%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT187^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 08:45:04 AM UTC 2026
% Result : Theorem 2.40s 1.39s
% Output : Refutation 2.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : DAT187^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.08 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.27 % Computer : n018.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Tue Feb 24 06:10:46 EST 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.27 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 ---- Original DTF file ---
% 0.09/0.34 thf(spec,logic,$$dhol).
% 0.09/0.34 %------------------------------------------------------------------------------
% 0.09/0.34 % File : DAT187^1 : TPTP v9.2.1. Released v7.0.0.
% 0.09/0.34 % Domain : Data Structures
% 0.09/0.34 % Problem : Lazy lists II 1278
% 0.09/0.34 % Version : [Bla16] axioms : Especial.
% 0.09/0.34 % English :
% 0.09/0.34
% 0.09/0.34 % Refs : [Fri04] Friedrich (2004), Lazy Lists II
% 0.09/0.34 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.09/0.34 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.09/0.34 % Source : [Bla16]
% 0.09/0.34 % Names : llist2__1278.p [Bla16]
% 0.09/0.34
% 0.09/0.34 % Status : Theorem
% 0.09/0.34 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.09/0.34 % Syntax : Number of formulae : 338 ( 118 unt; 58 typ; 0 def)
% 0.09/0.34 % Number of atoms : 788 ( 206 equ; 0 cnn)
% 0.09/0.34 % Maximal formula atoms : 13 ( 2 avg)
% 0.09/0.34 % Number of connectives : 4584 ( 68 ~; 10 |; 51 &;4086 @)
% 0.09/0.34 % ( 0 <=>; 369 =>; 0 <=; 0 <~>)
% 0.09/0.34 % Maximal formula depth : 19 ( 8 avg)
% 0.09/0.34 % Number of types : 3 ( 2 usr)
% 0.09/0.34 % Number of type conns : 140 ( 140 >; 0 *; 0 +; 0 <<)
% 0.09/0.34 % Number of symbols : 57 ( 56 usr; 6 con; 0-5 aty)
% 0.09/0.34 % Number of variables : 1006 ( 39 ^; 895 !; 25 ?;1006 :)
% 0.09/0.34 % ( 47 !>; 0 ?*; 0 @-; 0 @+)
% 0.09/0.34 % SPC : TH1_THM_EQU_NAR
% 0.09/0.34
% 0.09/0.34 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.09/0.34 % 2016-07-13 14:52:29.673
% 0.09/0.34 %------------------------------------------------------------------------------
% 0.09/0.34 %----Could-be-implicit typings (5)
% 0.09/0.34 thf(ty_t_Coinductive__List_Ollist,type,
% 0.09/0.34 coinductive_llist: $tType > $tType ).
% 0.09/0.34
% 0.09/0.34 thf(ty_t_Set_Oset,type,
% 0.09/0.34 set: $tType > $tType ).
% 0.09/0.34
% 0.09/0.34 thf(ty_t_Nat_Onat,type,
% 0.09/0.34 nat: $tType ).
% 0.09/0.34
% 0.09/0.34 thf(ty_t_itself,type,
% 0.09/0.34 itself: $tType > $tType ).
% 0.09/0.34
% 0.09/0.34 thf(ty_tf_a,type,
% 0.09/0.34 a: $tType ).
% 0.09/0.34
% 0.09/0.34 %----Explicit typings (53)
% 0.09/0.34 thf(sy_cl_HOL_Otype,type,
% 0.09/0.34 type:
% 0.09/0.34 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_cl_Orderings_Oord,type,
% 0.09/0.34 ord:
% 0.09/0.34 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_cl_Orderings_Otop,type,
% 0.09/0.34 top:
% 0.09/0.34 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_cl_Orderings_Oorder,type,
% 0.09/0.34 order:
% 0.09/0.34 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_cl_Orderings_Olinorder,type,
% 0.09/0.34 linorder:
% 0.09/0.34 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_cl_Orderings_Opreorder,type,
% 0.09/0.34 preorder:
% 0.09/0.34 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_cl_Orderings_Oorder__top,type,
% 0.09/0.34 order_top:
% 0.09/0.34 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.09/0.34 ordered_ab_group_add:
% 0.09/0.34 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.09/0.34 coindu328551480prefix:
% 0.09/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_Coinductive__List_Olappend,type,
% 0.09/0.34 coinductive_lappend:
% 0.09/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_Coinductive__List_Ollast,type,
% 0.09/0.34 coinductive_llast:
% 0.09/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.09/0.34 coinductive_LCons:
% 0.09/0.34 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.09/0.34 coinductive_LNil:
% 0.09/0.34 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.09/0.34 coindu1478340336prefix:
% 0.09/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.09/0.34 minus_minus:
% 0.09/0.34 !>[A: $tType] : ( A > A > A ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 0.09/0.34 lList2435255213lllsts:
% 0.09/0.34 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.09/0.34 lList2236698231inlsts:
% 0.09/0.34 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.09/0.35 lList21916056377ts_rec:
% 0.09/0.35 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinpref,type,
% 0.09/0.35 lList21202317876inpref:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.09/0.35 lList22096119349pslsts:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfliveness,type,
% 0.09/0.35 lList21015763786veness:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 0.09/0.35 lList21612149805nflsts:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsafety,type,
% 0.09/0.35 lList21015939545safety:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsuff,type,
% 0.09/0.35 lList2649413865nfsuff:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 0.09/0.35 lList2370560421utlast:
% 0.09/0.35 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 0.09/0.35 lList2508575361_ldrop:
% 0.09/0.35 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oliveness,type,
% 0.09/0.35 lList21805353693veness:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 0.09/0.35 lList2170638824_llast:
% 0.09/0.35 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 0.09/0.35 lList21232602520length:
% 0.09/0.35 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 0.09/0.35 lList2281150353e_lrev:
% 0.09/0.35 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 0.09/0.35 lList22119844313_ltake:
% 0.09/0.35 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opfinpref,type,
% 0.09/0.35 lList2467029176inpref:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposliveness,type,
% 0.09/0.35 lList21952340509veness:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.09/0.35 lList21148268032oslsts:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opossafety,type,
% 0.09/0.35 lList292406316safety:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opprefix__closed,type,
% 0.09/0.35 lList21974196564closed:
% 0.09/0.35 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oprefix__closed,type,
% 0.09/0.35 lList21638733016closed:
% 0.09/0.35 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osafety,type,
% 0.09/0.35 lList21350011628safety:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuff,type,
% 0.09/0.35 lList21475143548e_suff:
% 0.09/0.35 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuffix__closed,type,
% 0.09/0.35 lList2736192599closed:
% 0.09/0.35 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_Nat_OSuc,type,
% 0.09/0.35 suc: nat > nat ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.09/0.35 ord_less:
% 0.09/0.35 !>[A: $tType] : ( A > A > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.09/0.35 ord_less_eq:
% 0.09/0.35 !>[A: $tType] : ( A > A > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.09/0.35 top_top:
% 0.09/0.35 !>[A: $tType] : A ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_Pure_Otype,type,
% 0.09/0.35 type2:
% 0.09/0.35 !>[A: $tType] : ( itself @ A ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_Set_OCollect,type,
% 0.09/0.35 collect:
% 0.09/0.35 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_c_member,type,
% 0.09/0.35 member:
% 0.09/0.35 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_v_P,type,
% 0.09/0.35 p: set @ ( coinductive_llist @ a ) ).
% 0.09/0.35
% 0.09/0.35 thf(sy_v_r____,type,
% 0.09/0.35 r: coinductive_llist @ a ).
% 0.09/0.35
% 0.09/0.35 thf(sy_v_s____,type,
% 0.09/0.35 s: coinductive_llist @ a ).
% 0.09/0.35
% 0.09/0.35 thf(sy_v_t____,type,
% 0.09/0.35 t: coinductive_llist @ a ).
% 0.09/0.35
% 0.09/0.35 thf(sy_v_u____,type,
% 0.09/0.35 u: coinductive_llist @ a ).
% 0.09/0.35
% 0.09/0.35 thf(sy_v_v____,type,
% 0.09/0.35 v: coinductive_llist @ a ).
% 0.09/0.35
% 0.09/0.35 %----Relevant facts (256)
% 0.09/0.35 thf(fact_0_tP,axiom,
% 0.09/0.35 member @ ( coinductive_llist @ a ) @ t @ p ).
% 0.09/0.35
% 0.09/0.35 % tP
% 0.09/0.35 thf(fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062,axiom,
% 0.09/0.35 ( t
% 0.09/0.35 = ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ v ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % \<open>t = r @@ u @@ v\<close>
% 0.09/0.35 thf(fact_2_psafety,axiom,
% 0.09/0.35 lList292406316safety @ a @ ( top_top @ ( set @ a ) ) @ p ).
% 0.09/0.35
% 0.09/0.35 % psafety
% 0.09/0.35 thf(fact_3_scons,axiom,
% 0.09/0.35 ( s
% 0.09/0.35 = ( coinductive_lappend @ a @ r @ u ) ) ).
% 0.09/0.35
% 0.09/0.35 % scons
% 0.09/0.35 thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_At_A_061_Ar_A_064_064_Au_A_064_064_Av_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.09/0.35 ~ ! [V: coinductive_llist @ a] :
% 0.09/0.35 ( t
% 0.09/0.35 != ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ V ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % \<open>\<And>thesis. (\<And>v. t = r @@ u @@ v \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.09/0.35 thf(fact_5_alllsts__UNIV,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % alllsts_UNIV
% 0.09/0.35 thf(fact_6__092_060open_062r_A_092_060in_062_Apfinpref_AUNIV_As_092_060close_062,axiom,
% 0.09/0.35 member @ ( coinductive_llist @ a ) @ r @ ( lList2467029176inpref @ a @ ( top_top @ ( set @ a ) ) @ s ) ).
% 0.09/0.35
% 0.09/0.35 % \<open>r \<in> pfinpref UNIV s\<close>
% 0.09/0.35 thf(fact_7_lappT,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lappT
% 0.09/0.35 thf(fact_8_lapp__all__invT,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_all_invT
% 0.09/0.35 thf(fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062u_O_As_A_061_Ar_A_064_064_Au_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.09/0.35 ~ ! [U: coinductive_llist @ a] :
% 0.09/0.35 ( s
% 0.09/0.35 != ( coinductive_lappend @ a @ r @ U ) ) ).
% 0.09/0.35
% 0.09/0.35 % \<open>\<And>thesis. (\<And>u. s = r @@ u \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.09/0.35 thf(fact_10_UNIV__I,axiom,
% 0.09/0.35 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % UNIV_I
% 0.09/0.35 thf(fact_11_iso__tuple__UNIV__I,axiom,
% 0.09/0.35 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % iso_tuple_UNIV_I
% 0.09/0.35 thf(fact_12_top__apply,axiom,
% 0.09/0.35 ! [C: $tType,D: $tType] :
% 0.09/0.35 ( ( top @ C @ ( type2 @ C ) )
% 0.09/0.35 => ( ( top_top @ ( D > C ) )
% 0.09/0.35 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % top_apply
% 0.09/0.35 thf(fact_13_lappend__assoc,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.09/0.35 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.09/0.35 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lappend_assoc
% 0.09/0.35 thf(fact_14_UNIV__eq__I,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A] :
% 0.09/0.35 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.09/0.35 => ( ( top_top @ ( set @ A ) )
% 0.09/0.35 = A2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % UNIV_eq_I
% 0.09/0.35 thf(fact_15_UNIV__witness,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % UNIV_witness
% 0.09/0.35 thf(fact_16_posliveness__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList21952340509veness @ A )
% 0.09/0.35 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList22096119349pslsts @ A @ A3 ) )
% 0.09/0.35 => ? [Y: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % posliveness_def
% 0.09/0.35 thf(fact_17_suff__all,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21475143548e_suff @ A @ A2 @ S ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % suff_all
% 0.09/0.35 thf(fact_18_safetyD,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A ),T: coinductive_llist @ A] :
% 0.09/0.35 ( ( lList21350011628safety @ A @ A2 @ P2 )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [R2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R2 @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 0.09/0.35 => ? [X4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R2 @ X4 ) @ P2 ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ T @ P2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % safetyD
% 0.09/0.35 thf(fact_19_safetyE,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ( ( lList21350011628safety @ A @ A2 @ P2 )
% 0.09/0.35 => ! [X4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [Xa: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList21202317876inpref @ A @ A2 @ X4 ) )
% 0.09/0.35 => ? [Xb: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xb @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xa @ Xb ) @ P2 ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X4 @ P2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % safetyE
% 0.09/0.35 thf(fact_20_safetyI,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ( ! [T2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [X4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList21202317876inpref @ A @ A2 @ T2 ) )
% 0.09/0.35 => ? [Xa: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X4 @ Xa ) @ P2 ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ T2 @ P2 ) ) )
% 0.09/0.35 => ( lList21350011628safety @ A @ A2 @ P2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % safetyI
% 0.09/0.35 thf(fact_21_spos,axiom,
% 0.09/0.35 ( s
% 0.09/0.35 != ( coinductive_LNil @ a ) ) ).
% 0.09/0.35
% 0.09/0.35 % spos
% 0.09/0.35 thf(fact_22_st,axiom,
% 0.09/0.35 ord_less_eq @ ( coinductive_llist @ a ) @ s @ t ).
% 0.09/0.35
% 0.09/0.35 % st
% 0.09/0.35 thf(fact_23_top__set__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( top_top @ ( set @ A ) )
% 0.09/0.35 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % top_set_def
% 0.09/0.35 thf(fact_24_finpref__suff,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finpref_suff
% 0.09/0.35 thf(fact_25_safety__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList21350011628safety @ A )
% 0.09/0.35 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.09/0.35 => ( ! [Y: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21202317876inpref @ A @ A3 @ X2 ) )
% 0.09/0.35 => ? [Z: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X2 @ P ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % safety_def
% 0.09/0.35 thf(fact_26_safety__prefix__closed,axiom,
% 0.09/0.35 ! [A: $tType,P2: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ( ( lList21350011628safety @ A @ ( top_top @ ( set @ A ) ) @ P2 )
% 0.09/0.35 => ( lList21638733016closed @ A @ P2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % safety_prefix_closed
% 0.09/0.35 thf(fact_27_possafety__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList292406316safety @ A )
% 0.09/0.35 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList21148268032oslsts @ A @ A3 ) )
% 0.09/0.35 => ( ! [Y: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2467029176inpref @ A @ A3 @ X2 ) )
% 0.09/0.35 => ? [Z: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X2 @ P ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % possafety_def
% 0.09/0.35 thf(fact_28_possafetyI,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ( ! [T2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [X4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2467029176inpref @ A @ A2 @ T2 ) )
% 0.09/0.35 => ? [Xa: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X4 @ Xa ) @ P2 ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ T2 @ P2 ) ) )
% 0.09/0.35 => ( lList292406316safety @ A @ A2 @ P2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % possafetyI
% 0.09/0.35 thf(fact_29_possafetyE,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ( ( lList292406316safety @ A @ A2 @ P2 )
% 0.09/0.35 => ! [X4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [Xa: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2467029176inpref @ A @ A2 @ X4 ) )
% 0.09/0.35 => ? [Xb: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xb @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xa @ Xb ) @ P2 ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X4 @ P2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % possafetyE
% 0.09/0.35 thf(fact_30_possafetyD,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A ),T: coinductive_llist @ A] :
% 0.09/0.35 ( ( lList292406316safety @ A @ A2 @ P2 )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [R2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R2 @ ( lList2467029176inpref @ A @ A2 @ T ) )
% 0.09/0.35 => ? [X4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R2 @ X4 ) @ P2 ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ T @ P2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % possafetyD
% 0.09/0.35 thf(fact_31_pfinpref__iff,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2467029176inpref @ A @ A2 @ S ) )
% 0.09/0.35 = ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21202317876inpref @ A @ A2 @ S ) )
% 0.09/0.35 & ( X
% 0.09/0.35 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % pfinpref_iff
% 0.09/0.35 thf(fact_32_suff__finpref__iff,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 0.09/0.35 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % suff_finpref_iff
% 0.09/0.35 thf(fact_33_suff__appE,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) )
% 0.09/0.35 => ~ ! [S2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( T
% 0.09/0.35 != ( coinductive_lappend @ A @ R @ S2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % suff_appE
% 0.09/0.35 thf(fact_34_suff__LNil,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A] :
% 0.09/0.35 ( ( lList21475143548e_suff @ A @ A2 @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % suff_LNil
% 0.09/0.35 thf(fact_35_top__empty__eq,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( top_top @ ( A > $o ) )
% 0.09/0.35 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % top_empty_eq
% 0.09/0.35 thf(fact_36_order__refl,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( preorder @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.09/0.35
% 0.09/0.35 % order_refl
% 0.09/0.35 thf(fact_37_llist__le__refl,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A] : ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ S ) ).
% 0.09/0.35
% 0.09/0.35 % llist_le_refl
% 0.09/0.35 thf(fact_38_top1I,axiom,
% 0.09/0.35 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.09/0.35
% 0.09/0.35 % top1I
% 0.09/0.35 thf(fact_39_LNil__is__lappend__conv,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( ( coinductive_LNil @ A )
% 0.09/0.35 = ( coinductive_lappend @ A @ S @ T ) )
% 0.09/0.35 = ( ( S
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 & ( T
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % LNil_is_lappend_conv
% 0.09/0.35 thf(fact_40_lappend__is__LNil__conv,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( ( coinductive_lappend @ A @ S @ T )
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( ( S
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 & ( T
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lappend_is_LNil_conv
% 0.09/0.35 thf(fact_41_lappend__code_I1_J,axiom,
% 0.09/0.35 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.09/0.35 = Ys ) ).
% 0.09/0.35
% 0.09/0.35 % lappend_code(1)
% 0.09/0.35 thf(fact_42_lappend__LNil2,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.09/0.35 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = Xs ) ).
% 0.09/0.35
% 0.09/0.35 % lappend_LNil2
% 0.09/0.35 thf(fact_43_LNil__eq__lappend__iff,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( ( coinductive_LNil @ A )
% 0.09/0.35 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.09/0.35 = ( ( Xs
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 & ( Ys
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % LNil_eq_lappend_iff
% 0.09/0.35 thf(fact_44_lappend__eq__LNil__iff,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( ( Xs
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 & ( Ys
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lappend_eq_LNil_iff
% 0.09/0.35 thf(fact_45_mem__Collect__eq,axiom,
% 0.09/0.35 ! [A: $tType,A4: A,P2: A > $o] :
% 0.09/0.35 ( ( member @ A @ A4 @ ( collect @ A @ P2 ) )
% 0.09/0.35 = ( P2 @ A4 ) ) ).
