75/1.59 thf(tcon_Set_Oset___Groups_Ominus_7, axiom, (! [A8:$tType]: (((minus @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.75/1.59 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_8, axiom, ((bounded_lattice_top @ $o) @ (type2 @ $o))).
% 2.75/1.59 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_9, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 2.75/1.59 thf(tcon_HOL_Obool___Lattices_Olattice_10, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 2.75/1.59 thf(tcon_HOL_Obool___Orderings_Otop_11, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.75/1.59 thf(tcon_HOL_Obool___Groups_Ominus_12, axiom, ((minus @ $o) @ (type2 @ $o))).
% 2.75/1.59 thf(conj_0, conjecture, (p @ ((lList2281150353e_lrev @ a) @ la))).
% 2.75/1.59 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.OwTl828x0i/DTF2DTF25099.p
% 2.75/1.59 ------------------------
% 2.99/1.62 ---- Cleaned THF ---
% 2.99/1.62 thf(ty_t_Coinductive__List_Ollist,type,
% 2.99/1.62 coinductive_llist: $tType > $tType ).
% 2.99/1.62
% 2.99/1.62 thf(ty_t_Set_Oset,type,
% 2.99/1.62 set: $tType > $tType ).
% 2.99/1.62
% 2.99/1.62 thf(ty_t_itself,type,
% 2.99/1.62 itself: $tType > $tType ).
% 2.99/1.62
% 2.99/1.62 thf(ty_tf_a,type,
% 2.99/1.62 a: $tType ).
% 2.99/1.62
% 2.99/1.62 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.99/1.62 bounded_lattice:
% 2.99/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_cl_HOL_Otype,type,
% 2.99/1.62 type:
% 2.99/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_cl_Groups_Ominus,type,
% 2.99/1.62 minus:
% 2.99/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_cl_Orderings_Otop,type,
% 2.99/1.62 top:
% 2.99/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_cl_Lattices_Olattice,type,
% 2.99/1.62 lattice:
% 2.99/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.99/1.62 semilattice_sup:
% 2.99/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 2.99/1.62 bounded_lattice_top:
% 2.99/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.99/1.62 coindu328551480prefix:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Ogen__lset,type,
% 2.99/1.62 coinductive_gen_lset:
% 2.99/1.62 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Olappend,type,
% 2.99/1.62 coinductive_lappend:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Oldistinct,type,
% 2.99/1.62 coindu351974385stinct:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Olfilter,type,
% 2.99/1.62 coinductive_lfilter:
% 2.99/1.62 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Olfinite,type,
% 2.99/1.62 coinductive_lfinite:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Ollast,type,
% 2.99/1.62 coinductive_llast:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Ollexord,type,
% 2.99/1.62 coinductive_llexord:
% 2.99/1.62 !>[A: $tType] : ( ( A > A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.99/1.62 coinductive_LCons:
% 2.99/1.62 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.99/1.62 coinductive_LNil:
% 2.99/1.62 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 2.99/1.62 coinductive_lnull:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 2.99/1.62 coinductive_lset:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Olmember,type,
% 2.99/1.62 coinductive_lmember:
% 2.99/1.62 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.99/1.62 coindu1478340336prefix:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.99/1.62 minus_minus:
% 2.99/1.62 !>[A: $tType] : ( A > A > A ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_HOL_Oundefined,type,
% 2.99/1.62 undefined:
% 2.99/1.62 !>[A: $tType] : A ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 2.99/1.62 lList2435255213lllsts:
% 2.99/1.62 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp,type,
% 2.99/1.62 lList21511617539llstsp:
% 2.99/1.62 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 2.99/1.62 lList2236698231inlsts:
% 2.99/1.62 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 2.99/1.62 lList21916056377ts_rec:
% 2.99/1.62 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp,type,
% 2.99/1.62 lList2860480441nlstsp:
% 2.99/1.62 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 2.99/1.62 lList22096119349pslsts:
% 2.99/1.62 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 2.99/1.62 lList21612149805nflsts:
% 2.99/1.62 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 2.99/1.62 lList2370560421utlast:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 2.99/1.62 lList2170638824_llast:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 2.99/1.62 lList2281150353e_lrev:
% 2.99/1.62 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 2.99/1.62 lList21148268032oslsts:
% 2.99/1.62 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.99/1.62 sup_sup:
% 2.99/1.62 !>[A: $tType] : ( A > A > A ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.99/1.62 top_top:
% 2.99/1.62 !>[A: $tType] : A ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Pure_Otype,type,
% 2.99/1.62 type2:
% 2.99/1.62 !>[A: $tType] : ( itself @ A ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_Set_OCollect,type,
% 2.99/1.62 collect:
% 2.99/1.62 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_c_member,type,
% 2.99/1.62 member:
% 2.99/1.62 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(sy_v_A,type,
% 2.99/1.62 a2: set @ a ).
% 2.99/1.62
% 2.99/1.62 thf(sy_v_P,type,
% 2.99/1.62 p: ( coinductive_llist @ a ) > $o ).
% 2.99/1.62
% 2.99/1.62 thf(sy_v_l____,type,
% 2.99/1.62 l: coinductive_llist @ a ).
% 2.99/1.62
% 2.99/1.62 thf(sy_v_la______,type,
% 2.99/1.62 la: coinductive_llist @ a ).
% 2.99/1.62
% 2.99/1.62 thf(sy_v_xs,type,
% 2.99/1.62 xs: coinductive_llist @ a ).
% 2.99/1.62
% 2.99/1.62 thf(fact_0_init,axiom,
% 2.99/1.62 p @ ( coinductive_LNil @ a ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_1_LNil__fin_Ohyps,axiom,
% 2.99/1.62 ( la
% 2.99/1.62 = ( coinductive_LNil @ a ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_2_l__def,axiom,
% 2.99/1.62 ( l
% 2.99/1.62 = ( lList2281150353e_lrev @ a @ xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_3_lrev__LNil,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_4_lrevT,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_5_local_Ostep,axiom,
% 2.99/1.62 ! [Xs: coinductive_llist @ a,X: a] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ a ) @ Xs @ ( lList2236698231inlsts @ a @ a2 ) )
% 2.99/1.62 => ( ( p @ Xs )
% 2.99/1.62 => ( ( member @ a @ X @ a2 )
% 2.99/1.62 => ( p @ ( coinductive_lappend @ a @ Xs @ ( coinductive_LCons @ a @ X @ ( coinductive_LNil @ a ) ) ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_6_lrev__lrev__ident,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 2.99/1.62 = Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_7_lrev__is__lrev__conv,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.99/1.62 = ( lList2281150353e_lrev @ A @ Ys ) )
% 2.99/1.62 = ( Xs = Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_8_LNil__is__lrev__conv,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( ( ( coinductive_LNil @ A )
% 2.99/1.62 = ( lList2281150353e_lrev @ A @ Xs ) )
% 2.99/1.62 = ( Xs
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_9_lrev__is__LNil__conv,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( Xs
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_10_lbutlast__LNil,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_11_lrev__lappend,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_12_fin,axiom,
% 2.99/1.62 member @ ( coinductive_llist @ a ) @ xs @ ( lList2236698231inlsts @ a @ a2 ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_13__092_060open_062l_A_092_060in_062_AA_092_060_094sup_062_092_060star_062_092_060close_062,axiom,
% 2.99/1.62 member @ ( coinductive_llist @ a ) @ l @ ( lList2236698231inlsts @ a @ a2 ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_14_LNil__is__lappend__conv,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_LNil @ A )
% 2.99/1.62 = ( coinductive_lappend @ A @ S @ T ) )
% 2.99/1.62 = ( ( S
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 & ( T
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_15_lappend__is__LNil__conv,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lappend @ A @ S @ T )
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( ( S
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 & ( T
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_16_same__lappend__eq,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( ( coinductive_lappend @ A @ R @ S )
% 2.99/1.62 = ( coinductive_lappend @ A @ R @ T ) )
% 2.99/1.62 = ( S = T ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_17_lapp__fin__fin__iff,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_18_lbutlast__LCons,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( ( R
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.99/1.62 = ( coinductive_LNil @ A ) ) )
% 2.99/1.62 & ( ( R
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.99/1.62 = ( coinductive_LCons @ A @ A3 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_19_lrev__LCons,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.99/1.62 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A3 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_20_llistE,axiom,
% 2.99/1.62 ! [A: $tType,Y: coinductive_llist @ A] :
% 2.99/1.62 ( ( Y
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 => ~ ! [X21: A,X22: coinductive_llist @ A] :
% 2.99/1.62 ( Y
% 2.99/1.62 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_21_finT__simp,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_22_fin__finite,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_23_lappfin__finT,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_24_finlsts_Ocases,axiom,
% 2.99/1.62 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( A3
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 2.99/1.62 ( ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ A4 @ L ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ~ ( member @ A @ A4 @ A2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_25_finlsts_Osimps,axiom,
% 2.99/1.62 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 = ( ( A3
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [L2: coinductive_llist @ A,A5: A] :
% 2.99/1.62 ( ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.99/1.62 & ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_26_finlsts__induct,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ! [L: coinductive_llist @ A] :
% 2.99/1.62 ( ( L
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( P @ L ) )
% 2.99/1.62 => ( ! [A4: A,L: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( P @ L )
% 2.99/1.62 => ( ( member @ A @ A4 @ A2 )
% 2.99/1.62 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 2.99/1.62 => ( P @ X ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_27_finlsts_Oinducts,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( ! [L: coinductive_llist @ A,A4: A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( P @ L )
% 2.99/1.62 => ( ( member @ A @ A4 @ A2 )
% 2.99/1.62 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 2.99/1.62 => ( P @ X ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_28_finlsts_OLNil__fin,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_29_finlsts_OLCons__fin,axiom,
% 2.99/1.62 ! [A: $tType,L3: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( member @ A @ A3 @ A2 )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L3 ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_30_lapp__fin__fin__lemma,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_31_lappend__code_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.99/1.62 = Ys ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_32_lappend__LNil2,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = Xs ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_33_LNil__eq__lappend__iff,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_LNil @ A )
% 2.99/1.62 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( ( Xs
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 & ( Ys
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_34_lappend__eq__LNil__iff,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( ( Xs
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 & ( Ys
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_35_lappend__code_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 2.99/1.62 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_36_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 2.99/1.62 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A3: B] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 2.99/1.62 => ( ( ( R
% 2.99/1.62 = ( coinductive_LNil @ B ) )
% 2.99/1.62 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A3 @ R ) )
% 2.99/1.62 = A3 ) )
% 2.99/1.62 & ( ( R
% 2.99/1.62 != ( coinductive_LNil @ B ) )
% 2.99/1.62 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A3 @ R ) )
% 2.99/1.62 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_37_lappend__snocL1__conv__LCons2,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.99/1.62 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_38_llist_Oinject,axiom,
% 2.99/1.62 ! [A: $tType,X212: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_LCons @ A @ X212 @ X222 )
% 2.99/1.62 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.99/1.62 = ( ( X212 = Y21 )
% 2.99/1.62 & ( X222 = Y22 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_39_UNIV__I,axiom,
% 2.99/1.62 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_40_iso__tuple__UNIV__I,axiom,
% 2.99/1.62 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_41_top__apply,axiom,
% 2.99/1.62 ! [C: $tType,D: $tType] :
% 2.99/1.62 ( ( top @ C @ ( type2 @ C ) )
% 2.99/1.62 => ( ( top_top @ ( D > C ) )
% 2.99/1.62 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_42_top__set__def,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( top_top @ ( set @ A ) )
% 2.99/1.62 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_43_UNIV__witness,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_44_UNIV__eq__I,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A] :
% 2.99/1.62 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 2.99/1.62 => ( ( top_top @ ( set @ A ) )
% 2.99/1.62 = A2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_45_mem__Collect__eq,axiom,
% 2.99/1.62 ! [A: $tType,A3: A,P: A > $o] :
% 2.99/1.62 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.99/1.62 = ( P @ A3 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_46_Collect__mem__eq,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A] :
% 2.99/1.62 ( ( collect @ A
% 2.99/1.62 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 2.99/1.62 = A2 ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_47_Collect__cong,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.99/1.62 ( ! [X3: A] :
% 2.99/1.62 ( ( P @ X3 )
% 2.99/1.62 = ( Q @ X3 ) )
% 2.99/1.62 => ( ( collect @ A @ P )
% 2.99/1.62 = ( collect @ A @ Q ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_48_ext,axiom,
% 2.99/1.62 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.99/1.62 ( ! [X3: A] :
% 2.99/1.62 ( ( F @ X3 )
% 2.99/1.62 = ( G @ X3 ) )
% 2.99/1.62 => ( F = G ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_49_lappend__assoc,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 2.99/1.62 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_50_neq__LNil__conv,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( Xs
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 2.99/1.62 ( Xs
% 2.99/1.62 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_51_llist_Odistinct_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_LNil @ A )
% 2.99/1.62 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_52_lappend__LNil__LNil,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_53_fpslsts__iff,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.99/1.62 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 & ( S
% 2.99/1.62 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_54_poslsts__UNIV,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 = ( S
% 2.99/1.62 != ( coinductive_LNil @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_55_fpslsts__cases,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.99/1.62 => ~ ! [A4: A,Rs: coinductive_llist @ A] :
% 2.99/1.62 ( ( R
% 2.99/1.62 = ( coinductive_LCons @ A @ A4 @ Rs ) )
% 2.99/1.62 => ( ( member @ A @ A4 @ A2 )
% 2.99/1.62 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_56_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.99/1.62 = ( ( Xs
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [Xs2: coinductive_llist @ A] :
% 2.99/1.62 ( ( Xs
% 2.99/1.62 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 2.99/1.62 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_57_lstrict__prefix__code_I2_J,axiom,
% 2.99/1.62 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_58_lstrict__prefix__code_I3_J,axiom,
% 2.99/1.62 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.99/1.62 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_59_finlsts__rec__LCons__def,axiom,
% 2.99/1.62 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.99/1.62 ( ( F
% 2.99/1.62 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( F @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.99/1.62 = ( D2 @ A3 @ R @ ( F @ R ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_60_finlsts__rec__LCons,axiom,
% 2.99/1.62 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,A3: A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.99/1.62 = ( D2 @ A3 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ R ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_61_top1I,axiom,
% 2.99/1.62 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_62_lstrict__prefix__code_I4_J,axiom,
% 2.99/1.62 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 2.99/1.62 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 2.99/1.62 = ( ( X = Y )
% 2.99/1.62 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_63_lstrict__prefix__code_I1_J,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_64_llist__less__induct,axiom,
% 2.99/1.62 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ! [Xs3: coinductive_llist @ A] :
% 2.99/1.62 ( ! [Ys2: coinductive_llist @ A] :
% 2.99/1.62 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 2.99/1.62 => ( P @ Ys2 ) )
% 2.99/1.62 => ( P @ Xs3 ) )
% 2.99/1.62 => ( P @ Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_65_finlsts__rec__LNil,axiom,
% 2.99/1.62 ! [B: $tType,A: $tType,C2: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 2.99/1.62 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D2 @ ( coinductive_LNil @ B ) )
% 2.99/1.62 = C2 ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_66_finlsts__rec__LNil__def,axiom,
% 2.99/1.62 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 2.99/1.62 ( ( F
% 2.99/1.62 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 2.99/1.62 => ( ( F @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = C2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_67_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_68_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( Xs
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_69_top__empty__eq,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( top_top @ ( A > $o ) )
% 2.99/1.62 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_70_top__conj_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,P: $o,X: A] :
% 2.99/1.62 ( ( P
% 2.99/1.62 & ( top_top @ ( A > $o ) @ X ) )
% 2.99/1.62 = P ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_71_top__conj_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,X: A,P: $o] :
% 2.99/1.62 ( ( ( top_top @ ( A > $o ) @ X )
% 2.99/1.62 & P )
% 2.99/1.62 = P ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_72_poslsts__iff,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.99/1.62 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 & ( S
% 2.99/1.62 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_73_llast__singleton,axiom,
% 2.99/1.62 ! [A: $tType,X: A] :
% 2.99/1.62 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 2.99/1.62 = X ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_74_notfin__inf,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A] :
% 2.99/1.62 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.99/1.62 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_75_notinf__fin,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A] :
% 2.99/1.62 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.99/1.62 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_76_alllsts__UNIV,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_77_LConsE,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 = ( ( member @ A @ X @ A2 )
% 2.99/1.62 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_78_lapp__inf,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ( ( coinductive_lappend @ A @ S @ T )
% 2.99/1.62 = S ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_79_llast__LCons2,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Y: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 2.99/1.62 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_80_inflstsI,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_81_alllstsE,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_82_infsubsetall,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_83_inflstsE,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_84_lapp__allT__iff,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.99/1.62 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_85_infT__simp,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_86_alllsts_OLCons__all,axiom,