% 0.09/0.35
% 0.09/0.35 % mem_Collect_eq
% 0.09/0.35 thf(fact_46_Collect__mem__eq,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A] :
% 0.09/0.35 ( ( collect @ A
% 0.09/0.35 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.09/0.35 = A2 ) ).
% 0.09/0.35
% 0.09/0.35 % Collect_mem_eq
% 0.09/0.35 thf(fact_47_Collect__cong,axiom,
% 0.09/0.35 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.09/0.35 ( ! [X3: A] :
% 0.09/0.35 ( ( P2 @ X3 )
% 0.09/0.35 = ( Q @ X3 ) )
% 0.09/0.35 => ( ( collect @ A @ P2 )
% 0.09/0.35 = ( collect @ A @ Q ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % Collect_cong
% 0.09/0.35 thf(fact_48_ext,axiom,
% 0.09/0.35 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.09/0.35 ( ! [X3: A] :
% 0.09/0.35 ( ( F @ X3 )
% 0.09/0.35 = ( G @ X3 ) )
% 0.09/0.35 => ( F = G ) ) ).
% 0.09/0.35
% 0.09/0.35 % ext
% 0.09/0.35 thf(fact_49_same__lappend__eq,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( ( coinductive_lappend @ A @ R @ S )
% 0.09/0.35 = ( coinductive_lappend @ A @ R @ T ) )
% 0.09/0.35 = ( S = T ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % same_lappend_eq
% 0.09/0.35 thf(fact_50_lapp__fin__fin__iff,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_fin_fin_iff
% 0.09/0.35 thf(fact_51_le__LNil,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( S
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_LNil
% 0.09/0.35 thf(fact_52_LNil__le,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A] : ( ord_less_eq @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ S ) ).
% 0.09/0.35
% 0.09/0.35 % LNil_le
% 0.09/0.35 thf(fact_53_le__lappend,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A] : ( ord_less_eq @ ( coinductive_llist @ A ) @ R @ ( coinductive_lappend @ A @ R @ S ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_lappend
% 0.09/0.35 thf(fact_54_LNil__suff,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList21475143548e_suff @ A @ A2 @ S ) )
% 0.09/0.35 = ( S
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % LNil_suff
% 0.09/0.35 thf(fact_55_poslsts__UNIV,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 = ( S
% 0.09/0.35 != ( coinductive_LNil @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % poslsts_UNIV
% 0.09/0.35 thf(fact_56_fpslsts__iff,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.09/0.35 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 & ( S
% 0.09/0.35 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % fpslsts_iff
% 0.09/0.35 thf(fact_57_poslsts__iff,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.09/0.35 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( S
% 0.09/0.35 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % poslsts_iff
% 0.09/0.35 thf(fact_58_le__funD,axiom,
% 0.09/0.35 ! [B: $tType,A: $tType] :
% 0.09/0.35 ( ( ord @ B @ ( type2 @ B ) )
% 0.09/0.35 => ! [F: A > B,G: A > B,X: A] :
% 0.09/0.35 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.09/0.35 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_funD
% 0.09/0.35 thf(fact_59_le__funE,axiom,
% 0.09/0.35 ! [B: $tType,A: $tType] :
% 0.09/0.35 ( ( ord @ B @ ( type2 @ B ) )
% 0.09/0.35 => ! [F: A > B,G: A > B,X: A] :
% 0.09/0.35 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.09/0.35 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_funE
% 0.09/0.35 thf(fact_60_le__funI,axiom,
% 0.09/0.35 ! [B: $tType,A: $tType] :
% 0.09/0.35 ( ( ord @ B @ ( type2 @ B ) )
% 0.09/0.35 => ! [F: A > B,G: A > B] :
% 0.09/0.35 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.09/0.35 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_funI
% 0.09/0.35 thf(fact_61_le__fun__def,axiom,
% 0.09/0.35 ! [B: $tType,A: $tType] :
% 0.09/0.35 ( ( ord @ B @ ( type2 @ B ) )
% 0.09/0.35 => ( ( ord_less_eq @ ( A > B ) )
% 0.09/0.35 = ( ^ [F2: A > B,G2: A > B] :
% 0.09/0.35 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_fun_def
% 0.09/0.35 thf(fact_62_order__subst1,axiom,
% 0.09/0.35 ! [A: $tType,B: $tType] :
% 0.09/0.35 ( ( ( order @ B @ ( type2 @ B ) )
% 0.09/0.35 & ( order @ A @ ( type2 @ A ) ) )
% 0.09/0.35 => ! [A4: A,F: B > A,B2: B,C2: B] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A4 @ ( F @ B2 ) )
% 0.09/0.35 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.09/0.35 => ( ! [X3: B,Y2: B] :
% 0.09/0.35 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 0.09/0.35 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.09/0.35 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % order_subst1
% 0.09/0.35 thf(fact_63_order__subst2,axiom,
% 0.09/0.35 ! [A: $tType,C: $tType] :
% 0.09/0.35 ( ( ( order @ C @ ( type2 @ C ) )
% 0.09/0.35 & ( order @ A @ ( type2 @ A ) ) )
% 0.09/0.35 => ! [A4: A,B2: A,F: A > C,C2: C] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 0.09/0.35 => ( ! [X3: A,Y2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.09/0.35 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.09/0.35 => ( ord_less_eq @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % order_subst2
% 0.09/0.35 thf(fact_64_ord__eq__le__subst,axiom,
% 0.09/0.35 ! [A: $tType,B: $tType] :
% 0.09/0.35 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.09/0.35 & ( ord @ A @ ( type2 @ A ) ) )
% 0.09/0.35 => ! [A4: A,F: B > A,B2: B,C2: B] :
% 0.09/0.35 ( ( A4
% 0.09/0.35 = ( F @ B2 ) )
% 0.09/0.35 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.09/0.35 => ( ! [X3: B,Y2: B] :
% 0.09/0.35 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 0.09/0.35 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.09/0.35 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ord_eq_le_subst
% 0.09/0.35 thf(fact_65_ord__le__eq__subst,axiom,
% 0.09/0.35 ! [A: $tType,B: $tType] :
% 0.09/0.35 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.09/0.35 & ( ord @ A @ ( type2 @ A ) ) )
% 0.09/0.35 => ! [A4: A,B2: A,F: A > B,C2: B] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 => ( ( ( F @ B2 )
% 0.09/0.35 = C2 )
% 0.09/0.35 => ( ! [X3: A,Y2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.09/0.35 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.09/0.35 => ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ord_le_eq_subst
% 0.09/0.35 thf(fact_66_eq__iff,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ( ( ^ [Y3: A,Z2: A] : ( Y3 = Z2 ) )
% 0.09/0.35 = ( ^ [X2: A,Y: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.09/0.35 & ( ord_less_eq @ A @ Y @ X2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % eq_iff
% 0.09/0.35 thf(fact_67_antisym,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [X: A,Y4: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.09/0.35 => ( ( ord_less_eq @ A @ Y4 @ X )
% 0.09/0.35 => ( X = Y4 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % antisym
% 0.09/0.35 thf(fact_68_linear,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( linorder @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [X: A,Y4: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.09/0.35 | ( ord_less_eq @ A @ Y4 @ X ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % linear
% 0.09/0.35 thf(fact_69_eq__refl,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( preorder @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [X: A,Y4: A] :
% 0.09/0.35 ( ( X = Y4 )
% 0.09/0.35 => ( ord_less_eq @ A @ X @ Y4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % eq_refl
% 0.09/0.35 thf(fact_70_wlog__linorder__le,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( linorder @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [P2: A > A > $o,B2: A,A4: A] :
% 0.09/0.35 ( ! [A5: A,B3: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.09/0.35 => ( P2 @ A5 @ B3 ) )
% 0.09/0.35 => ( ( ( P2 @ B2 @ A4 )
% 0.09/0.35 => ( P2 @ A4 @ B2 ) )
% 0.09/0.35 => ( P2 @ A4 @ B2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % wlog_linorder_le
% 0.09/0.35 thf(fact_71_le__cases,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( linorder @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [X: A,Y4: A] :
% 0.09/0.35 ( ~ ( ord_less_eq @ A @ X @ Y4 )
% 0.09/0.35 => ( ord_less_eq @ A @ Y4 @ X ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_cases
% 0.09/0.35 thf(fact_72_order_Otrans,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A,B2: A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.09/0.35 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % order.trans
% 0.09/0.35 thf(fact_73_le__cases3,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( linorder @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [X: A,Y4: A,Z3: A] :
% 0.09/0.35 ( ( ( ord_less_eq @ A @ X @ Y4 )
% 0.09/0.35 => ~ ( ord_less_eq @ A @ Y4 @ Z3 ) )
% 0.09/0.35 => ( ( ( ord_less_eq @ A @ Y4 @ X )
% 0.09/0.35 => ~ ( ord_less_eq @ A @ X @ Z3 ) )
% 0.09/0.35 => ( ( ( ord_less_eq @ A @ X @ Z3 )
% 0.09/0.35 => ~ ( ord_less_eq @ A @ Z3 @ Y4 ) )
% 0.09/0.35 => ( ( ( ord_less_eq @ A @ Z3 @ Y4 )
% 0.09/0.35 => ~ ( ord_less_eq @ A @ Y4 @ X ) )
% 0.09/0.35 => ( ( ( ord_less_eq @ A @ Y4 @ Z3 )
% 0.09/0.35 => ~ ( ord_less_eq @ A @ Z3 @ X ) )
% 0.09/0.35 => ~ ( ( ord_less_eq @ A @ Z3 @ X )
% 0.09/0.35 => ~ ( ord_less_eq @ A @ X @ Y4 ) ) ) ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_cases3
% 0.09/0.35 thf(fact_74_antisym__conv,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [Y4: A,X: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ Y4 @ X )
% 0.09/0.35 => ( ( ord_less_eq @ A @ X @ Y4 )
% 0.09/0.35 = ( X = Y4 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % antisym_conv
% 0.09/0.35 thf(fact_75_ord__eq__le__trans,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ord @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A,B2: A,C2: A] :
% 0.09/0.35 ( ( A4 = B2 )
% 0.09/0.35 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.09/0.35 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ord_eq_le_trans
% 0.09/0.35 thf(fact_76_ord__le__eq__trans,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ord @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A,B2: A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 => ( ( B2 = C2 )
% 0.09/0.35 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ord_le_eq_trans
% 0.09/0.35 thf(fact_77_order__class_Oorder_Oantisym,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A,B2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 => ( ( ord_less_eq @ A @ B2 @ A4 )
% 0.09/0.35 => ( A4 = B2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % order_class.order.antisym
% 0.09/0.35 thf(fact_78_order__trans,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( preorder @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [X: A,Y4: A,Z3: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.09/0.35 => ( ( ord_less_eq @ A @ Y4 @ Z3 )
% 0.09/0.35 => ( ord_less_eq @ A @ X @ Z3 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % order_trans
% 0.09/0.35 thf(fact_79_dual__order_Orefl,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 0.09/0.35
% 0.09/0.35 % dual_order.refl
% 0.09/0.35 thf(fact_80_linorder__wlog,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( linorder @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [P2: A > A > $o,A4: A,B2: A] :
% 0.09/0.35 ( ! [A5: A,B3: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.09/0.35 => ( P2 @ A5 @ B3 ) )
% 0.09/0.35 => ( ! [A5: A,B3: A] :
% 0.09/0.35 ( ( P2 @ B3 @ A5 )
% 0.09/0.35 => ( P2 @ A5 @ B3 ) )
% 0.09/0.35 => ( P2 @ A4 @ B2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % linorder_wlog
% 0.09/0.35 thf(fact_81_dual__order_Otrans,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [B2: A,A4: A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ B2 @ A4 )
% 0.09/0.35 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.09/0.35 => ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % dual_order.trans
% 0.09/0.35 thf(fact_82_dual__order_Oantisym,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [B2: A,A4: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ B2 @ A4 )
% 0.09/0.35 => ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 => ( A4 = B2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % dual_order.antisym
% 0.09/0.35 thf(fact_83_pref__locally__linear,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,X: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ X )
% 0.09/0.35 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ T @ X )
% 0.09/0.35 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.09/0.35 | ( ord_less_eq @ ( coinductive_llist @ A ) @ T @ S ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % pref_locally_linear
% 0.09/0.35 thf(fact_84_prefix__closed__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList21638733016closed @ A )
% 0.09/0.35 = ( ^ [A3: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ A3 )
% 0.09/0.35 => ! [S3: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ X2 )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ S3 @ A3 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % prefix_closed_def
% 0.09/0.35 thf(fact_85_llist__le__anti__sym,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.09/0.35 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ T @ S )
% 0.09/0.35 => ( S = T ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_le_anti_sym
% 0.09/0.35 thf(fact_86_finlsts_OLNil__fin,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts.LNil_fin
% 0.09/0.35 thf(fact_87_llist__le__trans,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ R @ S )
% 0.09/0.35 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.09/0.35 => ( ord_less_eq @ ( coinductive_llist @ A ) @ R @ T ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_le_trans
% 0.09/0.35 thf(fact_88_llist__le__finT,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ R @ S )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_le_finT
% 0.09/0.35 thf(fact_89_finT__simp,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finT_simp
% 0.09/0.35 thf(fact_90_fin__finite,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % fin_finite
% 0.09/0.35 thf(fact_91_lappfin__finT,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lappfin_finT
% 0.09/0.35 thf(fact_92_lapp__fin__fin__lemma,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_fin_fin_lemma
% 0.09/0.35 thf(fact_93_finite__lemma,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B4 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B4 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finite_lemma
% 0.09/0.35 thf(fact_94_finsubsetall,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finsubsetall
% 0.09/0.35 thf(fact_95_top__greatest,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order_top @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ ( top_top @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % top_greatest
% 0.09/0.35 thf(fact_96_top_Oextremum__unique,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order_top @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.09/0.35 = ( A4
% 0.09/0.35 = ( top_top @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % top.extremum_unique
% 0.09/0.35 thf(fact_97_top_Oextremum__uniqueI,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order_top @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.09/0.35 => ( A4
% 0.09/0.35 = ( top_top @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % top.extremum_uniqueI
% 0.09/0.35 thf(fact_98_lappend__LNil__LNil,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 % lappend_LNil_LNil
% 0.09/0.35 thf(fact_99_llist__le__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) )
% 0.09/0.35 = ( ^ [S3: coinductive_llist @ A,T3: coinductive_llist @ A] :
% 0.09/0.35 ? [D2: coinductive_llist @ A] :
% 0.09/0.35 ( T3
% 0.09/0.35 = ( coinductive_lappend @ A @ S3 @ D2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_le_def
% 0.09/0.35 thf(fact_100_finpref__fin,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21202317876inpref @ A @ A2 @ S ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finpref_fin
% 0.09/0.35 thf(fact_101_alllsts_OLNil__all,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % alllsts.LNil_all
% 0.09/0.35 thf(fact_102_suff__finpref,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,R: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % suff_finpref
% 0.09/0.35 thf(fact_103_pprefix__closed__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList21974196564closed @ A )
% 0.09/0.35 = ( ^ [A3: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ A3 )
% 0.09/0.35 => ! [S3: coinductive_llist @ A] :
% 0.09/0.35 ( ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ X2 )
% 0.09/0.35 & ( S3
% 0.09/0.35 != ( coinductive_LNil @ A ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ S3 @ A3 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % pprefix_closed_def
% 0.09/0.35 thf(fact_104_livenessE,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A ),S: coinductive_llist @ A] :
% 0.09/0.35 ( ( lList21805353693veness @ A @ A2 @ P2 )
% 0.09/0.35 => ( ! [T2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ~ ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T2 ) @ P2 ) )
% 0.09/0.35 => ~ ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % livenessE
% 0.09/0.35 thf(fact_105_livenessI,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ( ! [S2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ? [X4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S2 @ X4 ) @ P2 ) ) )
% 0.09/0.35 => ( lList21805353693veness @ A @ A2 @ P2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % livenessI
% 0.09/0.35 thf(fact_106_liveness__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList21805353693veness @ A )
% 0.09/0.35 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.09/0.35 => ? [Y: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % liveness_def
% 0.09/0.35 thf(fact_107_suffix__closed__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList2736192599closed @ A )
% 0.09/0.35 = ( ^ [A3: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ A3 )
% 0.09/0.35 => ! [S3: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ X2 @ S3 )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ S3 @ A3 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % suffix_closed_def
% 0.09/0.35 thf(fact_108_lrev__lappend,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.09/0.35 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lrev_lappend
% 0.09/0.35 thf(fact_109_LNil__is__lrev__conv,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( ( coinductive_LNil @ A )
% 0.09/0.35 = ( lList2281150353e_lrev @ A @ Xs ) )
% 0.09/0.35 = ( Xs
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % LNil_is_lrev_conv
% 0.09/0.35 thf(fact_110_lrev__is__LNil__conv,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( Xs
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lrev_is_LNil_conv
% 0.09/0.35 thf(fact_111_top__conj_I2_J,axiom,
% 0.09/0.35 ! [A: $tType,P2: $o,X: A] :
% 0.09/0.35 ( ( P2
% 0.09/0.35 & ( top_top @ ( A > $o ) @ X ) )
% 0.09/0.35 = P2 ) ).
% 0.09/0.35
% 0.09/0.35 % top_conj(2)
% 0.09/0.35 thf(fact_112_lrev__LNil,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 % lrev_LNil
% 0.09/0.35 thf(fact_113_lrevT,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lrevT
% 0.09/0.35 thf(fact_114_lrev__is__lrev__conv,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.09/0.35 = ( lList2281150353e_lrev @ A @ Ys ) )
% 0.09/0.35 = ( Xs = Ys ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lrev_is_lrev_conv
% 0.09/0.35 thf(fact_115_lrev__lrev__ident,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 0.09/0.35 = Xs ) ) ).
% 0.09/0.35
% 0.09/0.35 % lrev_lrev_ident
% 0.09/0.35 thf(fact_116_finlsts__mono,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList2236698231inlsts @ A @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts_mono
% 0.09/0.35 thf(fact_117_alllsts__mono,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A2 ) @ ( lList2435255213lllsts @ A @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % alllsts_mono
% 0.09/0.35 thf(fact_118_fpslsts__mono,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList22096119349pslsts @ A @ A2 ) @ ( lList22096119349pslsts @ A @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % fpslsts_mono
% 0.09/0.35 thf(fact_119_poslsts__mono,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21148268032oslsts @ A @ A2 ) @ ( lList21148268032oslsts @ A @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % poslsts_mono
% 0.09/0.35 thf(fact_120_subset__UNIV,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % subset_UNIV
% 0.09/0.35 thf(fact_121_finpref__mono2,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.09/0.35 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21202317876inpref @ A @ A2 @ S ) @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finpref_mono2
% 0.09/0.35 thf(fact_122_suff__mono2,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.09/0.35 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21475143548e_suff @ A @ A2 @ T ) @ ( lList21475143548e_suff @ A @ A2 @ S ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % suff_mono2
% 0.09/0.35 thf(fact_123_top__conj_I1_J,axiom,
% 0.09/0.35 ! [A: $tType,X: A,P2: $o] :
% 0.09/0.35 ( ( ( top_top @ ( A > $o ) @ X )
% 0.09/0.35 & P2 )
% 0.09/0.35 = P2 ) ).