% 2.99/1.62 ! [A: $tType,L3: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ( ( member @ A @ A3 @ A2 )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L3 ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_87_alllsts_OLNil__all,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_88_inflsts__cases,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ~ ! [A4: A,L: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ( ( member @ A @ A4 @ A2 )
% 2.99/1.62 => ( S
% 2.99/1.62 != ( coinductive_LCons @ A @ A4 @ L ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_89_inflstsI2,axiom,
% 2.99/1.62 ! [A: $tType,A3: A,A2: set @ A,T: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ A3 @ A2 )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_90_lapp__all__invT,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_91_lappT,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_92_finsubsetall,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_93_finite__lemma,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_94_alllsts_Ocoinduct,axiom,
% 2.99/1.62 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( X4 @ X )
% 2.99/1.62 => ( ! [X3: coinductive_llist @ A] :
% 2.99/1.62 ( ( X4 @ X3 )
% 2.99/1.62 => ( ( X3
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [L4: coinductive_llist @ A,A6: A] :
% 2.99/1.62 ( ( X3
% 2.99/1.62 = ( coinductive_LCons @ A @ A6 @ L4 ) )
% 2.99/1.62 & ( ( X4 @ L4 )
% 2.99/1.62 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.99/1.62 & ( member @ A @ A6 @ A2 ) ) ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_95_alllsts_Osimps,axiom,
% 2.99/1.62 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 = ( ( A3
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [L2: coinductive_llist @ A,A5: A] :
% 2.99/1.62 ( ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.99/1.62 & ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_96_alllsts_Ocases,axiom,
% 2.99/1.62 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ( ( A3
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 2.99/1.62 ( ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ A4 @ L ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.99/1.62 => ~ ( member @ A @ A4 @ A2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_97_fin__inf__cases,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A] :
% 2.99/1.62 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_98_lapp__fin__infT,axiom,
% 2.99/1.62 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_99_lapp__inv2T,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 2.99/1.62 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_100_lapp__infT,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 2.99/1.62 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_101_app__invT,axiom,
% 2.99/1.62 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.99/1.62 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_102_inflsts__def,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lList21612149805nflsts @ A )
% 2.99/1.62 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A7 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_103_llast__lappend__LCons,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 2.99/1.62 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_104_fin__Un__inf,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.99/1.62 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_105_alllstsp_Ocoinduct,axiom,
% 2.99/1.62 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: A > $o] :
% 2.99/1.62 ( ( X4 @ X )
% 2.99/1.62 => ( ! [X3: coinductive_llist @ A] :
% 2.99/1.62 ( ( X4 @ X3 )
% 2.99/1.62 => ( ( X3
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [L4: coinductive_llist @ A,A6: A] :
% 2.99/1.62 ( ( X3
% 2.99/1.62 = ( coinductive_LCons @ A @ A6 @ L4 ) )
% 2.99/1.62 & ( ( X4 @ L4 )
% 2.99/1.62 | ( lList21511617539llstsp @ A @ A2 @ L4 ) )
% 2.99/1.62 & ( A2 @ A6 ) ) ) )
% 2.99/1.62 => ( lList21511617539llstsp @ A @ A2 @ X ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_106_finlstsp_Oinducts,axiom,
% 2.99/1.62 ! [A: $tType,A2: A > $o,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.99/1.62 ( ( lList2860480441nlstsp @ A @ A2 @ X )
% 2.99/1.62 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( ! [L: coinductive_llist @ A,A4: A] :
% 2.99/1.62 ( ( lList2860480441nlstsp @ A @ A2 @ L )
% 2.99/1.62 => ( ( P @ L )
% 2.99/1.62 => ( ( A2 @ A4 )
% 2.99/1.62 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 2.99/1.62 => ( P @ X ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_107_finlstsp_Osimps,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lList2860480441nlstsp @ A )
% 2.99/1.62 = ( ^ [A7: A > $o,A5: coinductive_llist @ A] :
% 2.99/1.62 ( ( A5
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [L2: coinductive_llist @ A,B3: A] :
% 2.99/1.62 ( ( A5
% 2.99/1.62 = ( coinductive_LCons @ A @ B3 @ L2 ) )
% 2.99/1.62 & ( lList2860480441nlstsp @ A @ A7 @ L2 )
% 2.99/1.62 & ( A7 @ B3 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_108_Un__iff,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 = ( ( member @ A @ C2 @ A2 )
% 2.99/1.62 | ( member @ A @ C2 @ B2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_109_UnCI,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 2.99/1.62 ( ( ~ ( member @ A @ C2 @ B2 )
% 2.99/1.62 => ( member @ A @ C2 @ A2 ) )
% 2.99/1.62 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_110_Diff__idemp,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 2.99/1.62 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_111_Diff__iff,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 = ( ( member @ A @ C2 @ A2 )
% 2.99/1.62 & ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_112_DiffI,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ A2 )
% 2.99/1.62 => ( ~ ( member @ A @ C2 @ B2 )
% 2.99/1.62 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_113_Un__Diff__cancel2,axiom,
% 2.99/1.62 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) @ A2 )
% 2.99/1.62 = ( sup_sup @ ( set @ A ) @ B2 @ A2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_114_Un__Diff__cancel,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 2.99/1.62 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_115_lfinite__code_I2_J,axiom,
% 2.99/1.62 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.99/1.62 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 2.99/1.62 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_116_lfinite__LCons,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.99/1.62 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_117_lfinite__code_I1_J,axiom,
% 2.99/1.62 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_118_lfinite__lappend,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_119_Un__left__commute,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 2.99/1.62 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_120_Un__left__absorb,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_121_Un__commute,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) )
% 2.99/1.62 = ( ^ [A7: set @ A,B4: set @ A] : ( sup_sup @ ( set @ A ) @ B4 @ A7 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_122_Un__absorb,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 2.99/1.62 = A2 ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_123_Un__assoc,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 2.99/1.62 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_124_ball__Un,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 2.99/1.62 ( ( ! [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 => ( P @ X2 ) ) )
% 2.99/1.62 = ( ! [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ A2 )
% 2.99/1.62 => ( P @ X2 ) )
% 2.99/1.62 & ! [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ B2 )
% 2.99/1.62 => ( P @ X2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_125_Un__Diff,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 2.99/1.62 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 2.99/1.62 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_126_bex__Un,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 2.99/1.62 ( ( ? [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 & ( P @ X2 ) ) )
% 2.99/1.62 = ( ? [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ A2 )
% 2.99/1.62 & ( P @ X2 ) )
% 2.99/1.62 | ? [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ B2 )
% 2.99/1.62 & ( P @ X2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_127_DiffD2,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 => ~ ( member @ A @ C2 @ B2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_128_DiffD1,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 => ( member @ A @ C2 @ A2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_129_DiffE,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 => ~ ( ( member @ A @ C2 @ A2 )
% 2.99/1.62 => ( member @ A @ C2 @ B2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_130_UnI2,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ B2 )
% 2.99/1.62 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_131_UnI1,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ A2 )
% 2.99/1.62 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_132_UnE,axiom,
% 2.99/1.62 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.99/1.62 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.99/1.62 => ( ~ ( member @ A @ C2 @ A2 )
% 2.99/1.62 => ( member @ A @ C2 @ B2 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_133_lfinite__LConsI,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_134_lfinite__LNil,axiom,
% 2.99/1.62 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_135_lappend__inf,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.99/1.62 = Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_136_Un__UNIV__left,axiom,
% 2.99/1.62 ! [A: $tType,B2: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 2.99/1.62 = ( top_top @ ( set @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_137_Un__UNIV__right,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A] :
% 2.99/1.62 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 2.99/1.62 = ( top_top @ ( set @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_138_lstrict__prefix__lfinite1,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 2.99/1.62 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_139_alllstsp_OLCons__all,axiom,
% 2.99/1.62 ! [A: $tType,A2: A > $o,L3: coinductive_llist @ A,A3: A] :
% 2.99/1.62 ( ( lList21511617539llstsp @ A @ A2 @ L3 )
% 2.99/1.62 => ( ( A2 @ A3 )
% 2.99/1.62 => ( lList21511617539llstsp @ A @ A2 @ ( coinductive_LCons @ A @ A3 @ L3 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_140_finlstsp_OLCons__fin,axiom,
% 2.99/1.62 ! [A: $tType,A2: A > $o,L3: coinductive_llist @ A,A3: A] :
% 2.99/1.62 ( ( lList2860480441nlstsp @ A @ A2 @ L3 )
% 2.99/1.62 => ( ( A2 @ A3 )
% 2.99/1.62 => ( lList2860480441nlstsp @ A @ A2 @ ( coinductive_LCons @ A @ A3 @ L3 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_141_alllstsp_OLNil__all,axiom,
% 2.99/1.62 ! [A: $tType,A2: A > $o] : ( lList21511617539llstsp @ A @ A2 @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_142_finlstsp_OLNil__fin,axiom,
% 2.99/1.62 ! [A: $tType,A2: A > $o] : ( lList2860480441nlstsp @ A @ A2 @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_143_lfinite_Ocases,axiom,
% 2.99/1.62 ! [A: $tType,A3: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ A3 )
% 2.99/1.62 => ( ( A3
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 => ~ ! [Xs3: coinductive_llist @ A] :
% 2.99/1.62 ( ? [X3: A] :
% 2.99/1.62 ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 2.99/1.62 => ~ ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_144_lfinite_Osimps,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( coinductive_lfinite @ A )
% 2.99/1.62 = ( ^ [A5: coinductive_llist @ A] :
% 2.99/1.62 ( ( A5
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [Xs4: coinductive_llist @ A,X2: A] :
% 2.99/1.62 ( ( A5
% 2.99/1.62 = ( coinductive_LCons @ A @ X2 @ Xs4 ) )
% 2.99/1.62 & ( coinductive_lfinite @ A @ Xs4 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_145_lfinite_Oinducts,axiom,
% 2.99/1.62 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ X )
% 2.99/1.62 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( ! [Xs3: coinductive_llist @ A,X3: A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.99/1.62 => ( ( P @ Xs3 )
% 2.99/1.62 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) )
% 2.99/1.62 => ( P @ X ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_146_lfinite__rev__induct,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.99/1.62 => ( ( P @ Xs3 )
% 2.99/1.62 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 2.99/1.62 => ( P @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_147_llimit__induct,axiom,
% 2.99/1.62 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( P @ ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.99/1.62 => ( ( P @ Xs3 )
% 2.99/1.62 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) )
% 2.99/1.62 => ( ( ! [Ys2: coinductive_llist @ A] :
% 2.99/1.62 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs )
% 2.99/1.62 => ( P @ Ys2 ) )
% 2.99/1.62 => ( P @ Xs ) )
% 2.99/1.62 => ( P @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_148_alllstsp_Ocases,axiom,
% 2.99/1.62 ! [A: $tType,A2: A > $o,A3: coinductive_llist @ A] :
% 2.99/1.62 ( ( lList21511617539llstsp @ A @ A2 @ A3 )
% 2.99/1.62 => ( ( A3
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 2.99/1.62 ( ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ A4 @ L ) )
% 2.99/1.62 => ( ( lList21511617539llstsp @ A @ A2 @ L )
% 2.99/1.62 => ~ ( A2 @ A4 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_149_alllstsp_Osimps,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lList21511617539llstsp @ A )
% 2.99/1.62 = ( ^ [A7: A > $o,A5: coinductive_llist @ A] :
% 2.99/1.62 ( ( A5
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [L2: coinductive_llist @ A,B3: A] :
% 2.99/1.62 ( ( A5
% 2.99/1.62 = ( coinductive_LCons @ A @ B3 @ L2 ) )
% 2.99/1.62 & ( lList21511617539llstsp @ A @ A7 @ L2 )
% 2.99/1.62 & ( A7 @ B3 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_150_finlstsp_Ocases,axiom,
% 2.99/1.62 ! [A: $tType,A2: A > $o,A3: coinductive_llist @ A] :
% 2.99/1.62 ( ( lList2860480441nlstsp @ A @ A2 @ A3 )
% 2.99/1.62 => ( ( A3
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 2.99/1.62 ( ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ A4 @ L ) )
% 2.99/1.62 => ( ( lList2860480441nlstsp @ A @ A2 @ L )
% 2.99/1.62 => ~ ( A2 @ A4 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_151_sup__top__left,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A] :
% 2.99/1.62 ( ( sup_sup @ A @ ( top_top @ A ) @ X )
% 2.99/1.62 = ( top_top @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_152_sup__top__right,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A] :
% 2.99/1.62 ( ( sup_sup @ A @ X @ ( top_top @ A ) )
% 2.99/1.62 = ( top_top @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_153_sup__apply,axiom,
% 2.99/1.62 ! [B: $tType,A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.99/1.62 => ( ( sup_sup @ ( A > B ) )
% 2.99/1.62 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_154_sup_Oidem,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [A3: A] :
% 2.99/1.62 ( ( sup_sup @ A @ A3 @ A3 )
% 2.99/1.62 = A3 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_155_sup__idem,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A] :
% 2.99/1.62 ( ( sup_sup @ A @ X @ X )
% 2.99/1.62 = X ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_156_minus__apply,axiom,
% 2.99/1.62 ! [B: $tType,A: $tType] :
% 2.99/1.62 ( ( minus @ B @ ( type2 @ B ) )
% 2.99/1.62 => ( ( minus_minus @ ( A > B ) )
% 2.99/1.62 = ( ^ [A7: A > B,B4: A > B,X2: A] : ( minus_minus @ B @ ( A7 @ X2 ) @ ( B4 @ X2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_157_sup_Oright__idem,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [A3: A,B5: A] :
% 2.99/1.62 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B5 ) @ B5 )
% 2.99/1.62 = ( sup_sup @ A @ A3 @ B5 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_158_sup__left__idem,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A,Y: A] :
% 2.99/1.62 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.99/1.62 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_159_sup_Oleft__idem,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [A3: A,B5: A] :
% 2.99/1.62 ( ( sup_sup @ A @ A3 @ ( sup_sup @ A @ A3 @ B5 ) )
% 2.99/1.62 = ( sup_sup @ A @ A3 @ B5 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_160_fun__diff__def,axiom,
% 2.99/1.62 ! [B: $tType,A: $tType] :
% 2.99/1.62 ( ( minus @ B @ ( type2 @ B ) )
% 2.99/1.62 => ( ( minus_minus @ ( A > B ) )
% 2.99/1.62 = ( ^ [A7: A > B,B4: A > B,X2: A] : ( minus_minus @ B @ ( A7 @ X2 ) @ ( B4 @ X2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_161_sup__left__commute,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A,Y: A,Z: A] :
% 2.99/1.62 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 2.99/1.62 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_162_sup_Oleft__commute,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [B5: A,A3: A,C2: A] :
% 2.99/1.62 ( ( sup_sup @ A @ B5 @ ( sup_sup @ A @ A3 @ C2 ) )
% 2.99/1.62 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B5 @ C2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_163_sup__commute,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ( ( sup_sup @ A )
% 2.99/1.62 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_164_sup_Ocommute,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ( ( sup_sup @ A )
% 2.99/1.62 = ( ^ [A5: A,B3: A] : ( sup_sup @ A @ B3 @ A5 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_165_sup__assoc,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A,Y: A,Z: A] :
% 2.99/1.62 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 2.99/1.62 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_166_sup_Oassoc,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [A3: A,B5: A,C2: A] :
% 2.99/1.62 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B5 ) @ C2 )
% 2.99/1.62 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B5 @ C2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_167_sup__fun__def,axiom,
% 2.99/1.62 ! [B: $tType,A: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.99/1.62 => ( ( sup_sup @ ( A > B ) )
% 2.99/1.62 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_168_inf__sup__aci_I5_J,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lattice @ A @ ( type2 @ A ) )
% 2.99/1.62 => ( ( sup_sup @ A )
% 2.99/1.62 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_169_inf__sup__aci_I6_J,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lattice @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A,Y: A,Z: A] :
% 2.99/1.62 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 2.99/1.62 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_170_inf__sup__aci_I7_J,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lattice @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A,Y: A,Z: A] :
% 2.99/1.62 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 2.99/1.62 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_171_inf__sup__aci_I8_J,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( lattice @ A @ ( type2 @ A ) )
% 2.99/1.62 => ! [X: A,Y: A] :
% 2.99/1.62 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.99/1.62 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_172_lset__lappend__lfinite,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( coinductive_lset @ A @ Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_173_lstrict__prefix__lappend__conv,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coindu1478340336prefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_174_lmember__code_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,X: A] :
% 2.99/1.62 ~ ( coinductive_lmember @ A @ X @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_175_lnull__lappend,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_176_lappend_Odisc__iff_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 2.99/1.62 = ( ~ ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_177_lappend_Oexhaust,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ~ ( coinductive_lnull @ A @ Ys ) )
% 2.99/1.62 => ( ~ ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_178_lzip_Oexhaust,axiom,
% 2.99/1.62 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 2.99/1.62 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 | ( coinductive_lnull @ B @ Ys ) )
% 2.99/1.62 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ( coinductive_lnull @ B @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_179_lset__lmember,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 = ( coinductive_lmember @ A @ X @ Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_180_lappend__lnull2,axiom,
% 2.99/1.62 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ Ys )
% 2.99/1.62 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.99/1.62 = Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_181_lappend__lnull1,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.99/1.62 = Ys ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_182_lappend_Odisc_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_lnull @ A @ Ys )
% 2.99/1.62 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_183_lappend_Odisc_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 | ~ ( coinductive_lnull @ A @ Ys ) )
% 2.99/1.62 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_184_lnull__def,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( coinductive_lnull @ A )
% 2.99/1.62 = ( ^ [Llist: coinductive_llist @ A] :
% 2.99/1.62 ( Llist
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_185_llist_Ocollapse_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,Llist2: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ Llist2 )
% 2.99/1.62 => ( Llist2