% 0.09/0.35
% 0.09/0.35 % top_conj(1)
% 0.09/0.35 thf(fact_124_lrev__LCons,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.09/0.35 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lrev_LCons
% 0.09/0.35 thf(fact_125_take__fin,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % take_fin
% 0.09/0.35 thf(fact_126_infsuff__finpref,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,R: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infsuff_finpref
% 0.09/0.35 thf(fact_127_ltake__fin,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ltake_fin
% 0.09/0.35 thf(fact_128_lbutlast__LNil,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 % lbutlast_LNil
% 0.09/0.35 thf(fact_129_subsetI,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ! [X3: A] :
% 0.09/0.35 ( ( member @ A @ X3 @ A2 )
% 0.09/0.35 => ( member @ A @ X3 @ B4 ) )
% 0.09/0.35 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.09/0.35
% 0.09/0.35 % subsetI
% 0.09/0.35 thf(fact_130_subset__antisym,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A2 )
% 0.09/0.35 => ( A2 = B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % subset_antisym
% 0.09/0.35 thf(fact_131_llist_Oinject,axiom,
% 0.09/0.35 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.09/0.35 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.09/0.35 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.09/0.35 = ( ( X21 = Y21 )
% 0.09/0.35 & ( X22 = Y22 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist.inject
% 0.09/0.35 thf(fact_132_lappend__code_I2_J,axiom,
% 0.09/0.35 ! [A: $tType,Xa2: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa2 @ X ) @ Ys )
% 0.09/0.35 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lappend_code(2)
% 0.09/0.35 thf(fact_133_LConsE,axiom,
% 0.09/0.35 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 = ( ( member @ A @ X @ A2 )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % LConsE
% 0.09/0.35 thf(fact_134_le__LCons,axiom,
% 0.09/0.35 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 0.09/0.35 = ( ( X = Y4 )
% 0.09/0.35 & ( ord_less_eq @ ( coinductive_llist @ A ) @ Xs @ Ys ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % le_LCons
% 0.09/0.35 thf(fact_135_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 0.09/0.35 ! [A: $tType,I: nat] :
% 0.09/0.35 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 % LList2_Mirabelle_hamjzmohle.ltake_LNil
% 0.09/0.35 thf(fact_136_lbutlast__LCons,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( ( R
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.09/0.35 = ( coinductive_LNil @ A ) ) )
% 0.09/0.35 & ( ( R
% 0.09/0.35 != ( coinductive_LNil @ A ) )
% 0.09/0.35 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.09/0.35 = ( coinductive_LCons @ A @ A4 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lbutlast_LCons
% 0.09/0.35 thf(fact_137_lbutlast__snoc,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( lList2370560421utlast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 0.09/0.35 = Xs ) ) ).
% 0.09/0.35
% 0.09/0.35 % lbutlast_snoc
% 0.09/0.35 thf(fact_138_set__mp,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A,X: A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ( member @ A @ X @ A2 )
% 0.09/0.35 => ( member @ A @ X @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % set_mp
% 0.09/0.35 thf(fact_139_in__mono,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A,X: A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ( member @ A @ X @ A2 )
% 0.09/0.35 => ( member @ A @ X @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % in_mono
% 0.09/0.35 thf(fact_140_subsetD,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ( member @ A @ C2 @ A2 )
% 0.09/0.35 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % subsetD
% 0.09/0.35 thf(fact_141_subsetCE,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ( member @ A @ C2 @ A2 )
% 0.09/0.35 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % subsetCE
% 0.09/0.35 thf(fact_142_equalityE,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( A2 = B4 )
% 0.09/0.35 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % equalityE
% 0.09/0.35 thf(fact_143_subset__eq,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) )
% 0.09/0.35 = ( ^ [A3: set @ A,B5: set @ A] :
% 0.09/0.35 ! [X2: A] :
% 0.09/0.35 ( ( member @ A @ X2 @ A3 )
% 0.09/0.35 => ( member @ A @ X2 @ B5 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % subset_eq
% 0.09/0.35 thf(fact_144_equalityD1,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( A2 = B4 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.09/0.35
% 0.09/0.35 % equalityD1
% 0.09/0.35 thf(fact_145_equalityD2,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( A2 = B4 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % equalityD2
% 0.09/0.35 thf(fact_146_set__rev__mp,axiom,
% 0.09/0.35 ! [A: $tType,X: A,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( member @ A @ X @ A2 )
% 0.09/0.35 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( member @ A @ X @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % set_rev_mp
% 0.09/0.35 thf(fact_147_subset__iff,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) )
% 0.09/0.35 = ( ^ [A3: set @ A,B5: set @ A] :
% 0.09/0.35 ! [T3: A] :
% 0.09/0.35 ( ( member @ A @ T3 @ A3 )
% 0.09/0.35 => ( member @ A @ T3 @ B5 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % subset_iff
% 0.09/0.35 thf(fact_148_rev__subsetD,axiom,
% 0.09/0.35 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( member @ A @ C2 @ A2 )
% 0.09/0.35 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % rev_subsetD
% 0.09/0.35 thf(fact_149_subset__refl,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.09/0.35
% 0.09/0.35 % subset_refl
% 0.09/0.35 thf(fact_150_Collect__mono,axiom,
% 0.09/0.35 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.09/0.35 ( ! [X3: A] :
% 0.09/0.35 ( ( P2 @ X3 )
% 0.09/0.35 => ( Q @ X3 ) )
% 0.09/0.35 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % Collect_mono
% 0.09/0.35 thf(fact_151_subset__trans,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A,C3: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % subset_trans
% 0.09/0.35 thf(fact_152_set__eq__subset,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ^ [Y3: set @ A,Z2: set @ A] : ( Y3 = Z2 ) )
% 0.09/0.35 = ( ^ [A3: set @ A,B5: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 0.09/0.35 & ( ord_less_eq @ ( set @ A ) @ B5 @ A3 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % set_eq_subset
% 0.09/0.35 thf(fact_153_contra__subsetD,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ~ ( member @ A @ C2 @ B4 )
% 0.09/0.35 => ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % contra_subsetD
% 0.09/0.35 thf(fact_154_Collect__mono__iff,axiom,
% 0.09/0.35 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) )
% 0.09/0.35 = ( ! [X2: A] :
% 0.09/0.35 ( ( P2 @ X2 )
% 0.09/0.35 => ( Q @ X2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % Collect_mono_iff
% 0.09/0.35 thf(fact_155_llistE,axiom,
% 0.09/0.35 ! [A: $tType,Y4: coinductive_llist @ A] :
% 0.09/0.35 ( ( Y4
% 0.09/0.35 != ( coinductive_LNil @ A ) )
% 0.09/0.35 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.09/0.35 ( Y4
% 0.09/0.35 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llistE
% 0.09/0.35 thf(fact_156_neq__LNil__conv,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.09/0.35 ( ( Xs
% 0.09/0.35 != ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.09/0.35 ( Xs
% 0.09/0.35 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % neq_LNil_conv
% 0.09/0.35 thf(fact_157_llist_Odistinct_I1_J,axiom,
% 0.09/0.35 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.09/0.35 ( ( coinductive_LNil @ A )
% 0.09/0.35 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist.distinct(1)
% 0.09/0.35 thf(fact_158_finlsts_OLCons__fin,axiom,
% 0.09/0.35 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ A @ A4 @ A2 )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts.LCons_fin
% 0.09/0.35 thf(fact_159_alllsts_OLCons__all,axiom,
% 0.09/0.35 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ A @ A4 @ A2 )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % alllsts.LCons_all
% 0.09/0.35 thf(fact_160_lappend__snocL1__conv__LCons2,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.09/0.35 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lappend_snocL1_conv_LCons2
% 0.09/0.35 thf(fact_161_finlsts_Oinducts,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P2: ( coinductive_llist @ A ) > $o] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( P2 @ ( coinductive_LNil @ A ) )
% 0.09/0.35 => ( ! [L2: coinductive_llist @ A,A5: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( P2 @ L2 )
% 0.09/0.35 => ( ( member @ A @ A5 @ A2 )
% 0.09/0.35 => ( P2 @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 0.09/0.35 => ( P2 @ X ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts.inducts
% 0.09/0.35 thf(fact_162_finlsts__induct,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P2: ( coinductive_llist @ A ) > $o] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [L2: coinductive_llist @ A] :
% 0.09/0.35 ( ( L2
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 => ( P2 @ L2 ) )
% 0.09/0.35 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( P2 @ L2 )
% 0.09/0.35 => ( ( member @ A @ A5 @ A2 )
% 0.09/0.35 => ( P2 @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 0.09/0.35 => ( P2 @ X ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts_induct
% 0.09/0.35 thf(fact_163_finlsts_Osimps,axiom,
% 0.09/0.35 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 = ( ( A4
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 | ? [L3: coinductive_llist @ A,A6: A] :
% 0.09/0.35 ( ( A4
% 0.09/0.35 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts.simps
% 0.09/0.35 thf(fact_164_finlsts_Ocases,axiom,
% 0.09/0.35 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( A4
% 0.09/0.35 != ( coinductive_LNil @ A ) )
% 0.09/0.35 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 0.09/0.35 ( ( A4
% 0.09/0.35 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts.cases
% 0.09/0.35 thf(fact_165_alllsts_Ocases,axiom,
% 0.09/0.35 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ( A4
% 0.09/0.35 != ( coinductive_LNil @ A ) )
% 0.09/0.35 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 0.09/0.35 ( ( A4
% 0.09/0.35 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % alllsts.cases
% 0.09/0.35 thf(fact_166_alllsts_Osimps,axiom,
% 0.09/0.35 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 = ( ( A4
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 | ? [L3: coinductive_llist @ A,A6: A] :
% 0.09/0.35 ( ( A4
% 0.09/0.35 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % alllsts.simps
% 0.09/0.35 thf(fact_167_alllsts_Ocoinduct,axiom,
% 0.09/0.35 ! [A: $tType,X5: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( X5 @ X )
% 0.09/0.35 => ( ! [X3: coinductive_llist @ A] :
% 0.09/0.35 ( ( X5 @ X3 )
% 0.09/0.35 => ( ( X3
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 | ? [L4: coinductive_llist @ A,A7: A] :
% 0.09/0.35 ( ( X3
% 0.09/0.35 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 0.09/0.35 & ( ( X5 @ L4 )
% 0.09/0.35 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.09/0.35 & ( member @ A @ A7 @ A2 ) ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % alllsts.coinduct
% 0.09/0.35 thf(fact_168_not__LCons__le__LNil,axiom,
% 0.09/0.35 ! [A: $tType,A4: A,L: coinductive_llist @ A] :
% 0.09/0.35 ~ ( ord_less_eq @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( coinductive_LNil @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 % not_LCons_le_LNil
% 0.09/0.35 thf(fact_169_fps__induct,axiom,
% 0.09/0.35 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,P2: ( coinductive_llist @ A ) > $o] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [A5: A] :
% 0.09/0.35 ( ( member @ A @ A5 @ A2 )
% 0.09/0.35 => ( P2 @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) )
% 0.09/0.35 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.09/0.35 => ( ( P2 @ L2 )
% 0.09/0.35 => ( ( member @ A @ A5 @ A2 )
% 0.09/0.35 => ( P2 @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 0.09/0.35 => ( P2 @ L ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % fps_induct
% 0.09/0.35 thf(fact_170_fpslsts__cases,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.09/0.35 => ~ ! [A5: A,Rs: coinductive_llist @ A] :
% 0.09/0.35 ( ( R
% 0.09/0.35 = ( coinductive_LCons @ A @ A5 @ Rs ) )
% 0.09/0.35 => ( ( member @ A @ A5 @ A2 )
% 0.09/0.35 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % fpslsts_cases
% 0.09/0.35 thf(fact_171_infsuff__mono2,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.09/0.35 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2649413865nfsuff @ A @ A2 @ T ) @ ( lList2649413865nfsuff @ A @ A2 @ S ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infsuff_mono2
% 0.09/0.35 thf(fact_172_lrev__induct,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,P2: ( coinductive_llist @ A ) > $o] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( P2 @ ( coinductive_LNil @ A ) )
% 0.09/0.35 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( P2 @ Xs3 )
% 0.09/0.35 => ( ( member @ A @ X3 @ A2 )
% 0.09/0.35 => ( P2 @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 0.09/0.35 => ( P2 @ Xs ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lrev_induct
% 0.09/0.35 thf(fact_173_finlsts__rev__cases,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( T
% 0.09/0.35 != ( coinductive_LNil @ A ) )
% 0.09/0.35 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ A @ A5 @ A2 )
% 0.09/0.35 => ( T
% 0.09/0.35 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts_rev_cases
% 0.09/0.35 thf(fact_174_llast__snoc,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 0.09/0.35 = X ) ) ).
% 0.09/0.35
% 0.09/0.35 % llast_snoc
% 0.09/0.35 thf(fact_175_LList2__Mirabelle__hamjzmohle_Ollast__lappend,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,Y4: coinductive_llist @ A,A4: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ Y4 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ X @ ( coinductive_LCons @ A @ A4 @ Y4 ) ) )
% 0.09/0.35 = ( lList2170638824_llast @ A @ ( coinductive_LCons @ A @ A4 @ Y4 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % LList2_Mirabelle_hamjzmohle.llast_lappend
% 0.09/0.35 thf(fact_176_lbutlast__lapp__llast,axiom,
% 0.09/0.35 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.09/0.35 => ( L
% 0.09/0.35 = ( coinductive_lappend @ A @ ( lList2370560421utlast @ A @ L ) @ ( coinductive_LCons @ A @ ( lList2170638824_llast @ A @ L ) @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lbutlast_lapp_llast
% 0.09/0.35 thf(fact_177_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 0.09/0.35 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A4: B] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 0.09/0.35 => ( ( ( R
% 0.09/0.35 = ( coinductive_LNil @ B ) )
% 0.09/0.35 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 0.09/0.35 = A4 ) )
% 0.09/0.35 & ( ( R
% 0.09/0.35 != ( coinductive_LNil @ B ) )
% 0.09/0.35 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 0.09/0.35 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % LList2_Mirabelle_hamjzmohle.llast_LCons
% 0.09/0.35 thf(fact_178_ltake__lappend__llength,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 0.09/0.35 = R ) ) ).
% 0.09/0.35
% 0.09/0.35 % ltake_lappend_llength
% 0.09/0.35 thf(fact_179_infsuff__finpref__iff,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21202317876inpref @ A @ A2 @ R ) )
% 0.09/0.35 = ( member @ ( coinductive_llist @ A ) @ R @ ( lList2649413865nfsuff @ A @ A2 @ T ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infsuff_finpref_iff
% 0.09/0.35 thf(fact_180_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 0.09/0.35 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 0.09/0.35 = ( ( Xs
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 | ? [Xs2: coinductive_llist @ A] :
% 0.09/0.35 ( ( Xs
% 0.09/0.35 = ( coinductive_LCons @ A @ Y4 @ Xs2 ) )
% 0.09/0.35 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.09/0.35 thf(fact_181_lapp__inf,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( coinductive_lappend @ A @ S @ T )
% 0.09/0.35 = S ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_inf
% 0.09/0.35 thf(fact_182_notfin__inf,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A] :
% 0.09/0.35 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.09/0.35 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % notfin_inf
% 0.09/0.35 thf(fact_183_notinf__fin,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A] :
% 0.09/0.35 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.09/0.35 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % notinf_fin
% 0.09/0.35 thf(fact_184_infsuff__LNil,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A] :
% 0.09/0.35 ( ( lList2649413865nfsuff @ A @ A2 @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( lList21612149805nflsts @ A @ A2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % infsuff_LNil
% 0.09/0.35 thf(fact_185_llength__take,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 0.09/0.35 = I ) ) ).
% 0.09/0.35
% 0.09/0.35 % llength_take
% 0.09/0.35 thf(fact_186_inflstsI,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % inflstsI
% 0.09/0.35 thf(fact_187_infsuff__inf,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2649413865nfsuff @ A @ A2 @ S ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infsuff_inf
% 0.09/0.35 thf(fact_188_infT__simp,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infT_simp
% 0.09/0.35 thf(fact_189_llist__inf__le,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.09/0.35 = ( S = T ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_inf_le
% 0.09/0.35 thf(fact_190_infsubsetall,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infsubsetall
% 0.09/0.35 thf(fact_191_inflstsI2,axiom,
% 0.09/0.35 ! [A: $tType,A4: A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ A @ A4 @ A2 )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % inflstsI2
% 0.09/0.35 thf(fact_192_inflsts__cases,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ A @ A5 @ A2 )
% 0.09/0.35 => ( S
% 0.09/0.35 != ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % inflsts_cases
% 0.09/0.35 thf(fact_193_fin__inf__cases,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A] :
% 0.09/0.35 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % fin_inf_cases
% 0.09/0.35 thf(fact_194_lapp__fin__infT,axiom,
% 0.09/0.35 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_fin_infT
% 0.09/0.35 thf(fact_195_lapp__inv2T,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 0.09/0.35 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_inv2T
% 0.09/0.35 thf(fact_196_lapp__infT,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 0.09/0.35 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_infT
% 0.09/0.35 thf(fact_197_app__invT,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % app_invT
% 0.09/0.35 thf(fact_198_alllstsE,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % alllstsE
% 0.09/0.35 thf(fact_199_prefix__lemma,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,Y4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ Y4 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ! [S2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S2 @ X )
% 0.09/0.35 => ( ord_less_eq @ ( coinductive_llist @ A ) @ S2 @ Y4 ) ) )
% 0.09/0.35 => ( X = Y4 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % prefix_lemma
% 0.09/0.35 thf(fact_200_inf__neqE,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,Y4: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ Y4 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( ( X != Y4 )
% 0.09/0.35 => ~ ! [S2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S2 @ X )
% 0.09/0.35 => ( ord_less_eq @ ( coinductive_llist @ A ) @ S2 @ Y4 ) ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % inf_neqE
% 0.09/0.35 thf(fact_201_inflsts__mono,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21612149805nflsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % inflsts_mono
% 0.09/0.35 thf(fact_202_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.09/0.35
% 0.09/0.35 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.09/0.35 thf(fact_203_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.09/0.35 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.09/0.35 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = ( Xs
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.09/0.35 thf(fact_204_finpref__infsuff,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finpref_infsuff
% 0.09/0.35 thf(fact_205_inflstsE,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % inflstsE
% 0.09/0.35 thf(fact_206_lapp__allT__iff,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.09/0.35 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_allT_iff
% 0.09/0.35 thf(fact_207_infsuff__appE,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) )
% 0.09/0.35 => ~ ! [S2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( T
% 0.09/0.35 != ( coinductive_lappend @ A @ R @ S2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infsuff_appE
% 0.09/0.35 thf(fact_208_infsafety__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList21015939545safety @ A )
% 0.09/0.35 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.09/0.35 => ( ! [Y: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21202317876inpref @ A @ A3 @ X2 ) )
% 0.09/0.35 => ? [Z: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P ) ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ X2 @ P ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infsafety_def
% 0.09/0.35 thf(fact_209_infliveness__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList21015763786veness @ A )
% 0.09/0.35 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.09/0.35 ! [X2: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.09/0.35 => ? [Y: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % infliveness_def
% 0.09/0.35 thf(fact_210_llength__drop__take,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.09/0.35 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 0.09/0.35 != ( coinductive_LNil @ A ) )
% 0.09/0.35 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 0.09/0.35 = I ) ) ).