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_186_llist_OdiscI_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,Llist2: coinductive_llist @ A] :
% 2.99/1.62 ( ( Llist2
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 => ( coinductive_lnull @ A @ Llist2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_187_llist_Odisc_I1_J,axiom,
% 2.99/1.62 ! [A: $tType] : ( coinductive_lnull @ A @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_188_not__lnull__conv,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( ~ ( coinductive_lnull @ A @ Xs ) )
% 2.99/1.62 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 2.99/1.62 ( Xs
% 2.99/1.62 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_189_llist_OdiscI_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,Llist2: coinductive_llist @ A,X212: A,X222: coinductive_llist @ A] :
% 2.99/1.62 ( ( Llist2
% 2.99/1.62 = ( coinductive_LCons @ A @ X212 @ X222 ) )
% 2.99/1.62 => ~ ( coinductive_lnull @ A @ Llist2 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_190_llist_Odisc_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 2.99/1.62 ~ ( coinductive_lnull @ A @ ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_191_llist_Oset__induct,axiom,
% 2.99/1.62 ! [A: $tType,X: A,A3: coinductive_llist @ A,P: A > ( coinductive_llist @ A ) > $o] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ A3 ) )
% 2.99/1.62 => ( ! [Z1: A,Z2: coinductive_llist @ A] : ( P @ Z1 @ ( coinductive_LCons @ A @ Z1 @ Z2 ) )
% 2.99/1.62 => ( ! [Z1: A,Z2: coinductive_llist @ A,Xa2: A] :
% 2.99/1.62 ( ( member @ A @ Xa2 @ ( coinductive_lset @ A @ Z2 ) )
% 2.99/1.62 => ( ( P @ Xa2 @ Z2 )
% 2.99/1.62 => ( P @ Xa2 @ ( coinductive_LCons @ A @ Z1 @ Z2 ) ) ) )
% 2.99/1.62 => ( P @ X @ A3 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_192_llist_Oset__cases,axiom,
% 2.99/1.62 ! [A: $tType,E: A,A3: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ E @ ( coinductive_lset @ A @ A3 ) )
% 2.99/1.62 => ( ! [Z2: coinductive_llist @ A] :
% 2.99/1.62 ( A3
% 2.99/1.62 != ( coinductive_LCons @ A @ E @ Z2 ) )
% 2.99/1.62 => ~ ! [Z1: A,Z2: coinductive_llist @ A] :
% 2.99/1.62 ( ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ Z1 @ Z2 ) )
% 2.99/1.62 => ~ ( member @ A @ E @ ( coinductive_lset @ A @ Z2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_193_lset__induct_H,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ( ! [Xs3: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.99/1.62 => ( ! [X5: A,Xs3: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.99/1.62 => ( ( P @ Xs3 )
% 2.99/1.62 => ( P @ ( coinductive_LCons @ A @ X5 @ Xs3 ) ) ) )
% 2.99/1.62 => ( P @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_194_lset__induct,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ( ! [Xs3: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.99/1.62 => ( ! [X5: A,Xs3: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.99/1.62 => ( ( X != X5 )
% 2.99/1.62 => ( ( P @ Xs3 )
% 2.99/1.62 => ( P @ ( coinductive_LCons @ A @ X5 @ Xs3 ) ) ) ) )
% 2.99/1.62 => ( P @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_195_lset__cases,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ( ! [Xs5: coinductive_llist @ A] :
% 2.99/1.62 ( Xs
% 2.99/1.62 != ( coinductive_LCons @ A @ X @ Xs5 ) )
% 2.99/1.62 => ~ ! [X5: A,Xs5: coinductive_llist @ A] :
% 2.99/1.62 ( ( Xs
% 2.99/1.62 = ( coinductive_LCons @ A @ X5 @ Xs5 ) )
% 2.99/1.62 => ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs5 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_196_llist_Oset__intros_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,A1: A,A22: coinductive_llist @ A] : ( member @ A @ A1 @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_197_llist_Oset__intros_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,X: A,A22: coinductive_llist @ A,A1: A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ A22 ) )
% 2.99/1.62 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_198_lset__intros_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A] : ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_199_lset__intros_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A,X6: A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X6 @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_200_lnull__imp__lfinite,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_201_in__lset__lappend__iff,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 2.99/1.62 = ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 | ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 & ( member @ A @ X @ ( coinductive_lset @ A @ Ys ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_202_lappend_Octr_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_lnull @ A @ Ys )
% 2.99/1.62 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_203_Coinductive__List_Ollast__LCons,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.99/1.62 ( ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.99/1.62 = X ) )
% 2.99/1.62 & ( ~ ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.99/1.62 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_204_lset__lappend__conv,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( coinductive_lset @ A @ Ys ) ) ) )
% 2.99/1.62 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( coinductive_lset @ A @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_205_split__llist,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ? [Ys3: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 2.99/1.62 ( ( Xs
% 2.99/1.62 = ( coinductive_lappend @ A @ Ys3 @ ( coinductive_LCons @ A @ X @ Zs2 ) ) )
% 2.99/1.62 & ( coinductive_lfinite @ A @ Ys3 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_206_split__llist__first,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ? [Ys3: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 2.99/1.62 ( ( Xs
% 2.99/1.62 = ( coinductive_lappend @ A @ Ys3 @ ( coinductive_LCons @ A @ X @ Zs2 ) ) )
% 2.99/1.62 & ( coinductive_lfinite @ A @ Ys3 )
% 2.99/1.62 & ~ ( member @ A @ X @ ( coinductive_lset @ A @ Ys3 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_207_lmember__code_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Y: A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lmember @ A @ X @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.99/1.62 = ( ( X = Y )
% 2.99/1.62 | ( coinductive_lmember @ A @ X @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_208_gen__lset__def,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( coinductive_gen_lset @ A )
% 2.99/1.62 = ( ^ [A7: set @ A,Xs4: coinductive_llist @ A] : ( sup_sup @ ( set @ A ) @ A7 @ ( coinductive_lset @ A @ Xs4 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_209_llast__lappend,axiom,
% 2.99/1.62 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lnull @ A @ Ys )
% 2.99/1.62 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( coinductive_llast @ A @ Xs ) ) )
% 2.99/1.62 & ( ~ ( coinductive_lnull @ A @ Ys )
% 2.99/1.62 => ( ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( coinductive_llast @ A @ Ys ) ) )
% 2.99/1.62 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( undefined @ A ) ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_210_lfilter__eq__LConsD,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,Ys: coinductive_llist @ A,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lfilter @ A @ P @ Ys )
% 2.99/1.62 = ( coinductive_LCons @ A @ X @ Xs ) )
% 2.99/1.62 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 2.99/1.62 ( ( Ys
% 2.99/1.62 = ( coinductive_lappend @ A @ Us @ ( coinductive_LCons @ A @ X @ Vs ) ) )
% 2.99/1.62 & ( coinductive_lfinite @ A @ Us )
% 2.99/1.62 & ! [X7: A] :
% 2.99/1.62 ( ( member @ A @ X7 @ ( coinductive_lset @ A @ Us ) )
% 2.99/1.62 => ~ ( P @ X7 ) )
% 2.99/1.62 & ( P @ X )
% 2.99/1.62 & ( Xs
% 2.99/1.62 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_211_lfilter__idem,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 2.99/1.62 = ( coinductive_lfilter @ A @ P @ Xs ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_212_lfilter__LCons,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( P @ X )
% 2.99/1.62 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.99/1.62 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) )
% 2.99/1.62 & ( ~ ( P @ X )
% 2.99/1.62 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.99/1.62 = ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_213_lfilter__LNil,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o] :
% 2.99/1.62 ( ( coinductive_lfilter @ A @ P @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_214_diverge__lfilter__LNil,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 2.99/1.62 ( ! [X3: A] :
% 2.99/1.62 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ~ ( P @ X3 ) )
% 2.99/1.62 => ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.99/1.62 = ( coinductive_LNil @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_215_lnull__lfilter,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 2.99/1.62 = ( ! [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ~ ( P @ X2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_216_lfilter__lappend__lfinite,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.99/1.62 = ( coinductive_lappend @ A @ ( coinductive_lfilter @ A @ P @ Xs ) @ ( coinductive_lfilter @ A @ P @ Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_217_LList2__Mirabelle__hamjzmohle_Ollast__LNil,axiom,
% 2.99/1.62 ! [B: $tType] :
% 2.99/1.62 ( ( lList2170638824_llast @ B @ ( coinductive_LNil @ B ) )
% 2.99/1.62 = ( undefined @ B ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_218_lfilter__id__conv,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.99/1.62 = Xs )
% 2.99/1.62 = ( ! [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ( P @ X2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_219_lfilter__cong,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,P: A > $o,Q: A > $o] :
% 2.99/1.62 ( ( Xs = Ys )
% 2.99/1.62 => ( ! [X3: A] :
% 2.99/1.62 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Ys ) )
% 2.99/1.62 => ( ( P @ X3 )
% 2.99/1.62 = ( Q @ X3 ) ) )
% 2.99/1.62 => ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.99/1.62 = ( coinductive_lfilter @ A @ Q @ Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_220_lfinite__lfilterI,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( coinductive_lfinite @ A @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_221_lfilter__LCons__seek,axiom,
% 2.99/1.62 ! [A: $tType,P2: A > $o,X: A,L3: coinductive_llist @ A] :
% 2.99/1.62 ( ~ ( P2 @ X )
% 2.99/1.62 => ( ( coinductive_lfilter @ A @ P2 @ ( coinductive_LCons @ A @ X @ L3 ) )
% 2.99/1.62 = ( coinductive_lfilter @ A @ P2 @ L3 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_222_lfilter__LCons__found,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( P @ X )