% 0.09/0.35
% 0.09/0.35 % llength_drop_take
% 0.09/0.35 thf(fact_211_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 0.09/0.35 ! [A: $tType,I: nat] :
% 0.09/0.35 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 % LList2_Mirabelle_hamjzmohle.ldrop_LNil
% 0.09/0.35 thf(fact_212_ldrop__fin__iffT,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ldrop_fin_iffT
% 0.09/0.35 thf(fact_213_ldrop__inf__iffT,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ldrop_inf_iffT
% 0.09/0.35 thf(fact_214_ldrop__infT,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ldrop_infT
% 0.09/0.35 thf(fact_215_ldropT,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ldropT
% 0.09/0.35 thf(fact_216_ldrop__finT,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ldrop_finT
% 0.09/0.35 thf(fact_217_drop__nonLNil,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.09/0.35 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 0.09/0.35 != ( coinductive_LNil @ A ) )
% 0.09/0.35 => ( T
% 0.09/0.35 != ( coinductive_LNil @ A ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % drop_nonLNil
% 0.09/0.35 thf(fact_218_ldrop__LNil__less,axiom,
% 0.09/0.35 ! [A: $tType,J: nat,I: nat,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ nat @ J @ I )
% 0.09/0.35 => ( ( ( lList2508575361_ldrop @ A @ T @ J )
% 0.09/0.35 = ( coinductive_LNil @ A ) )
% 0.09/0.35 => ( ( lList2508575361_ldrop @ A @ T @ I )
% 0.09/0.35 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ldrop_LNil_less
% 0.09/0.35 thf(fact_219_ltake__ldrop__id,axiom,
% 0.09/0.35 ! [A: $tType,X: coinductive_llist @ A,I: nat] :
% 0.09/0.35 ( ( coinductive_lappend @ A @ ( lList22119844313_ltake @ A @ X @ I ) @ ( lList2508575361_ldrop @ A @ X @ I ) )
% 0.09/0.35 = X ) ).
% 0.09/0.35
% 0.09/0.35 % ltake_ldrop_id
% 0.09/0.35 thf(fact_220_lapp__suff__llength,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( lList2508575361_ldrop @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 0.09/0.35 = S ) ) ).
% 0.09/0.35
% 0.09/0.35 % lapp_suff_llength
% 0.09/0.35 thf(fact_221_lstrict__prefix__code_I3_J,axiom,
% 0.09/0.35 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.09/0.35 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.09/0.35
% 0.09/0.35 % lstrict_prefix_code(3)
% 0.09/0.35 thf(fact_222_lstrict__prefix__code_I2_J,axiom,
% 0.09/0.35 ! [B: $tType,Y4: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y4 @ Ys ) ) ).
% 0.09/0.35
% 0.09/0.35 % lstrict_prefix_code(2)
% 0.09/0.35 thf(fact_223_lstrict__prefix__code_I4_J,axiom,
% 0.09/0.35 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y4: B,Ys: coinductive_llist @ B] :
% 0.09/0.35 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y4 @ Ys ) )
% 0.09/0.35 = ( ( X = Y4 )
% 0.09/0.35 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lstrict_prefix_code(4)
% 0.09/0.35 thf(fact_224_lstrict__prefix__code_I1_J,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.09/0.35
% 0.09/0.35 % lstrict_prefix_code(1)
% 0.09/0.35 thf(fact_225_llist__less__induct,axiom,
% 0.09/0.35 ! [A: $tType,P2: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.09/0.35 ( ! [Xs3: coinductive_llist @ A] :
% 0.09/0.35 ( ! [Ys2: coinductive_llist @ A] :
% 0.09/0.35 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.09/0.35 => ( P2 @ Ys2 ) )
% 0.09/0.35 => ( P2 @ Xs3 ) )
% 0.09/0.35 => ( P2 @ Xs ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_less_induct
% 0.09/0.35 thf(fact_226_finlsts__rec__LCons,axiom,
% 0.09/0.35 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C2: B,D3: A > ( coinductive_llist @ A ) > B > B,A4: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D3 @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.09/0.35 = ( D3 @ A4 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D3 @ R ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts_rec_LCons
% 0.09/0.35 thf(fact_227_finlsts__rec__LCons__def,axiom,
% 0.09/0.35 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D3: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.09/0.35 ( ( F
% 0.09/0.35 = ( lList21916056377ts_rec @ B @ A @ C2 @ D3 ) )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( F @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.09/0.35 = ( D3 @ A4 @ R @ ( F @ R ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts_rec_LCons_def
% 0.09/0.35 thf(fact_228_finlsts__rec__LNil__def,axiom,
% 0.09/0.35 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D3: A > ( coinductive_llist @ A ) > B > B] :
% 0.09/0.35 ( ( F
% 0.09/0.35 = ( lList21916056377ts_rec @ B @ A @ C2 @ D3 ) )
% 0.09/0.35 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.09/0.35 = C2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts_rec_LNil_def
% 0.09/0.35 thf(fact_229_finlsts__rec__LNil,axiom,
% 0.09/0.35 ! [B: $tType,A: $tType,C2: A,D3: B > ( coinductive_llist @ B ) > A > A] :
% 0.09/0.35 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D3 @ ( coinductive_LNil @ B ) )
% 0.09/0.35 = C2 ) ).
% 0.09/0.35
% 0.09/0.35 % finlsts_rec_LNil
% 0.09/0.35 thf(fact_230_inflsts__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( lList21612149805nflsts @ A )
% 0.09/0.35 = ( ^ [A3: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A3 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % inflsts_def
% 0.09/0.35 thf(fact_231_LList2__Mirabelle__hamjzmohle_Ollength__LCons,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( ( lList21232602520length @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.09/0.35 = ( suc @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % LList2_Mirabelle_hamjzmohle.llength_LCons
% 0.09/0.35 thf(fact_232_DiffI,axiom,
% 0.09/0.35 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( member @ A @ C2 @ A2 )
% 0.09/0.35 => ( ~ ( member @ A @ C2 @ B4 )
% 0.09/0.35 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % DiffI
% 0.09/0.35 thf(fact_233_Diff__iff,axiom,
% 0.09/0.35 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) )
% 0.09/0.35 = ( ( member @ A @ C2 @ A2 )
% 0.09/0.35 & ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % Diff_iff
% 0.09/0.35 thf(fact_234_Diff__idemp,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) @ B4 )
% 0.09/0.35 = ( minus_minus @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.09/0.35
% 0.09/0.35 % Diff_idemp
% 0.09/0.35 thf(fact_235_ltake__LCons__Suc,axiom,
% 0.09/0.35 ! [A: $tType,A4: A,L: coinductive_llist @ A,I: nat] :
% 0.09/0.35 ( ( lList22119844313_ltake @ A @ ( coinductive_LCons @ A @ A4 @ L ) @ ( suc @ I ) )
% 0.09/0.35 = ( coinductive_LCons @ A @ A4 @ ( lList22119844313_ltake @ A @ L @ I ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % ltake_LCons_Suc
% 0.09/0.35 thf(fact_236_DiffE,axiom,
% 0.09/0.35 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) )
% 0.09/0.35 => ~ ( ( member @ A @ C2 @ A2 )
% 0.09/0.35 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % DiffE
% 0.09/0.35 thf(fact_237_DiffD1,axiom,
% 0.09/0.35 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) )
% 0.09/0.35 => ( member @ A @ C2 @ A2 ) ) ).
% 0.09/0.35
% 0.09/0.35 % DiffD1
% 0.09/0.35 thf(fact_238_DiffD2,axiom,
% 0.09/0.35 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) )
% 0.09/0.35 => ~ ( member @ A @ C2 @ B4 ) ) ).
% 0.09/0.35
% 0.09/0.35 % DiffD2
% 0.09/0.35 thf(fact_239_Diff__mono,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,C3: set @ A,D4: set @ A,B4: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C3 )
% 0.09/0.35 => ( ( ord_less_eq @ ( set @ A ) @ D4 @ B4 )
% 0.09/0.35 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) @ ( minus_minus @ ( set @ A ) @ C3 @ D4 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % Diff_mono
% 0.09/0.35 thf(fact_240_Diff__subset,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) @ A2 ) ).
% 0.09/0.35
% 0.09/0.35 % Diff_subset
% 0.09/0.35 thf(fact_241_double__diff,axiom,
% 0.09/0.35 ! [A: $tType,A2: set @ A,B4: set @ A,C3: set @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.09/0.35 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 0.09/0.35 => ( ( minus_minus @ ( set @ A ) @ B4 @ ( minus_minus @ ( set @ A ) @ C3 @ A2 ) )
% 0.09/0.35 = A2 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % double_diff
% 0.09/0.35 thf(fact_242_lift__Suc__antimono__le,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [F: nat > A,N: nat,N2: nat] :
% 0.09/0.35 ( ! [N3: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.09/0.35 => ( ( ord_less_eq @ nat @ N @ N2 )
% 0.09/0.35 => ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ N ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lift_Suc_antimono_le
% 0.09/0.35 thf(fact_243_lift__Suc__mono__le,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( order @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [F: nat > A,N: nat,N2: nat] :
% 0.09/0.35 ( ! [N3: nat] : ( ord_less_eq @ A @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.09/0.35 => ( ( ord_less_eq @ nat @ N @ N2 )
% 0.09/0.35 => ( ord_less_eq @ A @ ( F @ N ) @ ( F @ N2 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % lift_Suc_mono_le
% 0.09/0.35 thf(fact_244_diff__mono,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A,B2: A,D3: A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 => ( ( ord_less_eq @ A @ D3 @ C2 )
% 0.09/0.35 => ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % diff_mono
% 0.09/0.35 thf(fact_245_diff__left__mono,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [B2: A,A4: A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ B2 @ A4 )
% 0.09/0.35 => ( ord_less_eq @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % diff_left_mono
% 0.09/0.35 thf(fact_246_diff__eq__diff__less__eq,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A,B2: A,C2: A,D3: A] :
% 0.09/0.35 ( ( ( minus_minus @ A @ A4 @ B2 )
% 0.09/0.35 = ( minus_minus @ A @ C2 @ D3 ) )
% 0.09/0.35 => ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 = ( ord_less_eq @ A @ C2 @ D3 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % diff_eq_diff_less_eq
% 0.09/0.35 thf(fact_247_diff__right__mono,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.09/0.35 => ! [A4: A,B2: A,C2: A] :
% 0.09/0.35 ( ( ord_less_eq @ A @ A4 @ B2 )
% 0.09/0.35 => ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B2 @ C2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % diff_right_mono
% 0.09/0.35 thf(fact_248_llast__singleton,axiom,
% 0.09/0.35 ! [A: $tType,X: A] :
% 0.09/0.35 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 0.09/0.35 = X ) ).
% 0.09/0.35
% 0.09/0.35 % llast_singleton
% 0.09/0.35 thf(fact_249_take__inf__less,axiom,
% 0.09/0.35 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.09/0.35 => ( ord_less @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ T ) ) ).
% 0.09/0.35
% 0.09/0.35 % take_inf_less
% 0.09/0.35 thf(fact_250_llast__LCons2,axiom,
% 0.09/0.35 ! [A: $tType,X: A,Y4: A,Xs: coinductive_llist @ A] :
% 0.09/0.35 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y4 @ Xs ) ) )
% 0.09/0.35 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y4 @ Xs ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llast_LCons2
% 0.09/0.35 thf(fact_251_less__LCons,axiom,
% 0.09/0.35 ! [A: $tType,A4: A,R: coinductive_llist @ A,B2: A,T: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ R ) @ ( coinductive_LCons @ A @ B2 @ T ) )
% 0.09/0.35 = ( ( A4 = B2 )
% 0.09/0.35 & ( ord_less @ ( coinductive_llist @ A ) @ R @ T ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % less_LCons
% 0.09/0.35 thf(fact_252_llist__less__finT,axiom,
% 0.09/0.35 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.09/0.35 ( ( ord_less @ ( coinductive_llist @ A ) @ R @ S )
% 0.09/0.35 => ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.09/0.35 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_less_finT
% 0.09/0.35 thf(fact_253_LNil__less__LCons,axiom,
% 0.09/0.35 ! [A: $tType,A4: A,T: coinductive_llist @ A] : ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) ) ).
% 0.09/0.35
% 0.09/0.35 % LNil_less_LCons
% 0.09/0.35 thf(fact_254_llist__less__def,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ord_less @ ( coinductive_llist @ A ) )
% 0.09/0.35 = ( ^ [S3: coinductive_llist @ A,T3: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ T3 )
% 0.09/0.35 & ( S3 != T3 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_less_def
% 0.09/0.35 thf(fact_255_llist__less__le__not__le,axiom,
% 0.09/0.35 ! [A: $tType] :
% 0.09/0.35 ( ( ord_less @ ( coinductive_llist @ A ) )
% 0.09/0.35 = ( ^ [S3: coinductive_llist @ A,T3: coinductive_llist @ A] :
% 0.09/0.35 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ T3 )
% 0.09/0.35 & ~ ( ord_less_eq @ ( coinductive_llist @ A ) @ T3 @ S3 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 % llist_less_le_not_le
% 0.09/0.35
% 0.09/0.35 %----Type constructors (23)
% 0.09/0.35 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.09/0.35 ! [A8: $tType,A9: $tType] :
% 0.09/0.35 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 0.09/0.35 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.09/0.35 ! [A8: $tType,A9: $tType] :
% 0.09/0.35 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.09/0.35 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.09/0.35 ! [A8: $tType,A9: $tType] :
% 0.09/0.35 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.09/0.35 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_fun___Orderings_Otop,axiom,
% 0.09/0.35 ! [A8: $tType,A9: $tType] :
% 0.09/0.35 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.09/0.35 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_fun___Orderings_Oord,axiom,
% 0.09/0.35 ! [A8: $tType,A9: $tType] :
% 0.09/0.35 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.09/0.35 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.09/0.35 preorder @ nat @ ( type2 @ nat ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.09/0.35 linorder @ nat @ ( type2 @ nat ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.09/0.35 order @ nat @ ( type2 @ nat ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.09/0.35 ord @ nat @ ( type2 @ nat ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Set_Oset___Orderings_Oorder__top_4,axiom,
% 0.09/0.35 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.09/0.35 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.09/0.35 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Set_Oset___Orderings_Otop_7,axiom,
% 0.09/0.35 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Set_Oset___Orderings_Oord_8,axiom,
% 0.09/0.35 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_HOL_Obool___Orderings_Oorder__top_9,axiom,
% 0.09/0.35 order_top @ $o @ ( type2 @ $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_HOL_Obool___Orderings_Opreorder_10,axiom,
% 0.09/0.35 preorder @ $o @ ( type2 @ $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_HOL_Obool___Orderings_Olinorder_11,axiom,
% 0.09/0.35 linorder @ $o @ ( type2 @ $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_HOL_Obool___Orderings_Oorder_12,axiom,
% 0.09/0.35 order @ $o @ ( type2 @ $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_HOL_Obool___Orderings_Otop_13,axiom,
% 0.09/0.35 top @ $o @ ( type2 @ $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_HOL_Obool___Orderings_Oord_14,axiom,
% 0.09/0.35 ord @ $o @ ( type2 @ $o ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_15,axiom,
% 0.09/0.35 ! [A8: $tType] : ( preorder @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_16,axiom,
% 0.09/0.35 ! [A8: $tType] : ( order @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_17,axiom,
% 0.09/0.35 ! [A8: $tType] : ( ord @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.09/0.35
% 0.09/0.35 %----Conjectures (1)
% 0.09/0.35 thf(conj_0,conjecture,
% 0.09/0.35 ? [X4: coinductive_llist @ a] :
% 0.09/0.35 ( ( member @ ( coinductive_llist @ a ) @ X4 @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
% 0.09/0.35 & ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ X4 ) @ p ) ) ).
% 0.09/0.35
% 0.09/0.35 %------------------------------------------------------------------------------
% 0.09/0.35 ------------------------
% 2.31/1.21 ---- Embedded in THF ---
% 2.31/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.31/1.21 %%% Generated on Tue Feb 24 06:10:46 EST 2026
% 2.31/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 2.31/1.21 %%% Logic specification used:
% 2.31/1.21 %%% thf(spec, logic, $$dhol).
% 2.31/1.21
% 2.31/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ssc2Uifky4/DTF2DTF10143.p
% 2.31/1.21 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.31/1.21 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.31/1.21 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.31/1.21 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.31/1.21 thf(ty_tf_a, type, a: $tType).
% 2.31/1.21 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.31/1.21 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.31/1.21 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.31/1.21 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.31/1.21 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.31/1.21 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.31/1.21 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.31/1.21 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.31/1.21 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.31/1.21 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.31/1.21 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.31/1.21 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.31/1.21 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.31/1.21 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.31/1.21 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts, type, lList2435255213lllsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts, type, lList2236698231inlsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.31/1.21 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)))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinpref, type, lList21202317876inpref: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ (coinductive_llist @ A))))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts, type, lList22096119349pslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfliveness, type, lList21015763786veness: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts, type, lList21612149805nflsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsafety, type, lList21015939545safety: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsuff, type, lList2649413865nfsuff: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ (coinductive_llist @ A))))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast, type, lList2370560421utlast: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop, type, lList2508575361_ldrop: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oliveness, type, lList21805353693veness: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast, type, lList2170638824_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength, type, lList21232602520length: (!> [A:$tType]: (((coinductive_llist @ A) > nat)))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev, type, lList2281150353e_lrev: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake, type, lList22119844313_ltake: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opfinpref, type, lList2467029176inpref: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ (coinductive_llist @ A))))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposliveness, type, lList21952340509veness: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts, type, lList21148268032oslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opossafety, type, lList292406316safety: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opprefix__closed, type, lList21974196564closed: (!> [A:$tType]: (((set @ (coinductive_llist @ A)) > $o)))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oprefix__closed, type, lList21638733016closed: (!> [A:$tType]: (((set @ (coinductive_llist @ A)) > $o)))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osafety, type, lList21350011628safety: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuff, type, lList21475143548e_suff: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ (coinductive_llist @ A))))))).