% 2.99/1.62 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.99/1.62 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_223_lfilter__empty__conv,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( ! [X2: A] :
% 2.99/1.62 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ~ ( P @ X2 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_224_lfilter__eq__lappend__lfiniteD,axiom,
% 2.99/1.62 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.99/1.62 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.99/1.62 = ( coinductive_lappend @ A @ Ys @ Zs ) )
% 2.99/1.62 => ( ( coinductive_lfinite @ A @ Ys )
% 2.99/1.62 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 2.99/1.62 ( ( Xs
% 2.99/1.62 = ( coinductive_lappend @ A @ Us @ Vs ) )
% 2.99/1.62 & ( coinductive_lfinite @ A @ Us )
% 2.99/1.62 & ( Ys
% 2.99/1.62 = ( coinductive_lfilter @ A @ P @ Us ) )
% 2.99/1.62 & ( Zs
% 2.99/1.62 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_225_Coinductive__List_Ollast__LNil,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = ( undefined @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_226_llast__linfinite,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ( coinductive_llast @ A @ Xs )
% 2.99/1.62 = ( undefined @ A ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_227_gen__lset__code_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,A2: set @ A] :
% 2.99/1.62 ( ( coinductive_gen_lset @ A @ A2 @ ( coinductive_LNil @ A ) )
% 2.99/1.62 = A2 ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_228_ldistinct_Ocases,axiom,
% 2.99/1.62 ! [A: $tType,A3: coinductive_llist @ A] :
% 2.99/1.62 ( ( coindu351974385stinct @ A @ A3 )
% 2.99/1.62 => ( ( A3
% 2.99/1.62 != ( coinductive_LNil @ A ) )
% 2.99/1.62 => ~ ! [X3: A,Xs3: coinductive_llist @ A] :
% 2.99/1.62 ( ( A3
% 2.99/1.62 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 2.99/1.62 => ( ~ ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs3 ) )
% 2.99/1.62 => ~ ( coindu351974385stinct @ A @ Xs3 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_229_ldistinct_Osimps,axiom,
% 2.99/1.62 ! [A: $tType] :
% 2.99/1.62 ( ( coindu351974385stinct @ A )
% 2.99/1.62 = ( ^ [A5: coinductive_llist @ A] :
% 2.99/1.62 ( ( A5
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [X2: A,Xs4: coinductive_llist @ A] :
% 2.99/1.62 ( ( A5
% 2.99/1.62 = ( coinductive_LCons @ A @ X2 @ Xs4 ) )
% 2.99/1.62 & ~ ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs4 ) )
% 2.99/1.62 & ( coindu351974385stinct @ A @ Xs4 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_230_ldistinct__LNil__code,axiom,
% 2.99/1.62 ! [A: $tType] : ( coindu351974385stinct @ A @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_231_ldistinct__LCons,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coindu351974385stinct @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.99/1.62 = ( ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 & ( coindu351974385stinct @ A @ Xs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_232_ldistinct__lfilterI,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 2.99/1.62 ( ( coindu351974385stinct @ A @ Xs )
% 2.99/1.62 => ( coindu351974385stinct @ A @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_233_ldistinct_OLCons,axiom,
% 2.99/1.62 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ( ( coindu351974385stinct @ A @ Xs )
% 2.99/1.62 => ( coindu351974385stinct @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_234_ldistinct_OLNil,axiom,
% 2.99/1.62 ! [A: $tType] : ( coindu351974385stinct @ A @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_235_ldistinct_Ocoinduct,axiom,
% 2.99/1.62 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A] :
% 2.99/1.62 ( ( X4 @ X )
% 2.99/1.62 => ( ! [X3: coinductive_llist @ A] :
% 2.99/1.62 ( ( X4 @ X3 )
% 2.99/1.62 => ( ( X3
% 2.99/1.62 = ( coinductive_LNil @ A ) )
% 2.99/1.62 | ? [Xa3: A,Xs6: coinductive_llist @ A] :
% 2.99/1.62 ( ( X3
% 2.99/1.62 = ( coinductive_LCons @ A @ Xa3 @ Xs6 ) )
% 2.99/1.62 & ~ ( member @ A @ Xa3 @ ( coinductive_lset @ A @ Xs6 ) )
% 2.99/1.62 & ( ( X4 @ Xs6 )
% 2.99/1.62 | ( coindu351974385stinct @ A @ Xs6 ) ) ) ) )
% 2.99/1.62 => ( coindu351974385stinct @ A @ X ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_236_llexord__lappend__leftD,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 2.99/1.62 => ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ! [X3: A] :
% 2.99/1.62 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ~ ( R @ X3 @ X3 ) )
% 2.99/1.62 => ( coinductive_llexord @ A @ R @ Ys @ Zs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_237_llexord__lappend__left,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,R: A > A > $o,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lfinite @ A @ Xs )
% 2.99/1.62 => ( ! [X3: A] :
% 2.99/1.62 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 2.99/1.62 => ~ ( R @ X3 @ X3 ) )
% 2.99/1.62 => ( ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 2.99/1.62 = ( coinductive_llexord @ A @ R @ Ys @ Zs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_238_llexord__refl,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ Xs @ Xs ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_239_llexord__LCons__LCons,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.99/1.62 = ( ( ( X = Y )
% 2.99/1.62 & ( coinductive_llexord @ A @ R @ Xs @ Ys ) )
% 2.99/1.62 | ( R @ X @ Y ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_240_llexord__code_I1_J,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ ( coinductive_LNil @ A ) @ Ys ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_241_llexord__LNil__right,axiom,
% 2.99/1.62 ! [A: $tType,Ys: coinductive_llist @ A,R: A > A > $o,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ Ys )
% 2.99/1.62 => ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 2.99/1.62 = ( coinductive_lnull @ A @ Xs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_242_lnull__llexord,axiom,
% 2.99/1.62 ! [A: $tType,Xs: coinductive_llist @ A,R: A > A > $o,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_lnull @ A @ Xs )
% 2.99/1.62 => ( coinductive_llexord @ A @ R @ Xs @ Ys ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_243_llexord__trans,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 2.99/1.62 => ( ( coinductive_llexord @ A @ R @ Ys @ Zs )
% 2.99/1.62 => ( ! [A4: A,B6: A,C4: A] :
% 2.99/1.62 ( ( R @ A4 @ B6 )
% 2.99/1.62 => ( ( R @ B6 @ C4 )
% 2.99/1.62 => ( R @ A4 @ C4 ) ) )
% 2.99/1.62 => ( coinductive_llexord @ A @ R @ Xs @ Zs ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_244_llexord__linear,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ! [X3: A,Y3: A] :
% 2.99/1.62 ( ( R @ X3 @ Y3 )
% 2.99/1.62 | ( X3 = Y3 )
% 2.99/1.62 | ( R @ Y3 @ X3 ) )
% 2.99/1.62 => ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 2.99/1.62 | ( coinductive_llexord @ A @ R @ Ys @ Xs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_245_llexord__antisym,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 2.99/1.62 => ( ( coinductive_llexord @ A @ R @ Ys @ Xs )
% 2.99/1.62 => ( ! [A4: A,B6: A] :
% 2.99/1.62 ( ( R @ A4 @ B6 )
% 2.99/1.62 => ~ ( R @ B6 @ A4 ) )
% 2.99/1.62 => ( Xs = Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_246_llexord__append__right,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_247_llexord__lappend__leftI,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_llexord @ A @ R @ Ys @ Zs )
% 2.99/1.62 => ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_248_llexord__LNil,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ ( coinductive_LNil @ A ) @ Ys ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_249_llexord__code_I3_J,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.99/1.62 = ( ( R @ X @ Y )
% 2.99/1.62 | ( ( X = Y )
% 2.99/1.62 & ( coinductive_llexord @ A @ R @ Xs @ Ys ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_250_llexord__LCons__left,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 2.99/1.62 = ( ? [Y2: A,Ys4: coinductive_llist @ A] :
% 2.99/1.62 ( ( Ys
% 2.99/1.62 = ( coinductive_LCons @ A @ Y2 @ Ys4 ) )
% 2.99/1.62 & ( ( ( X = Y2 )
% 2.99/1.62 & ( coinductive_llexord @ A @ R @ Xs @ Ys4 ) )
% 2.99/1.62 | ( R @ X @ Y2 ) ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_251_llexord__LCons__eq,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 2.99/1.62 ( ( coinductive_llexord @ A @ R @ Xs @ Ys )
% 2.99/1.62 => ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_252_llexord__LCons__less,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,X: A,Y: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.99/1.62 ( ( R @ X @ Y )
% 2.99/1.62 => ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(fact_253_llexord__code_I2_J,axiom,
% 2.99/1.62 ! [A: $tType,R: A > A > $o,X: A,Xs: coinductive_llist @ A] :
% 2.99/1.62 ~ ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LNil @ A ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.99/1.62 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.99/1.62 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.99/1.62 ! [A8: $tType,A9: $tType] :
% 2.99/1.62 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.99/1.62 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 2.99/1.62 ! [A8: $tType,A9: $tType] :
% 2.99/1.62 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.99/1.62 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.99/1.62 ! [A8: $tType,A9: $tType] :
% 2.99/1.62 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 2.99/1.62 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.99/1.62 ! [A8: $tType,A9: $tType] :
% 2.99/1.62 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 2.99/1.62 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_fun___Orderings_Otop,axiom,
% 2.99/1.62 ! [A8: $tType,A9: $tType] :
% 2.99/1.62 ( ( top @ A9 @ ( type2 @ A9 ) )
% 2.99/1.62 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_fun___Groups_Ominus,axiom,
% 2.99/1.62 ! [A8: $tType,A9: $tType] :
% 2.99/1.62 ( ( minus @ A9 @ ( type2 @ A9 ) )
% 2.99/1.62 => ( minus @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_3,axiom,
% 2.99/1.62 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_4,axiom,
% 2.99/1.62 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_Set_Oset___Lattices_Olattice_5,axiom,
% 2.99/1.62 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_Set_Oset___Orderings_Otop_6,axiom,
% 2.99/1.62 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_Set_Oset___Groups_Ominus_7,axiom,
% 2.99/1.62 ! [A8: $tType] : ( minus @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_8,axiom,
% 2.99/1.62 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_9,axiom,
% 2.99/1.62 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_HOL_Obool___Lattices_Olattice_10,axiom,
% 2.99/1.62 lattice @ $o @ ( type2 @ $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_HOL_Obool___Orderings_Otop_11,axiom,
% 2.99/1.62 top @ $o @ ( type2 @ $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(tcon_HOL_Obool___Groups_Ominus_12,axiom,
% 2.99/1.62 minus @ $o @ ( type2 @ $o ) ).