% 2.31/1.21 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuffix__closed, type, lList2736192599closed: (!> [A:$tType]: (((set @ (coinductive_llist @ A)) > $o)))).
% 2.31/1.21 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.31/1.21 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.31/1.21 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.31/1.21 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.31/1.21 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.31/1.21 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.31/1.21 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.31/1.21 thf(sy_v_P, type, p: (set @ (coinductive_llist @ a))).
% 2.31/1.21 thf(sy_v_r____, type, r: (coinductive_llist @ a)).
% 2.31/1.21 thf(sy_v_s____, type, s: (coinductive_llist @ a)).
% 2.31/1.21 thf(sy_v_t____, type, t: (coinductive_llist @ a)).
% 2.31/1.21 thf(sy_v_u____, type, u: (coinductive_llist @ a)).
% 2.31/1.21 thf(sy_v_v____, type, v: (coinductive_llist @ a)).
% 2.31/1.21 thf(fact_0_tP, axiom, (((member @ (coinductive_llist @ a)) @ t) @ p)).
% 2.31/1.21 thf(fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062, axiom, (t = (((coinductive_lappend @ a) @ r) @ (((coinductive_lappend @ a) @ u) @ v)))).
% 2.31/1.21 thf(fact_2_psafety, axiom, (((lList292406316safety @ a) @ (top_top @ (set @ a))) @ p)).
% 2.31/1.21 thf(fact_3_scons, axiom, (s = (((coinductive_lappend @ a) @ r) @ u))).
% 2.31/1.21 thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_At_A_061_Ar_A_064_064_Au_A_064_064_Av_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [V:(coinductive_llist @ a)]: ((t != (((coinductive_lappend @ a) @ r) @ (((coinductive_lappend @ a) @ u) @ V)))))))).
% 2.31/1.21 thf(fact_5_alllsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ (top_top @ (set @ A))))))).
% 2.31/1.21 thf(fact_6__092_060open_062r_A_092_060in_062_Apfinpref_AUNIV_As_092_060close_062, axiom, (((member @ (coinductive_llist @ a)) @ r) @ (((lList2467029176inpref @ a) @ (top_top @ (set @ a))) @ s))).
% 2.31/1.21 thf(fact_7_lappT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_8_lapp__all__invT, axiom, (! [A:$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)))))).
% 2.31/1.21 thf(fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062u_O_As_A_061_Ar_A_064_064_Au_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [U:(coinductive_llist @ a)]: ((s != (((coinductive_lappend @ a) @ r) @ U))))))).
% 2.31/1.21 thf(fact_10_UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.31/1.21 thf(fact_11_iso__tuple__UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.31/1.21 thf(fact_12_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X2:D]: ((top_top @ C)))))))).
% 2.31/1.21 thf(fact_13_lappend__assoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ Zs) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_lappend @ A) @ Ys) @ Zs)))))).
% 2.31/1.21 thf(fact_14_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.31/1.21 thf(fact_15_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 2.31/1.21 thf(fact_16_posliveness__def, axiom, (! [A:$tType]: (((lList21952340509veness @ A) = (^ [A3:(set @ A),P:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList22096119349pslsts @ A) @ A3)) => (? [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ ((lList2435255213lllsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X2) @ Y)) @ P))))))))))))).
% 2.31/1.21 thf(fact_17_suff__all, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ (((lList21475143548e_suff @ A) @ A2) @ S)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_18_safetyD, axiom, (! [A:$tType,A2:(set @ A),P2:(set @ (coinductive_llist @ A)),T:(coinductive_llist @ A)]: (((((lList21350011628safety @ A) @ A2) @ P2) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => ((! [R2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R2) @ (((lList21202317876inpref @ A) @ A2) @ T)) => (? [X4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X4) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R2) @ X4)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ T) @ P2))))))).
% 2.31/1.21 thf(fact_19_safetyE, axiom, (! [A:$tType,A2:(set @ A),P2:(set @ (coinductive_llist @ A))]: (((((lList21350011628safety @ A) @ A2) @ P2) => (! [X4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X4) @ ((lList2435255213lllsts @ A) @ A2)) => ((! [Xa:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xa) @ (((lList21202317876inpref @ A) @ A2) @ X4)) => (? [Xb:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xb) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Xa) @ Xb)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ X4) @ P2))))))))).
% 2.31/1.21 thf(fact_20_safetyI, axiom, (! [A:$tType,A2:(set @ A),P2:(set @ (coinductive_llist @ A))]: (((! [T2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T2) @ ((lList2435255213lllsts @ A) @ A2)) => ((! [X4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X4) @ (((lList21202317876inpref @ A) @ A2) @ T2)) => (? [Xa:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xa) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X4) @ Xa)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ T2) @ P2))))) => (((lList21350011628safety @ A) @ A2) @ P2))))).
% 2.31/1.21 thf(fact_21_spos, axiom, (s != (coinductive_LNil @ a))).
% 2.31/1.21 thf(fact_22_st, axiom, (((ord_less_eq @ (coinductive_llist @ a)) @ s) @ t)).
% 2.31/1.21 thf(fact_23_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.31/1.21 thf(fact_24_finpref__suff, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ (((lList21202317876inpref @ A) @ A2) @ T)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ T) @ (((lList21475143548e_suff @ A) @ A2) @ R))))))).
% 2.31/1.21 thf(fact_25_safety__def, axiom, (! [A:$tType]: (((lList21350011628safety @ A) = (^ [A3:(set @ A),P:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList2435255213lllsts @ A) @ A3)) => ((! [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ (((lList21202317876inpref @ A) @ A3) @ X2)) => (? [Z:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Z) @ ((lList2435255213lllsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Y) @ Z)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ X2) @ P))))))))))).
% 2.31/1.21 thf(fact_26_safety__prefix__closed, axiom, (! [A:$tType,P2:(set @ (coinductive_llist @ A))]: (((((lList21350011628safety @ A) @ (top_top @ (set @ A))) @ P2) => ((lList21638733016closed @ A) @ P2))))).
% 2.31/1.21 thf(fact_27_possafety__def, axiom, (! [A:$tType]: (((lList292406316safety @ A) = (^ [A3:(set @ A),P:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList21148268032oslsts @ A) @ A3)) => ((! [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ (((lList2467029176inpref @ A) @ A3) @ X2)) => (? [Z:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Z) @ ((lList2435255213lllsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Y) @ Z)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ X2) @ P))))))))))).
% 2.31/1.21 thf(fact_28_possafetyI, axiom, (! [A:$tType,A2:(set @ A),P2:(set @ (coinductive_llist @ A))]: (((! [T2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T2) @ ((lList21148268032oslsts @ A) @ A2)) => ((! [X4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X4) @ (((lList2467029176inpref @ A) @ A2) @ T2)) => (? [Xa:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xa) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X4) @ Xa)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ T2) @ P2))))) => (((lList292406316safety @ A) @ A2) @ P2))))).
% 2.31/1.21 thf(fact_29_possafetyE, axiom, (! [A:$tType,A2:(set @ A),P2:(set @ (coinductive_llist @ A))]: (((((lList292406316safety @ A) @ A2) @ P2) => (! [X4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X4) @ ((lList21148268032oslsts @ A) @ A2)) => ((! [Xa:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xa) @ (((lList2467029176inpref @ A) @ A2) @ X4)) => (? [Xb:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xb) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Xa) @ Xb)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ X4) @ P2))))))))).
% 2.31/1.21 thf(fact_30_possafetyD, axiom, (! [A:$tType,A2:(set @ A),P2:(set @ (coinductive_llist @ A)),T:(coinductive_llist @ A)]: (((((lList292406316safety @ A) @ A2) @ P2) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21148268032oslsts @ A) @ A2)) => ((! [R2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R2) @ (((lList2467029176inpref @ A) @ A2) @ T)) => (? [X4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X4) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R2) @ X4)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ T) @ P2))))))).
% 2.31/1.21 thf(fact_31_pfinpref__iff, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ (((lList2467029176inpref @ A) @ A2) @ S)) = ((((member @ (coinductive_llist @ A)) @ X) @ (((lList21202317876inpref @ A) @ A2) @ S)) & (X != (coinductive_LNil @ A))))))).
% 2.31/1.21 thf(fact_32_suff__finpref__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ R) @ (((lList21202317876inpref @ A) @ A2) @ T)) = (((member @ (coinductive_llist @ A)) @ T) @ (((lList21475143548e_suff @ A) @ A2) @ R)))))))).
% 2.31/1.21 thf(fact_33_suff__appE, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ (((lList21475143548e_suff @ A) @ A2) @ R)) => (~ ((! [S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList2435255213lllsts @ A) @ A2)) => (T != (((coinductive_lappend @ A) @ R) @ S2)))))))))))).
% 2.31/1.21 thf(fact_34_suff__LNil, axiom, (! [A:$tType,A2:(set @ A)]: (((((lList21475143548e_suff @ A) @ A2) @ (coinductive_LNil @ A)) = ((lList2435255213lllsts @ A) @ A2))))).
% 2.31/1.21 thf(fact_35_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A))))))))).
% 2.31/1.21 thf(fact_36_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.31/1.21 thf(fact_37_llist__le__refl, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ S)))).
% 2.31/1.21 thf(fact_38_top1I, axiom, (! [A:$tType,X:A]: (((top_top @ (A > $o)) @ X)))).
% 2.31/1.21 thf(fact_39_LNil__is__lappend__conv, axiom, (! [A:$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))))))).
% 2.31/1.21 thf(fact_40_lappend__is__LNil__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ S) @ T) = (coinductive_LNil @ A)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.31/1.21 thf(fact_41_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.31/1.21 thf(fact_42_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 2.31/1.21 thf(fact_43_LNil__eq__lappend__iff, axiom, (! [A:$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))))))).
% 2.31/1.21 thf(fact_44_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.31/1.21 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P2:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P2)) = (P2 @ A4))))).
% 2.31/1.21 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 2.31/1.21 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P2 @ X3) = (Q @ X3)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.31/1.21 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.31/1.21 thf(fact_49_same__lappend__eq, axiom, (! [A:$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)))))).
% 2.31/1.21 thf(fact_50_lapp__fin__fin__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_51_le__LNil, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ (coinductive_LNil @ A)) = (S = (coinductive_LNil @ A)))))).
% 2.31/1.21 thf(fact_52_LNil__le, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((ord_less_eq @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ S)))).
% 2.31/1.21 thf(fact_53_le__lappend, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A)]: ((((ord_less_eq @ (coinductive_llist @ A)) @ R) @ (((coinductive_lappend @ A) @ R) @ S))))).
% 2.31/1.21 thf(fact_54_LNil__suff, axiom, (! [A:$tType,A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (((lList21475143548e_suff @ A) @ A2) @ S)) = (S = (coinductive_LNil @ A)))))).
% 2.31/1.21 thf(fact_55_poslsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ (top_top @ (set @ A)))) = (S != (coinductive_LNil @ A)))))).
% 2.31/1.21 thf(fact_56_fpslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList22096119349pslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) & (S != (coinductive_LNil @ A))))))).
% 2.31/1.21 thf(fact_57_poslsts__iff, axiom, (! [A:$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))))))).
% 2.31/1.21 thf(fact_58_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.31/1.21 thf(fact_59_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.31/1.21 thf(fact_60_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.31/1.21 thf(fact_61_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 2.31/1.21 thf(fact_62_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A4) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X3:B,Y2:B]: (((((ord_less_eq @ B) @ X3) @ Y2) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A4) @ (F @ C2))))))))))).
% 2.31/1.21 thf(fact_63_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,B2:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A4) @ B2) => ((((ord_less_eq @ C) @ (F @ B2)) @ C2) => ((! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ C) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less_eq @ C) @ (F @ A4)) @ C2)))))))))).
% 2.31/1.21 thf(fact_64_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B2:B,C2:B]: (((A4 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X3:B,Y2:B]: (((((ord_less_eq @ B) @ X3) @ Y2) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A4) @ (F @ C2))))))))))).
% 2.31/1.21 thf(fact_65_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,B2:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A4) @ B2) => (((F @ B2) = C2) => ((! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less_eq @ B) @ (F @ A4)) @ C2)))))))))).
% 2.31/1.21 thf(fact_66_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y3:A,Z2:A]: ((Y3 = Z2))) = (^ [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) & (((ord_less_eq @ A) @ Y) @ X2))))))))).
% 2.31/1.21 thf(fact_67_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => ((((ord_less_eq @ A) @ Y4) @ X) => (X = Y4))))))))).
% 2.31/1.21 thf(fact_68_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) | (((ord_less_eq @ A) @ Y4) @ X)))))))).
% 2.31/1.21 thf(fact_69_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y4:A]: (((X = Y4) => (((ord_less_eq @ A) @ X) @ Y4)))))))).
% 2.31/1.21 thf(fact_70_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P2:(A > (A > $o)),B2:A,A4:A]: (((! [A5:A,B3:A]: (((((ord_less_eq @ A) @ A5) @ B3) => ((P2 @ A5) @ B3)))) => ((((P2 @ B2) @ A4) => ((P2 @ A4) @ B2)) => ((P2 @ A4) @ B2))))))))).
% 2.31/1.21 thf(fact_71_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y4:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y4))) => (((ord_less_eq @ A) @ Y4) @ X)))))))).
% 2.31/1.21 thf(fact_72_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 2.31/1.21 thf(fact_73_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y4:A,Z3:A]: ((((((ord_less_eq @ A) @ X) @ Y4) => (~ ((((ord_less_eq @ A) @ Y4) @ Z3)))) => (((((ord_less_eq @ A) @ Y4) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z3)))) => (((((ord_less_eq @ A) @ X) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ Y4)))) => (((((ord_less_eq @ A) @ Z3) @ Y4) => (~ ((((ord_less_eq @ A) @ Y4) @ X)))) => (((((ord_less_eq @ A) @ Y4) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ X)))) => (~ (((((ord_less_eq @ A) @ Z3) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y4))))))))))))))))).
% 2.31/1.21 thf(fact_74_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y4:A,X:A]: (((((ord_less_eq @ A) @ Y4) @ X) => ((((ord_less_eq @ A) @ X) @ Y4) = (X = Y4))))))))).
% 2.31/1.21 thf(fact_75_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((A4 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 2.31/1.21 thf(fact_76_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 2.31/1.21 thf(fact_77_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((ord_less_eq @ A) @ A4) @ B2) => ((((ord_less_eq @ A) @ B2) @ A4) => (A4 = B2))))))))).
% 2.31/1.21 thf(fact_78_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y4:A,Z3:A]: (((((ord_less_eq @ A) @ X) @ Y4) => ((((ord_less_eq @ A) @ Y4) @ Z3) => (((ord_less_eq @ A) @ X) @ Z3))))))))).
% 2.31/1.21 thf(fact_79_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A]: ((((ord_less_eq @ A) @ A4) @ A4))))))).
% 2.31/1.21 thf(fact_80_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P2:(A > (A > $o)),A4:A,B2:A]: (((! [A5:A,B3:A]: (((((ord_less_eq @ A) @ A5) @ B3) => ((P2 @ A5) @ B3)))) => ((! [A5:A,B3:A]: ((((P2 @ B3) @ A5) => ((P2 @ A5) @ B3)))) => ((P2 @ A4) @ B2))))))))).
% 2.31/1.21 thf(fact_81_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A4) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A4))))))))).
% 2.31/1.21 thf(fact_82_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A4:A]: (((((ord_less_eq @ A) @ B2) @ A4) => ((((ord_less_eq @ A) @ A4) @ B2) => (A4 = B2))))))))).
% 2.31/1.21 thf(fact_83_pref__locally__linear, axiom, (! [A:$tType,S:(coinductive_llist @ A),X:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ X) => ((((ord_less_eq @ (coinductive_llist @ A)) @ T) @ X) => ((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ T) | (((ord_less_eq @ (coinductive_llist @ A)) @ T) @ S))))))).
% 2.31/1.21 thf(fact_84_prefix__closed__def, axiom, (! [A:$tType]: (((lList21638733016closed @ A) = (^ [A3:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ A3) => (! [S3:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S3) @ X2) => (((member @ (coinductive_llist @ A)) @ S3) @ A3))))))))))))).
% 2.31/1.21 thf(fact_85_llist__le__anti__sym, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ T) => ((((ord_less_eq @ (coinductive_llist @ A)) @ T) @ S) => (S = T)))))).
% 2.31/1.21 thf(fact_86_finlsts_OLNil__fin, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2236698231inlsts @ A) @ A2))))).
% 2.31/1.21 thf(fact_87_llist__le__trans, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ R) @ S) => ((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ T) => (((ord_less_eq @ (coinductive_llist @ A)) @ R) @ T)))))).
% 2.31/1.21 thf(fact_88_llist__le__finT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ R) @ S) => ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_89_finT__simp, axiom, (! [A:$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)))))))).
% 2.31/1.21 thf(fact_90_fin__finite, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.31/1.21 thf(fact_91_lappfin__finT, axiom, (! [A:$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))))))).
% 2.31/1.21 thf(fact_92_lapp__fin__fin__lemma, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_93_finite__lemma, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),B4:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ B4)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ B4))))))).
% 2.31/1.21 thf(fact_94_finsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_95_top__greatest, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: ((((ord_less_eq @ A) @ A4) @ (top_top @ A)))))))).
% 2.31/1.21 thf(fact_96_top_Oextremum__unique, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A4) = (A4 = (top_top @ A))))))))).
% 2.31/1.21 thf(fact_97_top_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A4) => (A4 = (top_top @ A))))))))).
% 2.31/1.21 thf(fact_98_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.31/1.21 thf(fact_99_llist__le__def, axiom, (! [A:$tType]: (((ord_less_eq @ (coinductive_llist @ A)) = (^ [S3:(coinductive_llist @ A),T3:(coinductive_llist @ A)]: ((? [D2:(coinductive_llist @ A)]: ((T3 = (((coinductive_lappend @ A) @ S3) @ D2)))))))))).
% 2.31/1.21 thf(fact_100_finpref__fin, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ (((lList21202317876inpref @ A) @ A2) @ S)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_101_alllsts_OLNil__all, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2435255213lllsts @ A) @ A2))))).
% 2.31/1.21 thf(fact_102_suff__finpref, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),R:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T) @ (((lList21475143548e_suff @ A) @ A2) @ R)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ (((lList21202317876inpref @ A) @ A2) @ T))))))).