% 2.99/1.62
% 2.99/1.62 thf(conj_0,conjecture,
% 2.99/1.62 p @ ( lList2281150353e_lrev @ a @ la ) ).
% 2.99/1.62 ------------------------
% 2.99/1.64 % (25371)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25099 for (2999ds/183Mi)
% 2.99/1.64 % (25377)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25099 for (2999ds/18Mi)
% 2.99/1.65 % (25377)Instruction limit reached!
% 2.99/1.65 % (25377)------------------------------
% 2.99/1.65 % (25377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (25377)Termination reason: Unknown
% 2.99/1.65 % (25377)Termination phase: shuffling
% 2.99/1.65
% 2.99/1.65 % (25377)Memory used [KB]: 1663
% 2.99/1.65 % (25377)Time elapsed: 0.008 s
% 2.99/1.65 % (25377)Instructions burned: 19 (million)
% 2.99/1.65 % (25377)------------------------------
% 2.99/1.65 % (25377)------------------------------
% 2.99/1.65 % (25372)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_25099 for (2999ds/4Mi)
% 2.99/1.65 % (25373)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_25099 for (2999ds/27Mi)
% 2.99/1.65 % (25374)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25099 for (2999ds/2Mi)
% 2.99/1.65 % (25375)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_25099 for (2999ds/2Mi)
% 2.99/1.65 % (25376)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_25099 for (2999ds/275Mi)
% 2.99/1.65 % (25374)Instruction limit reached!
% 2.99/1.65 % (25374)------------------------------
% 2.99/1.65 % (25374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (25374)Termination reason: Unknown
% 2.99/1.65 % (25374)Termination phase: shuffling
% 2.99/1.65
% 2.99/1.65 % (25374)Memory used [KB]: 1279
% 2.99/1.65 % (25374)Time elapsed: 0.004 s
% 2.99/1.65 % (25374)Instructions burned: 3 (million)
% 2.99/1.65 % (25374)------------------------------
% 2.99/1.65 % (25374)------------------------------
% 2.99/1.65 % (25375)Instruction limit reached!
% 2.99/1.65 % (25375)------------------------------
% 2.99/1.65 % (25375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (25375)Termination reason: Unknown
% 2.99/1.65 % (25375)Termination phase: shuffling
% 2.99/1.65
% 2.99/1.65 % (25375)Memory used [KB]: 1279
% 2.99/1.65 % (25375)Time elapsed: 0.004 s
% 2.99/1.65 % (25375)Instructions burned: 3 (million)
% 2.99/1.65 % (25375)------------------------------
% 2.99/1.65 % (25375)------------------------------
% 2.99/1.65 % (25372)Instruction limit reached!
% 2.99/1.65 % (25372)------------------------------
% 2.99/1.65 % (25372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (25372)Termination reason: Unknown
% 2.99/1.65 % (25372)Termination phase: shuffling
% 2.99/1.65
% 2.99/1.65 % (25372)Memory used [KB]: 1407
% 2.99/1.65 % (25372)Time elapsed: 0.005 s
% 2.99/1.65 % (25372)Instructions burned: 5 (million)
% 2.99/1.65 % (25372)------------------------------
% 2.99/1.65 % (25372)------------------------------
% 2.99/1.66 % (25378)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25099 for (2999ds/3Mi)
% 2.99/1.66 % (25378)Instruction limit reached!
% 2.99/1.66 % (25378)------------------------------
% 2.99/1.66 % (25378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.66 % (25378)Termination reason: Unknown
% 2.99/1.66 % (25378)Termination phase: shuffling
% 2.99/1.66
% 2.99/1.66 % (25378)Memory used [KB]: 1279
% 2.99/1.66 % (25378)Time elapsed: 0.003 s
% 2.99/1.66 % (25378)Instructions burned: 3 (million)
% 2.99/1.66 % (25378)------------------------------
% 2.99/1.66 % (25378)------------------------------
% 2.99/1.66 % (25373)Instruction limit reached!
% 2.99/1.66 % (25373)------------------------------
% 2.99/1.66 % (25373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.66 % (25373)Termination reason: Unknown
% 2.99/1.66 % (25373)Termination phase: Property scanning
% 2.99/1.66
% 2.99/1.66 % (25373)Memory used [KB]: 1663
% 2.99/1.66 % (25373)Time elapsed: 0.019 s
% 2.99/1.66 % (25373)Instructions burned: 29 (million)
% 2.99/1.66 % (25373)------------------------------
% 2.99/1.66 % (25373)------------------------------
% 2.99/1.67 % (25380)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_25099 for (2999ds/15Mi)
% 2.99/1.67 % (25379)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_25099 for (2999ds/37Mi)
% 2.99/1.67 % (25381)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_25099 for (2999ds/3Mi)
% 2.99/1.67 % (25382)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_25099 for (2999ds/1041Mi)
% 2.99/1.67 % (25381)Instruction limit reached!
% 2.99/1.67 % (25381)------------------------------
% 2.99/1.67 % (25381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.67 % (25381)Termination reason: Unknown
% 2.99/1.67 % (25381)Termination phase: shuffling
% 2.99/1.67
% 2.99/1.67 % (25381)Memory used [KB]: 1279
% 2.99/1.67 % (25381)Time elapsed: 0.004 s
% 2.99/1.67 % (25381)Instructions burned: 3 (million)
% 2.99/1.67 % (25381)------------------------------
% 2.99/1.67 % (25381)------------------------------
% 2.99/1.67 % (25380)Instruction limit reached!
% 2.99/1.67 % (25380)------------------------------
% 2.99/1.67 % (25380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.67 % (25380)Termination reason: Unknown
% 2.99/1.67 % (25380)Termination phase: shuffling
% 2.99/1.67
% 2.99/1.67 % (25380)Memory used [KB]: 1535
% 2.99/1.67 % (25380)Time elapsed: 0.010 s
% 2.99/1.67 % (25380)Instructions burned: 16 (million)
% 2.99/1.67 % (25380)------------------------------
% 2.99/1.67 % (25380)------------------------------
% 2.99/1.68 % (25383)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25099 for (2999ds/7Mi)
% 2.99/1.68 % (25376)First to succeed.
% 2.99/1.68 % (25383)Instruction limit reached!
% 2.99/1.68 % (25383)------------------------------
% 2.99/1.68 % (25383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.68 % (25383)Termination reason: Unknown
% 2.99/1.68 % (25383)Termination phase: shuffling
% 2.99/1.68
% 2.99/1.68 % (25383)Memory used [KB]: 1407
% 2.99/1.68 % (25383)Time elapsed: 0.005 s
% 2.99/1.68 % (25383)Instructions burned: 8 (million)
% 2.99/1.68 % (25383)------------------------------
% 2.99/1.68 % (25383)------------------------------
% 2.99/1.68 % (25376)Refutation found. Thanks to Tanya!
% 2.99/1.68 % SZS status Theorem for DTF2THF_25099
% 2.99/1.68 % SZS output start Proof for DTF2THF_25099
% 2.99/1.68 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.99/1.68 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 2.99/1.68 thf(type_def_8, type, set: ($tType) > $tType).
% 2.99/1.68 thf(type_def_9, type, a: $tType).
% 2.99/1.68 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 2.99/1.68 thf(func_def_1, type, set: ($tType) > $tType).
% 2.99/1.68 thf(func_def_2, type, itself: ($tType) > $tType).
% 2.99/1.68 thf(func_def_3, type, a: $tType).
% 2.99/1.68 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.99/1.68 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.99/1.68 thf(func_def_6, type, minus: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.99/1.68 thf(func_def_7, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.99/1.68 thf(func_def_8, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.99/1.68 thf(func_def_9, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.99/1.68 thf(func_def_10, type, bounded_lattice_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.99/1.68 thf(func_def_11, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_12, type, coinductive_gen_lset: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ X0)).
% 2.99/1.68 thf(func_def_13, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_14, type, coindu351974385stinct: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_15, type, coinductive_lfilter: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_16, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_17, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.99/1.68 thf(func_def_18, type, coinductive_llexord: !>[X0: $tType]:((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_19, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_20, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_21, type, coinductive_lnull: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_22, type, coinductive_lset: !>[X0: $tType]:(coinductive_llist @ X0 > set @ X0)).
% 2.99/1.68 thf(func_def_23, type, coinductive_lmember: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_24, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_25, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.99/1.68 thf(func_def_26, type, undefined: !>[X0: $tType]:(X0)).
% 2.99/1.68 thf(func_def_27, type, lList2435255213lllsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_28, type, lList21511617539llstsp: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_29, type, lList2236698231inlsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_30, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0)).
% 2.99/1.68 thf(func_def_31, type, lList2860480441nlstsp: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > $o)).
% 2.99/1.68 thf(func_def_32, type, lList22096119349pslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_33, type, lList21612149805nflsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_34, type, lList2370560421utlast: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_35, type, lList2170638824_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.99/1.68 thf(func_def_36, type, lList2281150353e_lrev: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_37, type, lList21148268032oslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_38, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.99/1.68 thf(func_def_39, type, top_top: !>[X0: $tType]:(X0)).
% 2.99/1.68 thf(func_def_40, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.99/1.68 thf(func_def_41, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.99/1.68 thf(func_def_42, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.99/1.68 thf(func_def_43, type, a2: set @ a).
% 2.99/1.68 thf(func_def_44, type, p: coinductive_llist @ a > $o).
% 2.99/1.68 thf(func_def_45, type, l: coinductive_llist @ a).
% 2.99/1.68 thf(func_def_46, type, la: coinductive_llist @ a).
% 2.99/1.68 thf(func_def_47, type, xs: coinductive_llist @ a).
% 2.99/1.68 thf(func_def_61, type, sK0: !>[X0: $tType]:(X0)).
% 2.99/1.68 thf(func_def_62, type, sK1: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_63, type, sK2: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.99/1.68 thf(func_def_64, type, sK3: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_65, type, sK4: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.99/1.68 thf(func_def_66, type, sK5: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_67, type, sK6: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.99/1.68 thf(func_def_68, type, sK7: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_69, type, sK8: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_70, type, sK9: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.99/1.68 thf(func_def_71, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.99/1.68 thf(func_def_72, type, sK11: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.99/1.68 thf(func_def_73, type, sK12: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_74, type, sK13: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.99/1.68 thf(func_def_75, type, sK14: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.99/1.68 thf(func_def_76, type, sK15: !>[X0: $tType]:(set @ X0 > X0)).
% 2.99/1.68 thf(func_def_78, type, ph17: !>[X0: $tType]:(X0)).
% 2.99/1.68 thf(f939,plain,(
% 2.99/1.68 $false),
% 2.99/1.68 inference(subsumption_resolution,[status(thm)],[f938,f894])).
% 2.99/1.68 thf(f894,plain,(
% 2.99/1.68 ((p @ coinductive_LNil @ a) = $true)),
% 2.99/1.68 inference(cnf_transformation,[status(thm)],[f609])).
% 2.99/1.68 thf(f609,plain,(
% 2.99/1.68 ((p @ coinductive_LNil @ a) = $true)),
% 2.99/1.68 inference(fool_elimination,[status(thm)],[f608])).
% 2.99/1.68 thf(f608,plain,(
% 2.99/1.68 (p @ coinductive_LNil @ a)),
% 2.99/1.68 inference(rectify,[status(thm)],[f1])).
% 2.99/1.68 thf(f1,axiom,(
% 2.99/1.68 (p @ coinductive_LNil @ a)),
% 2.99/1.68 file('/export/starexec/sandbox/tmp/tmp.OwTl828x0i/DTF2THF_25099.p',fact_0_init)).
% 2.99/1.68 thf(f938,plain,(
% 2.99/1.68 ((p @ coinductive_LNil @ a) != $true)),
% 2.99/1.68 inference(forward_demodulation,[status(thm)],[f913,f849])).
% 2.99/1.68 thf(f849,plain,(
% 2.99/1.68 ( ! [X0 : $tType] : ((coinductive_LNil @ X0 = (lList2281150353e_lrev @ X0 @ coinductive_LNil @ X0))) )),
% 2.99/1.68 inference(cnf_transformation,[status(thm)],[f4])).
% 2.99/1.68 thf(f4,axiom,(
% 2.99/1.68 ! [X0 : $tType] : (coinductive_LNil @ X0 = (lList2281150353e_lrev @ X0 @ coinductive_LNil @ X0))),
% 2.99/1.68 file('/export/starexec/sandbox/tmp/tmp.OwTl828x0i/DTF2THF_25099.p',fact_3_lrev__LNil)).
% 2.99/1.68 thf(f913,plain,(
% 2.99/1.68 ((p @ (lList2281150353e_lrev @ a @ coinductive_LNil @ a)) != $true)),
% 2.99/1.68 inference(definition_unfolding,[status(thm)],[f845,f888])).
% 2.99/1.68 thf(f888,plain,(
% 2.99/1.68 (coinductive_LNil @ a = la)),
% 2.99/1.68 inference(cnf_transformation,[status(thm)],[f2])).
% 2.99/1.68 thf(f2,axiom,(
% 2.99/1.68 (coinductive_LNil @ a = la)),
% 2.99/1.68 file('/export/starexec/sandbox/tmp/tmp.OwTl828x0i/DTF2THF_25099.p',fact_1_LNil__fin_Ohyps)).
% 2.99/1.68 thf(f845,plain,(
% 2.99/1.68 ((p @ (lList2281150353e_lrev @ a @ la)) != $true)),
% 2.99/1.68 inference(cnf_transformation,[status(thm)],[f744])).
% 2.99/1.68 thf(f744,plain,(
% 2.99/1.68 ((p @ (lList2281150353e_lrev @ a @ la)) != $true)),
% 2.99/1.68 inference(flattening,[status(thm)],[f335])).
% 2.99/1.68 thf(f335,plain,(
% 2.99/1.68 ~((p @ (lList2281150353e_lrev @ a @ la)) = $true)),
% 2.99/1.68 inference(fool_elimination,[status(thm)],[f334])).
% 2.99/1.68 thf(f334,plain,(
% 2.99/1.68 ~(p @ (lList2281150353e_lrev @ a @ la))),
% 2.99/1.68 inference(rectify,[status(thm)],[f274])).
% 2.99/1.68 thf(f274,negated_conjecture,(
% 2.99/1.68 ~(p @ (lList2281150353e_lrev @ a @ la))),
% 2.99/1.68 inference(negated_conjecture,[status(cth)],[f273])).
% 2.99/1.68 thf(f273,conjecture,(
% 2.99/1.68 (p @ (lList2281150353e_lrev @ a @ la))),
% 2.99/1.68 file('/export/starexec/sandbox/tmp/tmp.OwTl828x0i/DTF2THF_25099.p',conj_0)).
% 2.99/1.68 % SZS output end Proof for DTF2THF_25099
% 2.99/1.68 % (25376)------------------------------
% 2.99/1.68 % (25376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.68 % (25376)Termination reason: Refutation
% 2.99/1.68
% 2.99/1.68 % (25376)Memory used [KB]: 6268
% 2.99/1.68 % (25376)Time elapsed: 0.034 s
% 2.99/1.68 % (25376)Instructions burned: 53 (million)
% 2.99/1.68 % (25376)------------------------------
% 2.99/1.68 % (25376)------------------------------
% 2.99/1.68 % (25370)Success in time 0.055 s
%------------------------------------------------------------------------------