% 2.31/1.21 thf(fact_103_pprefix__closed__def, axiom, (! [A:$tType]: (((lList21974196564closed @ A) = (^ [A3:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ A3) => (! [S3:(coinductive_llist @ A)]: ((((((ord_less_eq @ (coinductive_llist @ A)) @ S3) @ X2) & (S3 != (coinductive_LNil @ A))) => (((member @ (coinductive_llist @ A)) @ S3) @ A3))))))))))))).
% 2.31/1.21 thf(fact_104_livenessE, axiom, (! [A:$tType,A2:(set @ A),P2:(set @ (coinductive_llist @ A)),S:(coinductive_llist @ A)]: (((((lList21805353693veness @ A) @ A2) @ P2) => ((! [T2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T2) @ ((lList2435255213lllsts @ A) @ A2)) => (~ ((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T2)) @ P2)))))) => (~ ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2))))))))).
% 2.31/1.21 thf(fact_105_livenessI, axiom, (! [A:$tType,A2:(set @ A),P2:(set @ (coinductive_llist @ A))]: (((! [S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList2236698231inlsts @ A) @ A2)) => (? [X4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X4) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S2) @ X4)) @ P2))))))) => (((lList21805353693veness @ A) @ A2) @ P2))))).
% 2.31/1.21 thf(fact_106_liveness__def, axiom, (! [A:$tType]: (((lList21805353693veness @ A) = (^ [A3:(set @ A),P:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList2236698231inlsts @ A) @ A3)) => (? [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ ((lList2435255213lllsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X2) @ Y)) @ P))))))))))))).
% 2.31/1.21 thf(fact_107_suffix__closed__def, axiom, (! [A:$tType]: (((lList2736192599closed @ A) = (^ [A3:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ A3) => (! [S3:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ X2) @ S3) => (((member @ (coinductive_llist @ A)) @ S3) @ A3))))))))))))).
% 2.31/1.21 thf(fact_108_lrev__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Ys) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ Ys)) @ ((lList2281150353e_lrev @ A) @ Xs)))))))).
% 2.31/1.21 thf(fact_109_LNil__is__lrev__conv, axiom, (! [A:$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))))))).
% 2.31/1.21 thf(fact_110_lrev__is__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A))))))).
% 2.31/1.21 thf(fact_111_top__conj_I2_J, axiom, (! [A:$tType,P2:$o,X:A]: (((P2 & ((top_top @ (A > $o)) @ X)) = P2)))).
% 2.31/1.21 thf(fact_112_lrev__LNil, axiom, (! [A:$tType]: ((((lList2281150353e_lrev @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.31/1.21 thf(fact_113_lrevT, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ ((lList2281150353e_lrev @ A) @ Xs)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_114_lrev__is__lrev__conv, axiom, (! [A:$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))))))).
% 2.31/1.21 thf(fact_115_lrev__lrev__ident, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ ((lList2281150353e_lrev @ A) @ Xs)) = Xs))))).
% 2.31/1.21 thf(fact_116_finlsts__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A2)) @ ((lList2236698231inlsts @ A) @ B4)))))).
% 2.31/1.21 thf(fact_117_alllsts__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A2)) @ ((lList2435255213lllsts @ A) @ B4)))))).
% 2.31/1.21 thf(fact_118_fpslsts__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((lList22096119349pslsts @ A) @ A2)) @ ((lList22096119349pslsts @ A) @ B4)))))).
% 2.31/1.21 thf(fact_119_poslsts__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((lList21148268032oslsts @ A) @ A2)) @ ((lList21148268032oslsts @ A) @ B4)))))).
% 2.31/1.21 thf(fact_120_subset__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (top_top @ (set @ A)))))).
% 2.31/1.21 thf(fact_121_finpref__mono2, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A),A2:(set @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ T) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ (((lList21202317876inpref @ A) @ A2) @ S)) @ (((lList21202317876inpref @ A) @ A2) @ T)))))).
% 2.31/1.21 thf(fact_122_suff__mono2, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A),A2:(set @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ T) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ (((lList21475143548e_suff @ A) @ A2) @ T)) @ (((lList21475143548e_suff @ A) @ A2) @ S)))))).
% 2.31/1.21 thf(fact_123_top__conj_I1_J, axiom, (! [A:$tType,X:A,P2:$o]: (((((top_top @ (A > $o)) @ X) & P2) = P2)))).
% 2.31/1.21 thf(fact_124_lrev__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2281150353e_lrev @ A) @ (((coinductive_LCons @ A) @ A4) @ R)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ R)) @ (((coinductive_LCons @ A) @ A4) @ (coinductive_LNil @ A)))))))).
% 2.31/1.21 thf(fact_125_take__fin, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ T) @ I)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_126_infsuff__finpref, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),R:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T) @ (((lList2649413865nfsuff @ A) @ A2) @ R)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ (((lList21202317876inpref @ A) @ A2) @ T))))))).
% 2.31/1.21 thf(fact_127_ltake__fin, axiom, (! [A:$tType,R:(coinductive_llist @ A),I:nat]: ((((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ R) @ I)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))).
% 2.31/1.21 thf(fact_128_lbutlast__LNil, axiom, (! [A:$tType]: ((((lList2370560421utlast @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.31/1.21 thf(fact_129_subsetI, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B4)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B4))))).
% 2.31/1.21 thf(fact_130_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ A2) => (A2 = B4)))))).
% 2.31/1.21 thf(fact_131_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X22) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.31/1.21 thf(fact_132_lappend__code_I2_J, axiom, (! [A:$tType,Xa2:A,X:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_LCons @ A) @ Xa2) @ X)) @ Ys) = (((coinductive_LCons @ A) @ Xa2) @ (((coinductive_lappend @ A) @ X) @ Ys)))))).
% 2.31/1.21 thf(fact_133_LConsE, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ ((lList2435255213lllsts @ A) @ A2)) = ((((member @ A) @ X) @ A2) & (((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_134_le__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),Y4:A,Ys:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y4) @ Ys)) = ((X = Y4) & (((ord_less_eq @ (coinductive_llist @ A)) @ Xs) @ Ys)))))).
% 2.31/1.21 thf(fact_135_LList2__Mirabelle__hamjzmohle_Oltake__LNil, axiom, (! [A:$tType,I:nat]: (((((lList22119844313_ltake @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 2.31/1.21 thf(fact_136_lbutlast__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((R = (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A4) @ R)) = (coinductive_LNil @ A))) & ((R != (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A4) @ R)) = (((coinductive_LCons @ A) @ A4) @ ((lList2370560421utlast @ A) @ R))))))))).
% 2.31/1.21 thf(fact_137_lbutlast__snoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),X:A]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2370560421utlast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A)))) = Xs))))).
% 2.31/1.21 thf(fact_138_set__mp, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B4)))))).
% 2.31/1.21 thf(fact_139_in__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B4)))))).
% 2.31/1.21 thf(fact_140_subsetD, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B4)))))).
% 2.31/1.21 thf(fact_141_subsetCE, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B4)))))).
% 2.31/1.21 thf(fact_142_equalityE, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((A2 = B4) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (~ ((((ord_less_eq @ (set @ A)) @ B4) @ A2)))))))))).
% 2.31/1.21 thf(fact_143_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B5:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A3) => (((member @ A) @ X2) @ B5)))))))))).
% 2.31/1.21 thf(fact_144_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((A2 = B4) => (((ord_less_eq @ (set @ A)) @ A2) @ B4))))).
% 2.31/1.21 thf(fact_145_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((A2 = B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A2))))).
% 2.31/1.21 thf(fact_146_set__rev__mp, axiom, (! [A:$tType,X:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ X) @ A2) => ((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((member @ A) @ X) @ B4)))))).
% 2.31/1.21 thf(fact_147_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B5:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A3) => (((member @ A) @ T3) @ B5)))))))))).
% 2.31/1.21 thf(fact_148_rev__subsetD, axiom, (! [A:$tType,C2:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A2) => ((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((member @ A) @ C2) @ B4)))))).
% 2.31/1.21 thf(fact_149_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 2.31/1.21 thf(fact_150_Collect__mono, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P2 @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)))))).
% 2.31/1.21 thf(fact_151_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C3) => (((ord_less_eq @ (set @ A)) @ A2) @ C3)))))).
% 2.31/1.21 thf(fact_152_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z2:(set @ A)]: ((Y3 = Z2))) = (^ [A3:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A3)))))))).
% 2.31/1.21 thf(fact_153_contra__subsetD, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((~ ((((member @ A) @ C2) @ B4))) => (~ ((((member @ A) @ C2) @ A2)))))))).
% 2.31/1.21 thf(fact_154_Collect__mono__iff, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P2 @ X2) => (Q @ X2)))))))).
% 2.31/1.21 thf(fact_155_llistE, axiom, (! [A:$tType,Y4:(coinductive_llist @ A)]: (((Y4 != (coinductive_LNil @ A)) => (~ ((! [X212:A,X222:(coinductive_llist @ A)]: ((Y4 != (((coinductive_LCons @ A) @ X212) @ X222)))))))))).
% 2.31/1.21 thf(fact_156_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X2:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs2)))))))).
% 2.31/1.21 thf(fact_157_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X21) @ X22))))).
% 2.31/1.21 thf(fact_158_finlsts_OLCons__fin, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A4) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ L)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_159_alllsts_OLCons__all, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ A) @ A4) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ L)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_160_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y4:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y4) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y4) @ Ys)))))).
% 2.31/1.21 thf(fact_161_finlsts_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P2:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((P2 @ (coinductive_LNil @ A)) => ((! [L2:(coinductive_llist @ A),A5:A]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P2 @ L2) => ((((member @ A) @ A5) @ A2) => (P2 @ (((coinductive_LCons @ A) @ A5) @ L2))))))) => (P2 @ X))))))).
% 2.31/1.21 thf(fact_162_finlsts__induct, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P2:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((! [L2:(coinductive_llist @ A)]: (((L2 = (coinductive_LNil @ A)) => (P2 @ L2)))) => ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P2 @ L2) => ((((member @ A) @ A5) @ A2) => (P2 @ (((coinductive_LCons @ A) @ A5) @ L2))))))) => (P2 @ X))))))).
% 2.31/1.21 thf(fact_163_finlsts_Osimps, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2236698231inlsts @ A) @ A2)) = ((A4 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A6:A]: (((A4 = (((coinductive_LCons @ A) @ A6) @ L3)) & ((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ A) @ A6) @ A2)))))))))).
% 2.31/1.21 thf(fact_164_finlsts_Ocases, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2236698231inlsts @ A) @ A2)) => ((A4 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A5:A]: (((A4 = (((coinductive_LCons @ A) @ A5) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => (~ ((((member @ A) @ A5) @ A2)))))))))))))).
% 2.31/1.21 thf(fact_165_alllsts_Ocases, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2435255213lllsts @ A) @ A2)) => ((A4 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A5:A]: (((A4 = (((coinductive_LCons @ A) @ A5) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2435255213lllsts @ A) @ A2)) => (~ ((((member @ A) @ A5) @ A2)))))))))))))).
% 2.31/1.21 thf(fact_166_alllsts_Osimps, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2435255213lllsts @ A) @ A2)) = ((A4 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A6:A]: (((A4 = (((coinductive_LCons @ A) @ A6) @ L3)) & ((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ A) @ A6) @ A2)))))))))).
% 2.31/1.21 thf(fact_167_alllsts_Ocoinduct, axiom, (! [A:$tType,X5:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A),A2:(set @ A)]: (((X5 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X5 @ X3) => ((X3 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A7:A]: (((X3 = (((coinductive_LCons @ A) @ A7) @ L4)) & (((X5 @ L4) | (((member @ (coinductive_llist @ A)) @ L4) @ ((lList2435255213lllsts @ A) @ A2))) & (((member @ A) @ A7) @ A2))))))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_168_not__LCons__le__LNil, axiom, (! [A:$tType,A4:A,L:(coinductive_llist @ A)]: ((~ ((((ord_less_eq @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ L)) @ (coinductive_LNil @ A))))))).
% 2.31/1.21 thf(fact_169_fps__induct, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),P2:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList22096119349pslsts @ A) @ A2)) => ((! [A5:A]: (((((member @ A) @ A5) @ A2) => (P2 @ (((coinductive_LCons @ A) @ A5) @ (coinductive_LNil @ A)))))) => ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList22096119349pslsts @ A) @ A2)) => ((P2 @ L2) => ((((member @ A) @ A5) @ A2) => (P2 @ (((coinductive_LCons @ A) @ A5) @ L2))))))) => (P2 @ L))))))).
% 2.31/1.21 thf(fact_170_fpslsts__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList22096119349pslsts @ A) @ A2)) => (~ ((! [A5:A,Rs:(coinductive_llist @ A)]: (((R = (((coinductive_LCons @ A) @ A5) @ Rs)) => ((((member @ A) @ A5) @ A2) => (~ ((((member @ (coinductive_llist @ A)) @ Rs) @ ((lList2236698231inlsts @ A) @ A2)))))))))))))).
% 2.31/1.21 thf(fact_171_infsuff__mono2, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A),A2:(set @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ T) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ (((lList2649413865nfsuff @ A) @ A2) @ T)) @ (((lList2649413865nfsuff @ A) @ A2) @ S)))))).
% 2.31/1.21 thf(fact_172_lrev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),P2:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => ((P2 @ (coinductive_LNil @ A)) => ((! [X3:A,Xs3:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs3) @ ((lList2236698231inlsts @ A) @ A2)) => ((P2 @ Xs3) => ((((member @ A) @ X3) @ A2) => (P2 @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A))))))))) => (P2 @ Xs))))))).
% 2.31/1.21 thf(fact_173_finlsts__rev__cases, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => ((T != (coinductive_LNil @ A)) => (~ ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A5) @ A2) => (T != (((coinductive_lappend @ A) @ L2) @ (((coinductive_LCons @ A) @ A5) @ (coinductive_LNil @ A))))))))))))))).
% 2.31/1.21 thf(fact_174_llast__snoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),X:A]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2170638824_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A)))) = X))))).
% 2.31/1.21 thf(fact_175_LList2__Mirabelle__hamjzmohle_Ollast__lappend, axiom, (! [A:$tType,X:(coinductive_llist @ A),Y4:(coinductive_llist @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Y4) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2170638824_llast @ A) @ (((coinductive_lappend @ A) @ X) @ (((coinductive_LCons @ A) @ A4) @ Y4))) = ((lList2170638824_llast @ A) @ (((coinductive_LCons @ A) @ A4) @ Y4)))))))).
% 2.31/1.21 thf(fact_176_lbutlast__lapp__llast, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList22096119349pslsts @ A) @ A2)) => (L = (((coinductive_lappend @ A) @ ((lList2370560421utlast @ A) @ L)) @ (((coinductive_LCons @ A) @ ((lList2170638824_llast @ A) @ L)) @ (coinductive_LNil @ A)))))))).
% 2.31/1.21 thf(fact_177_LList2__Mirabelle__hamjzmohle_Ollast__LCons, axiom, (! [B:$tType,R:(coinductive_llist @ B),A2:(set @ B),A4:B]: (((((member @ (coinductive_llist @ B)) @ R) @ ((lList2236698231inlsts @ B) @ A2)) => (((R = (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A4) @ R)) = A4)) & ((R != (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A4) @ R)) = ((lList2170638824_llast @ B) @ R)))))))).
% 2.31/1.21 thf(fact_178_ltake__lappend__llength, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((lList22119844313_ltake @ A) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21232602520length @ A) @ R)) = R))))).
% 2.31/1.21 thf(fact_179_infsuff__finpref__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ (((lList21202317876inpref @ A) @ A2) @ R)) = (((member @ (coinductive_llist @ A)) @ R) @ (((lList2649413865nfsuff @ A) @ A2) @ T)))))))).
% 2.31/1.21 thf(fact_180_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y4:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y4) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y4) @ Xs2)) & (((coindu328551480prefix @ A) @ Xs2) @ Ys))))))))).
% 2.31/1.21 thf(fact_181_lapp__inf, axiom, (! [A:$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))))).
% 2.31/1.21 thf(fact_182_notfin__inf, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.31/1.21 thf(fact_183_notinf__fin, axiom, (! [A:$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)))))))).
% 2.31/1.21 thf(fact_184_infsuff__LNil, axiom, (! [A:$tType,A2:(set @ A)]: (((((lList2649413865nfsuff @ A) @ A2) @ (coinductive_LNil @ A)) = ((lList21612149805nflsts @ A) @ A2))))).
% 2.31/1.21 thf(fact_185_llength__take, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((lList21232602520length @ A) @ (((lList22119844313_ltake @ A) @ T) @ I)) = I))))).
% 2.31/1.21 thf(fact_186_inflstsI, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_187_infsuff__inf, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ (((lList2649413865nfsuff @ A) @ A2) @ S)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_188_infT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.31/1.21 thf(fact_189_llist__inf__le, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => ((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ T) = (S = T)))))).
% 2.31/1.21 thf(fact_190_infsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_191_inflstsI2, axiom, (! [A:$tType,A4:A,A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ A) @ A4) @ A2) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_192_inflsts__cases, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => (~ ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ A) @ A5) @ A2) => (S != (((coinductive_LCons @ A) @ A5) @ L2)))))))))))).
% 2.31/1.21 thf(fact_193_fin__inf__cases, axiom, (! [A:$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)))))))).
% 2.31/1.21 thf(fact_194_lapp__fin__infT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_195_lapp__inv2T, axiom, (! [A:$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))))))).
% 2.31/1.21 thf(fact_196_lapp__infT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A2)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_197_app__invT, axiom, (! [A:$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))))))).
% 2.31/1.21 thf(fact_198_alllstsE, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_199_prefix__lemma, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),Y4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ Y4) @ ((lList21612149805nflsts @ A) @ A2)) => ((! [S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList2236698231inlsts @ A) @ A2)) => ((((ord_less_eq @ (coinductive_llist @ A)) @ S2) @ X) => (((ord_less_eq @ (coinductive_llist @ A)) @ S2) @ Y4))))) => (X = Y4))))))).
% 2.31/1.21 thf(fact_200_inf__neqE, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),Y4:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ Y4) @ ((lList21612149805nflsts @ A) @ A2)) => ((X != Y4) => (~ ((! [S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList2236698231inlsts @ A) @ A2)) => ((((ord_less_eq @ (coinductive_llist @ A)) @ S2) @ X) => (((ord_less_eq @ (coinductive_llist @ A)) @ S2) @ Y4))))))))))))).
% 2.31/1.21 thf(fact_201_inflsts__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((lList21612149805nflsts @ A) @ A2)) @ ((lList21612149805nflsts @ A) @ B4)))))).
% 2.31/1.21 thf(fact_202_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.31/1.21 thf(fact_203_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 2.31/1.21 thf(fact_204_finpref__infsuff, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ (((lList21202317876inpref @ A) @ A2) @ T)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ T) @ (((lList2649413865nfsuff @ A) @ A2) @ R))))))).
% 2.31/1.21 thf(fact_205_inflstsE, axiom, (! [A:$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))))))))))).
% 2.31/1.21 thf(fact_206_lapp__allT__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A2)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_207_infsuff__appE, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ (((lList2649413865nfsuff @ A) @ A2) @ R)) => (~ ((! [S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList21612149805nflsts @ A) @ A2)) => (T != (((coinductive_lappend @ A) @ R) @ S2)))))))))))).
% 2.31/1.21 thf(fact_208_infsafety__def, axiom, (! [A:$tType]: (((lList21015939545safety @ A) = (^ [A3:(set @ A),P:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList21612149805nflsts @ A) @ A3)) => ((! [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ (((lList21202317876inpref @ A) @ A3) @ X2)) => (? [Z:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Z) @ ((lList21612149805nflsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Y) @ Z)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ X2) @ P))))))))))).
% 2.31/1.21 thf(fact_209_infliveness__def, axiom, (! [A:$tType]: (((lList21015763786veness @ A) = (^ [A3:(set @ A),P:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList2236698231inlsts @ A) @ A3)) => (? [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ ((lList21612149805nflsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X2) @ Y)) @ P))))))))))))).
% 2.31/1.21 thf(fact_210_llength__drop__take, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: ((((((lList2508575361_ldrop @ A) @ T) @ I) != (coinductive_LNil @ A)) => (((lList21232602520length @ A) @ (((lList22119844313_ltake @ A) @ T) @ I)) = I))))).
% 2.31/1.21 thf(fact_211_LList2__Mirabelle__hamjzmohle_Oldrop__LNil, axiom, (! [A:$tType,I:nat]: (((((lList2508575361_ldrop @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 2.31/1.21 thf(fact_212_ldrop__fin__iffT, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) = (((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.31/1.21 thf(fact_213_ldrop__inf__iffT, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))) = (((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.31/1.21 thf(fact_214_ldrop__infT, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList21612149805nflsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_215_ldropT, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_216_ldrop__finT, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.31/1.21 thf(fact_217_drop__nonLNil, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: ((((((lList2508575361_ldrop @ A) @ T) @ I) != (coinductive_LNil @ A)) => (T != (coinductive_LNil @ A)))))).
% 2.31/1.21 thf(fact_218_ldrop__LNil__less, axiom, (! [A:$tType,J:nat,I:nat,T:(coinductive_llist @ A)]: (((((ord_less_eq @ nat) @ J) @ I) => (((((lList2508575361_ldrop @ A) @ T) @ J) = (coinductive_LNil @ A)) => ((((lList2508575361_ldrop @ A) @ T) @ I) = (coinductive_LNil @ A))))))).
% 2.31/1.21 thf(fact_219_ltake__ldrop__id, axiom, (! [A:$tType,X:(coinductive_llist @ A),I:nat]: (((((coinductive_lappend @ A) @ (((lList22119844313_ltake @ A) @ X) @ I)) @ (((lList2508575361_ldrop @ A) @ X) @ I)) = X)))).
% 2.31/1.21 thf(fact_220_lapp__suff__llength, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((lList2508575361_ldrop @ A) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21232602520length @ A) @ R)) = S))))).
% 2.31/1.21 thf(fact_221_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (coinductive_LNil @ B))))))).
% 2.31/1.21 thf(fact_222_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y4:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y4) @ Ys))))).
% 2.31/1.21 thf(fact_223_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B),Y4:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (((coinductive_LCons @ B) @ Y4) @ Ys)) = ((X = Y4) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 2.31/1.21 thf(fact_224_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.31/1.21 thf(fact_225_llist__less__induct, axiom, (! [A:$tType,P2:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs3:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs3) => (P2 @ Ys2)))) => (P2 @ Xs3)))) => (P2 @ Xs))))).
% 2.31/1.21 thf(fact_226_finlsts__rec__LCons, axiom, (! [B:$tType,A:$tType,R:(coinductive_llist @ A),A2:(set @ A),C2:B,D3:(A > ((coinductive_llist @ A) > (B > B))),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((((lList21916056377ts_rec @ B) @ A) @ C2) @ D3) @ (((coinductive_LCons @ A) @ A4) @ R)) = (((D3 @ A4) @ R) @ (((((lList21916056377ts_rec @ B) @ A) @ C2) @ D3) @ R))))))).
% 2.31/1.21 thf(fact_227_finlsts__rec__LCons__def, axiom, (! [B:$tType,A:$tType,F:((coinductive_llist @ A) > B),C2:B,D3:(A > ((coinductive_llist @ A) > (B > B))),R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D3)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((F @ (((coinductive_LCons @ A) @ A4) @ R)) = (((D3 @ A4) @ R) @ (F @ R)))))))).
% 2.31/1.21 thf(fact_228_finlsts__rec__LNil__def, axiom, (! [A:$tType,B:$tType,F:((coinductive_llist @ A) > B),C2:B,D3:(A > ((coinductive_llist @ A) > (B > B)))]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D3)) => ((F @ (coinductive_LNil @ A)) = C2))))).
% 2.31/1.21 thf(fact_229_finlsts__rec__LNil, axiom, (! [B:$tType,A:$tType,C2:A,D3:(B > ((coinductive_llist @ B) > (A > A)))]: (((((((lList21916056377ts_rec @ A) @ B) @ C2) @ D3) @ (coinductive_LNil @ B)) = C2)))).
% 2.31/1.21 thf(fact_230_inflsts__def, axiom, (! [A:$tType]: (((lList21612149805nflsts @ A) = (^ [A3:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A3)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))))).
% 2.31/1.21 thf(fact_231_LList2__Mirabelle__hamjzmohle_Ollength__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList21232602520length @ A) @ (((coinductive_LCons @ A) @ A4) @ R)) = (suc @ ((lList21232602520length @ A) @ R))))))).
% 2.31/1.21 thf(fact_232_DiffI, axiom, (! [A:$tType,C2:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A2) => ((~ ((((member @ A) @ C2) @ B4))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B4))))))).
% 2.31/1.21 thf(fact_233_Diff__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B4)) = ((((member @ A) @ C2) @ A2) & (~ ((((member @ A) @ C2) @ B4)))))))).
% 2.31/1.21 thf(fact_234_Diff__idemp, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B4)) @ B4) = (((minus_minus @ (set @ A)) @ A2) @ B4))))).
% 2.31/1.21 thf(fact_235_ltake__LCons__Suc, axiom, (! [A:$tType,A4:A,L:(coinductive_llist @ A),I:nat]: (((((lList22119844313_ltake @ A) @ (((coinductive_LCons @ A) @ A4) @ L)) @ (suc @ I)) = (((coinductive_LCons @ A) @ A4) @ (((lList22119844313_ltake @ A) @ L) @ I)))))).
% 2.31/1.21 thf(fact_236_DiffE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B4)) => (~ (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B4)))))))).
% 2.31/1.21 thf(fact_237_DiffD1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B4)) => (((member @ A) @ C2) @ A2))))).
% 2.31/1.21 thf(fact_238_DiffD2, axiom, (! [A:$tType,C2:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B4)) => (~ ((((member @ A) @ C2) @ B4))))))).
% 2.31/1.21 thf(fact_239_Diff__mono, axiom, (! [A:$tType,A2:(set @ A),C3:(set @ A),D4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C3) => ((((ord_less_eq @ (set @ A)) @ D4) @ B4) => (((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B4)) @ (((minus_minus @ (set @ A)) @ C3) @ D4))))))).
% 2.31/1.21 thf(fact_240_Diff__subset, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B4)) @ A2)))).
% 2.31/1.21 thf(fact_241_double__diff, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C3) => ((((minus_minus @ (set @ A)) @ B4) @ (((minus_minus @ (set @ A)) @ C3) @ A2)) = A2)))))).
% 2.31/1.21 thf(fact_242_lift__Suc__antimono__le, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [F:(nat > A),N:nat,N2:nat]: (((! [N3:nat]: ((((ord_less_eq @ A) @ (F @ (suc @ N3))) @ (F @ N3)))) => ((((ord_less_eq @ nat) @ N) @ N2) => (((ord_less_eq @ A) @ (F @ N2)) @ (F @ N)))))))))).
% 2.31/1.21 thf(fact_243_lift__Suc__mono__le, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [F:(nat > A),N:nat,N2:nat]: (((! [N3:nat]: ((((ord_less_eq @ A) @ (F @ N3)) @ (F @ (suc @ N3))))) => ((((ord_less_eq @ nat) @ N) @ N2) => (((ord_less_eq @ A) @ (F @ N)) @ (F @ N2)))))))))).
% 2.31/1.21 thf(fact_244_diff__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A,D3:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B2) => ((((ord_less_eq @ A) @ D3) @ C2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ (((minus_minus @ A) @ B2) @ D3)))))))))).
% 2.31/1.21 thf(fact_245_diff__left__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A4) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C2) @ A4)) @ (((minus_minus @ A) @ C2) @ B2))))))))).
% 2.31/1.21 thf(fact_246_diff__eq__diff__less__eq, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A,D3:A]: ((((((minus_minus @ A) @ A4) @ B2) = (((minus_minus @ A) @ C2) @ D3)) => ((((ord_less_eq @ A) @ A4) @ B2) = (((ord_less_eq @ A) @ C2) @ D3))))))))).
% 2.31/1.21 thf(fact_247_diff__right__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ (((minus_minus @ A) @ B2) @ C2))))))))).
% 2.31/1.21 thf(fact_248_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) = X)))).
% 2.31/1.21 thf(fact_249_take__inf__less, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))) => (((ord_less @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ T) @ I)) @ T))))).
% 2.31/1.21 thf(fact_250_llast__LCons2, axiom, (! [A:$tType,X:A,Y4:A,Xs:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y4) @ Xs))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y4) @ Xs)))))).
% 2.31/1.21 thf(fact_251_less__LCons, axiom, (! [A:$tType,A4:A,R:(coinductive_llist @ A),B2:A,T:(coinductive_llist @ A)]: (((((ord_less @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ R)) @ (((coinductive_LCons @ A) @ B2) @ T)) = ((A4 = B2) & (((ord_less @ (coinductive_llist @ A)) @ R) @ T)))))).
% 2.31/1.21 thf(fact_252_llist__less__finT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((ord_less @ (coinductive_llist @ A)) @ R) @ S) => ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.31/1.21 thf(fact_253_LNil__less__LCons, axiom, (! [A:$tType,A4:A,T:(coinductive_llist @ A)]: ((((ord_less @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (((coinductive_LCons @ A) @ A4) @ T))))).
% 2.31/1.21 thf(fact_254_llist__less__def, axiom, (! [A:$tType]: (((ord_less @ (coinductive_llist @ A)) = (^ [S3:(coinductive_llist @ A),T3:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S3) @ T3) & (S3 != T3)))))))).
% 2.31/1.21 thf(fact_255_llist__less__le__not__le, axiom, (! [A:$tType]: (((ord_less @ (coinductive_llist @ A)) = (^ [S3:(coinductive_llist @ A),T3:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S3) @ T3) & (~ ((((ord_less_eq @ (coinductive_llist @ A)) @ T3) @ S3)))))))))).
% 2.31/1.21 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A8:$tType,A9:$tType]: ((((order_top @ A9) @ (type2 @ A9)) => ((order_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.31/1.21 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.31/1.21 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A9) @ (type2 @ A9)) => ((order @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.31/1.21 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.31/1.21 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.31/1.21 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.31/1.21 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.31/1.21 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, ((order @ nat) @ (type2 @ nat))).
% 2.31/1.21 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, ((ord @ nat) @ (type2 @ nat))).
% 2.31/1.21 thf(tcon_Set_Oset___Orderings_Oorder__top_4, axiom, (! [A8:$tType]: (((order_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.31/1.21 thf(tcon_Set_Oset___Orderings_Opreorder_5, axiom, (! [A8:$tType]: (((preorder @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.31/1.21 thf(tcon_Set_Oset___Orderings_Oorder_6, axiom, (! [A8:$tType]: (((order @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.31/1.21 thf(tcon_Set_Oset___Orderings_Otop_7, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.31/1.21 thf(tcon_Set_Oset___Orderings_Oord_8, axiom, (! [A8:$tType]: (((ord @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.31/1.21 thf(tcon_HOL_Obool___Orderings_Oorder__top_9, axiom, ((order_top @ $o) @ (type2 @ $o))).
% 2.31/1.21 thf(tcon_HOL_Obool___Orderings_Opreorder_10, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.31/1.21 thf(tcon_HOL_Obool___Orderings_Olinorder_11, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.31/1.21 thf(tcon_HOL_Obool___Orderings_Oorder_12, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.31/1.21 thf(tcon_HOL_Obool___Orderings_Otop_13, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.31/1.21 thf(tcon_HOL_Obool___Orderings_Oord_14, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.31/1.21 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_15, axiom, (! [A8:$tType]: (((preorder @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.31/1.21 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_16, axiom, (! [A8:$tType]: (((order @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.31/1.21 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_17, axiom, (! [A8:$tType]: (((ord @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.31/1.21 thf(conj_0, conjecture, (? [X4:(coinductive_llist @ a)]: (((((member @ (coinductive_llist @ a)) @ X4) @ ((lList2435255213lllsts @ a) @ (top_top @ (set @ a)))) & (((member @ (coinductive_llist @ a)) @ (((coinductive_lappend @ a) @ r) @ X4)) @ p))))).
% 2.31/1.21 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ssc2Uifky4/DTF2DTF10143.p
% 2.31/1.21 ------------------------
% 2.31/1.26 ---- Cleaned THF ---
% 2.31/1.26 thf(ty_t_Coinductive__List_Ollist,type,
% 2.31/1.26 coinductive_llist: $tType > $tType ).
% 2.31/1.26
% 2.31/1.26 thf(ty_t_Set_Oset,type,
% 2.31/1.26 set: $tType > $tType ).
% 2.31/1.26
% 2.31/1.26 thf(ty_t_Nat_Onat,type,
% 2.31/1.26 nat: $tType ).
% 2.31/1.26
% 2.31/1.26 thf(ty_t_itself,type,
% 2.31/1.26 itself: $tType > $tType ).
% 2.31/1.26
% 2.31/1.26 thf(ty_tf_a,type,
% 2.31/1.26 a: $tType ).
% 2.31/1.26
% 2.31/1.26 thf(sy_cl_HOL_Otype,type,
% 2.31/1.26 type:
% 2.31/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_cl_Orderings_Oord,type,
% 2.31/1.26 ord:
% 2.31/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_cl_Orderings_Otop,type,
% 2.31/1.26 top:
% 2.31/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_cl_Orderings_Oorder,type,
% 2.31/1.26 order:
% 2.31/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_cl_Orderings_Olinorder,type,
% 2.31/1.26 linorder:
% 2.31/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_cl_Orderings_Opreorder,type,
% 2.31/1.26 preorder:
% 2.31/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_cl_Orderings_Oorder__top,type,
% 2.31/1.26 order_top:
% 2.31/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.31/1.26 ordered_ab_group_add:
% 2.31/1.26 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.31/1.26 coindu328551480prefix:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Coinductive__List_Olappend,type,
% 2.31/1.26 coinductive_lappend:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Coinductive__List_Ollast,type,
% 2.31/1.26 coinductive_llast:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.31/1.26 coinductive_LCons:
% 2.31/1.26 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.31/1.26 coinductive_LNil:
% 2.31/1.26 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.31/1.26 coindu1478340336prefix:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.31/1.26 minus_minus:
% 2.31/1.26 !>[A: $tType] : ( A > A > A ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 2.31/1.26 lList2435255213lllsts:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 2.31/1.26 lList2236698231inlsts:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 2.31/1.26 lList21916056377ts_rec:
% 2.31/1.26 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinpref,type,
% 2.31/1.26 lList21202317876inpref:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 2.31/1.26 lList22096119349pslsts:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfliveness,type,
% 2.31/1.26 lList21015763786veness:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 2.31/1.26 lList21612149805nflsts:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsafety,type,
% 2.31/1.26 lList21015939545safety:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsuff,type,
% 2.31/1.26 lList2649413865nfsuff:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 2.31/1.26 lList2370560421utlast:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 2.31/1.26 lList2508575361_ldrop:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oliveness,type,
% 2.31/1.26 lList21805353693veness:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 2.31/1.26 lList2170638824_llast:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 2.31/1.26 lList21232602520length:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 2.31/1.26 lList2281150353e_lrev:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 2.31/1.26 lList22119844313_ltake:
% 2.31/1.26 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opfinpref,type,
% 2.31/1.26 lList2467029176inpref:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposliveness,type,
% 2.31/1.26 lList21952340509veness:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 2.31/1.26 lList21148268032oslsts:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opossafety,type,
% 2.31/1.26 lList292406316safety:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opprefix__closed,type,
% 2.31/1.26 lList21974196564closed:
% 2.31/1.26 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oprefix__closed,type,
% 2.31/1.26 lList21638733016closed:
% 2.31/1.26 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osafety,type,
% 2.31/1.26 lList21350011628safety:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuff,type,
% 2.31/1.26 lList21475143548e_suff:
% 2.31/1.26 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuffix__closed,type,
% 2.31/1.26 lList2736192599closed:
% 2.31/1.26 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Nat_OSuc,type,
% 2.31/1.26 suc: nat > nat ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.31/1.26 ord_less:
% 2.31/1.26 !>[A: $tType] : ( A > A > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.31/1.26 ord_less_eq:
% 2.31/1.26 !>[A: $tType] : ( A > A > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.31/1.26 top_top:
% 2.31/1.26 !>[A: $tType] : A ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Pure_Otype,type,
% 2.31/1.26 type2:
% 2.31/1.26 !>[A: $tType] : ( itself @ A ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_Set_OCollect,type,
% 2.31/1.26 collect:
% 2.31/1.26 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_c_member,type,
% 2.31/1.26 member:
% 2.31/1.26 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_v_P,type,
% 2.31/1.26 p: set @ ( coinductive_llist @ a ) ).
% 2.31/1.26
% 2.31/1.26 thf(sy_v_r____,type,
% 2.31/1.26 r: coinductive_llist @ a ).
% 2.31/1.26
% 2.31/1.26 thf(sy_v_s____,type,
% 2.31/1.26 s: coinductive_llist @ a ).
% 2.31/1.26
% 2.31/1.26 thf(sy_v_t____,type,
% 2.31/1.26 t: coinductive_llist @ a ).
% 2.31/1.26
% 2.31/1.26 thf(sy_v_u____,type,
% 2.31/1.26 u: coinductive_llist @ a ).
% 2.31/1.26
% 2.31/1.26 thf(sy_v_v____,type,
% 2.31/1.26 v: coinductive_llist @ a ).
% 2.31/1.26
% 2.31/1.26 thf(fact_0_tP,axiom,
% 2.31/1.26 member @ ( coinductive_llist @ a ) @ t @ p ).
% 2.31/1.26
% 2.31/1.26 thf(fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062,axiom,
% 2.31/1.26 ( t
% 2.31/1.26 = ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ v ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_2_psafety,axiom,
% 2.31/1.26 lList292406316safety @ a @ ( top_top @ ( set @ a ) ) @ p ).
% 2.31/1.26
% 2.31/1.26 thf(fact_3_scons,axiom,
% 2.31/1.26 ( s
% 2.31/1.26 = ( coinductive_lappend @ a @ r @ u ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_At_A_061_Ar_A_064_064_Au_A_064_064_Av_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.31/1.26 ~ ! [V: coinductive_llist @ a] :
% 2.31/1.26 ( t
% 2.31/1.26 != ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ V ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_5_alllsts__UNIV,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_6__092_060open_062r_A_092_060in_062_Apfinpref_AUNIV_As_092_060close_062,axiom,
% 2.31/1.26 member @ ( coinductive_llist @ a ) @ r @ ( lList2467029176inpref @ a @ ( top_top @ ( set @ a ) ) @ s ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_7_lappT,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_8_lapp__all__invT,axiom,
% 2.31/1.26 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062u_O_As_A_061_Ar_A_064_064_Au_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.31/1.26 ~ ! [U: coinductive_llist @ a] :
% 2.31/1.26 ( s
% 2.31/1.26 != ( coinductive_lappend @ a @ r @ U ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_10_UNIV__I,axiom,
% 2.31/1.26 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_11_iso__tuple__UNIV__I,axiom,
% 2.31/1.26 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_12_top__apply,axiom,
% 2.31/1.26 ! [C: $tType,D: $tType] :
% 2.31/1.26 ( ( top @ C @ ( type2 @ C ) )
% 2.31/1.26 => ( ( top_top @ ( D > C ) )
% 2.31/1.26 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_13_lappend__assoc,axiom,
% 2.31/1.26 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.31/1.26 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 2.31/1.26 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_14_UNIV__eq__I,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A] :
% 2.31/1.26 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 2.31/1.26 => ( ( top_top @ ( set @ A ) )
% 2.31/1.26 = A2 ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_15_UNIV__witness,axiom,
% 2.31/1.26 ! [A: $tType] :
% 2.31/1.26 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_16_posliveness__def,axiom,
% 2.31/1.26 ! [A: $tType] :
% 2.31/1.26 ( ( lList21952340509veness @ A )
% 2.31/1.26 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.31/1.26 ! [X2: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList22096119349pslsts @ A @ A3 ) )
% 2.31/1.26 => ? [Y: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P ) ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_17_suff__all,axiom,
% 2.31/1.26 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21475143548e_suff @ A @ A2 @ S ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_18_safetyD,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A ),T: coinductive_llist @ A] :
% 2.31/1.26 ( ( lList21350011628safety @ A @ A2 @ P2 )
% 2.31/1.26 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( ! [R2: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ R2 @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 2.31/1.26 => ? [X4: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R2 @ X4 ) @ P2 ) ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ T @ P2 ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_19_safetyE,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.31/1.26 ( ( lList21350011628safety @ A @ A2 @ P2 )
% 2.31/1.26 => ! [X4: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( ! [Xa: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList21202317876inpref @ A @ A2 @ X4 ) )
% 2.31/1.26 => ? [Xb: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Xb @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xa @ Xb ) @ P2 ) ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ X4 @ P2 ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_20_safetyI,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.31/1.26 ( ! [T2: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( ! [X4: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList21202317876inpref @ A @ A2 @ T2 ) )
% 2.31/1.26 => ? [Xa: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X4 @ Xa ) @ P2 ) ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ T2 @ P2 ) ) )
% 2.31/1.26 => ( lList21350011628safety @ A @ A2 @ P2 ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_21_spos,axiom,
% 2.31/1.26 ( s
% 2.31/1.26 != ( coinductive_LNil @ a ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_22_st,axiom,
% 2.31/1.26 ord_less_eq @ ( coinductive_llist @ a ) @ s @ t ).
% 2.31/1.26
% 2.31/1.26 thf(fact_23_top__set__def,axiom,
% 2.31/1.26 ! [A: $tType] :
% 2.31/1.26 ( ( top_top @ ( set @ A ) )
% 2.31/1.26 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_24_finpref__suff,axiom,
% 2.31/1.26 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 2.31/1.26 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_25_safety__def,axiom,
% 2.31/1.26 ! [A: $tType] :
% 2.31/1.26 ( ( lList21350011628safety @ A )
% 2.31/1.26 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.31/1.26 ! [X2: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.31/1.26 => ( ! [Y: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21202317876inpref @ A @ A3 @ X2 ) )
% 2.31/1.26 => ? [Z: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P ) ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ X2 @ P ) ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_26_safety__prefix__closed,axiom,
% 2.31/1.26 ! [A: $tType,P2: set @ ( coinductive_llist @ A )] :
% 2.31/1.26 ( ( lList21350011628safety @ A @ ( top_top @ ( set @ A ) ) @ P2 )
% 2.31/1.26 => ( lList21638733016closed @ A @ P2 ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_27_possafety__def,axiom,
% 2.31/1.26 ! [A: $tType] :
% 2.31/1.26 ( ( lList292406316safety @ A )
% 2.31/1.26 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.31/1.26 ! [X2: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList21148268032oslsts @ A @ A3 ) )
% 2.31/1.26 => ( ! [Y: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2467029176inpref @ A @ A3 @ X2 ) )
% 2.31/1.26 => ? [Z: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P ) ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ X2 @ P ) ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_28_possafetyI,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.31/1.26 ( ! [T2: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.31/1.26 => ( ! [X4: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2467029176inpref @ A @ A2 @ T2 ) )
% 2.31/1.26 => ? [Xa: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X4 @ Xa ) @ P2 ) ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ T2 @ P2 ) ) )
% 2.31/1.26 => ( lList292406316safety @ A @ A2 @ P2 ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_29_possafetyE,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.31/1.26 ( ( lList292406316safety @ A @ A2 @ P2 )
% 2.31/1.26 => ! [X4: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.31/1.26 => ( ! [Xa: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2467029176inpref @ A @ A2 @ X4 ) )
% 2.31/1.26 => ? [Xb: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ Xb @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xa @ Xb ) @ P2 ) ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ X4 @ P2 ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_30_possafetyD,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A ),T: coinductive_llist @ A] :
% 2.31/1.26 ( ( lList292406316safety @ A @ A2 @ P2 )
% 2.31/1.26 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.31/1.26 => ( ! [R2: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ R2 @ ( lList2467029176inpref @ A @ A2 @ T ) )
% 2.31/1.26 => ? [X4: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R2 @ X4 ) @ P2 ) ) )
% 2.31/1.26 => ( member @ ( coinductive_llist @ A ) @ T @ P2 ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_31_pfinpref__iff,axiom,
% 2.31/1.26 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2467029176inpref @ A @ A2 @ S ) )
% 2.31/1.26 = ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21202317876inpref @ A @ A2 @ S ) )
% 2.31/1.26 & ( X
% 2.31/1.26 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_32_suff__finpref__iff,axiom,
% 2.31/1.26 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.26 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 2.31/1.26 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_33_suff__appE,axiom,
% 2.31/1.26 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.26 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) )
% 2.31/1.26 => ~ ! [S2: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.26 => ( T
% 2.31/1.26 != ( coinductive_lappend @ A @ R @ S2 ) ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_34_suff__LNil,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A] :
% 2.31/1.26 ( ( lList21475143548e_suff @ A @ A2 @ ( coinductive_LNil @ A ) )
% 2.31/1.26 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_35_top__empty__eq,axiom,
% 2.31/1.26 ! [A: $tType] :
% 2.31/1.26 ( ( top_top @ ( A > $o ) )
% 2.31/1.26 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_36_order__refl,axiom,
% 2.31/1.26 ! [A: $tType] :
% 2.31/1.26 ( ( preorder @ A @ ( type2 @ A ) )
% 2.31/1.26 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_37_llist__le__refl,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A] : ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ S ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_38_top1I,axiom,
% 2.31/1.26 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_39_LNil__is__lappend__conv,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.31/1.26 ( ( ( coinductive_LNil @ A )
% 2.31/1.26 = ( coinductive_lappend @ A @ S @ T ) )
% 2.31/1.26 = ( ( S
% 2.31/1.26 = ( coinductive_LNil @ A ) )
% 2.31/1.26 & ( T
% 2.31/1.26 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_40_lappend__is__LNil__conv,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.31/1.26 ( ( ( coinductive_lappend @ A @ S @ T )
% 2.31/1.26 = ( coinductive_LNil @ A ) )
% 2.31/1.26 = ( ( S
% 2.31/1.26 = ( coinductive_LNil @ A ) )
% 2.31/1.26 & ( T
% 2.31/1.26 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_41_lappend__code_I1_J,axiom,
% 2.31/1.26 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.31/1.26 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.31/1.26 = Ys ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_42_lappend__LNil2,axiom,
% 2.31/1.26 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.31/1.26 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.31/1.26 = Xs ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_43_LNil__eq__lappend__iff,axiom,
% 2.31/1.26 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.31/1.26 ( ( ( coinductive_LNil @ A )
% 2.31/1.26 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.31/1.26 = ( ( Xs
% 2.31/1.26 = ( coinductive_LNil @ A ) )
% 2.31/1.26 & ( Ys
% 2.31/1.26 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_44_lappend__eq__LNil__iff,axiom,
% 2.31/1.26 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.31/1.26 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.31/1.26 = ( coinductive_LNil @ A ) )
% 2.31/1.26 = ( ( Xs
% 2.31/1.26 = ( coinductive_LNil @ A ) )
% 2.31/1.26 & ( Ys
% 2.31/1.26 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_45_mem__Collect__eq,axiom,
% 2.31/1.26 ! [A: $tType,A4: A,P2: A > $o] :
% 2.31/1.26 ( ( member @ A @ A4 @ ( collect @ A @ P2 ) )
% 2.31/1.26 = ( P2 @ A4 ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_46_Collect__mem__eq,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A] :
% 2.31/1.26 ( ( collect @ A
% 2.31/1.26 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 2.31/1.26 = A2 ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_47_Collect__cong,axiom,
% 2.31/1.26 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.31/1.26 ( ! [X3: A] :
% 2.31/1.26 ( ( P2 @ X3 )
% 2.31/1.26 = ( Q @ X3 ) )
% 2.31/1.26 => ( ( collect @ A @ P2 )
% 2.31/1.26 = ( collect @ A @ Q ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_48_ext,axiom,
% 2.31/1.26 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.31/1.26 ( ! [X3: A] :
% 2.31/1.26 ( ( F @ X3 )
% 2.31/1.26 = ( G @ X3 ) )
% 2.31/1.26 => ( F = G ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_49_same__lappend__eq,axiom,
% 2.31/1.26 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.26 => ( ( ( coinductive_lappend @ A @ R @ S )
% 2.31/1.26 = ( coinductive_lappend @ A @ R @ T ) )
% 2.31/1.26 = ( S = T ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_50_lapp__fin__fin__iff,axiom,
% 2.31/1.26 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.26 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.26 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_51_le__LNil,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A] :
% 2.31/1.26 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ ( coinductive_LNil @ A ) )
% 2.31/1.26 = ( S
% 2.31/1.26 = ( coinductive_LNil @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_52_LNil__le,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A] : ( ord_less_eq @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ S ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_53_le__lappend,axiom,
% 2.31/1.26 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A] : ( ord_less_eq @ ( coinductive_llist @ A ) @ R @ ( coinductive_lappend @ A @ R @ S ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_54_LNil__suff,axiom,
% 2.31/1.26 ! [A: $tType,A2: set @ A,S: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList21475143548e_suff @ A @ A2 @ S ) )
% 2.31/1.26 = ( S
% 2.31/1.26 = ( coinductive_LNil @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_55_poslsts__UNIV,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A] :
% 2.31/1.26 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.26 = ( S
% 2.31/1.26 != ( coinductive_LNil @ A ) ) ) ).
% 2.31/1.26
% 2.31/1.26 thf(fact_56_fpslsts__iff,axiom,
% 2.31/1.26 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.31/1.27 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 & ( S
% 2.31/1.27 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_57_poslsts__iff,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.31/1.27 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 & ( S
% 2.31/1.27 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_58_le__funD,axiom,
% 2.31/1.27 ! [B: $tType,A: $tType] :
% 2.31/1.27 ( ( ord @ B @ ( type2 @ B ) )
% 2.31/1.27 => ! [F: A > B,G: A > B,X: A] :
% 2.31/1.27 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.31/1.27 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_59_le__funE,axiom,
% 2.31/1.27 ! [B: $tType,A: $tType] :
% 2.31/1.27 ( ( ord @ B @ ( type2 @ B ) )
% 2.31/1.27 => ! [F: A > B,G: A > B,X: A] :
% 2.31/1.27 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.31/1.27 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_60_le__funI,axiom,
% 2.31/1.27 ! [B: $tType,A: $tType] :
% 2.31/1.27 ( ( ord @ B @ ( type2 @ B ) )
% 2.31/1.27 => ! [F: A > B,G: A > B] :
% 2.31/1.27 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 2.31/1.27 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_61_le__fun__def,axiom,
% 2.31/1.27 ! [B: $tType,A: $tType] :
% 2.31/1.27 ( ( ord @ B @ ( type2 @ B ) )
% 2.31/1.27 => ( ( ord_less_eq @ ( A > B ) )
% 2.31/1.27 = ( ^ [F2: A > B,G2: A > B] :
% 2.31/1.27 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_62_order__subst1,axiom,
% 2.31/1.27 ! [A: $tType,B: $tType] :
% 2.31/1.27 ( ( ( order @ B @ ( type2 @ B ) )
% 2.31/1.27 & ( order @ A @ ( type2 @ A ) ) )
% 2.31/1.27 => ! [A4: A,F: B > A,B2: B,C2: B] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A4 @ ( F @ B2 ) )
% 2.31/1.27 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.31/1.27 => ( ! [X3: B,Y2: B] :
% 2.31/1.27 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 2.31/1.27 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.31/1.27 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_63_order__subst2,axiom,
% 2.31/1.27 ! [A: $tType,C: $tType] :
% 2.31/1.27 ( ( ( order @ C @ ( type2 @ C ) )
% 2.31/1.27 & ( order @ A @ ( type2 @ A ) ) )
% 2.31/1.27 => ! [A4: A,B2: A,F: A > C,C2: C] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 2.31/1.27 => ( ! [X3: A,Y2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.31/1.27 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.31/1.27 => ( ord_less_eq @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_64_ord__eq__le__subst,axiom,
% 2.31/1.27 ! [A: $tType,B: $tType] :
% 2.31/1.27 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.31/1.27 & ( ord @ A @ ( type2 @ A ) ) )
% 2.31/1.27 => ! [A4: A,F: B > A,B2: B,C2: B] :
% 2.31/1.27 ( ( A4
% 2.31/1.27 = ( F @ B2 ) )
% 2.31/1.27 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.31/1.27 => ( ! [X3: B,Y2: B] :
% 2.31/1.27 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 2.31/1.27 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.31/1.27 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_65_ord__le__eq__subst,axiom,
% 2.31/1.27 ! [A: $tType,B: $tType] :
% 2.31/1.27 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.31/1.27 & ( ord @ A @ ( type2 @ A ) ) )
% 2.31/1.27 => ! [A4: A,B2: A,F: A > B,C2: B] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 => ( ( ( F @ B2 )
% 2.31/1.27 = C2 )
% 2.31/1.27 => ( ! [X3: A,Y2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.31/1.27 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.31/1.27 => ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_66_eq__iff,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ( ( ^ [Y3: A,Z2: A] : ( Y3 = Z2 ) )
% 2.31/1.27 = ( ^ [X2: A,Y: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.31/1.27 & ( ord_less_eq @ A @ Y @ X2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_67_antisym,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [X: A,Y4: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ X @ Y4 )
% 2.31/1.27 => ( ( ord_less_eq @ A @ Y4 @ X )
% 2.31/1.27 => ( X = Y4 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_68_linear,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( linorder @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [X: A,Y4: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ X @ Y4 )
% 2.31/1.27 | ( ord_less_eq @ A @ Y4 @ X ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_69_eq__refl,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( preorder @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [X: A,Y4: A] :
% 2.31/1.27 ( ( X = Y4 )
% 2.31/1.27 => ( ord_less_eq @ A @ X @ Y4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_70_wlog__linorder__le,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( linorder @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [P2: A > A > $o,B2: A,A4: A] :
% 2.31/1.27 ( ! [A5: A,B3: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A5 @ B3 )
% 2.31/1.27 => ( P2 @ A5 @ B3 ) )
% 2.31/1.27 => ( ( ( P2 @ B2 @ A4 )
% 2.31/1.27 => ( P2 @ A4 @ B2 ) )
% 2.31/1.27 => ( P2 @ A4 @ B2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_71_le__cases,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( linorder @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [X: A,Y4: A] :
% 2.31/1.27 ( ~ ( ord_less_eq @ A @ X @ Y4 )
% 2.31/1.27 => ( ord_less_eq @ A @ Y4 @ X ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_72_order_Otrans,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A,B2: A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.31/1.27 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_73_le__cases3,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( linorder @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [X: A,Y4: A,Z3: A] :
% 2.31/1.27 ( ( ( ord_less_eq @ A @ X @ Y4 )
% 2.31/1.27 => ~ ( ord_less_eq @ A @ Y4 @ Z3 ) )
% 2.31/1.27 => ( ( ( ord_less_eq @ A @ Y4 @ X )
% 2.31/1.27 => ~ ( ord_less_eq @ A @ X @ Z3 ) )
% 2.31/1.27 => ( ( ( ord_less_eq @ A @ X @ Z3 )
% 2.31/1.27 => ~ ( ord_less_eq @ A @ Z3 @ Y4 ) )
% 2.31/1.27 => ( ( ( ord_less_eq @ A @ Z3 @ Y4 )
% 2.31/1.27 => ~ ( ord_less_eq @ A @ Y4 @ X ) )
% 2.31/1.27 => ( ( ( ord_less_eq @ A @ Y4 @ Z3 )
% 2.31/1.27 => ~ ( ord_less_eq @ A @ Z3 @ X ) )
% 2.31/1.27 => ~ ( ( ord_less_eq @ A @ Z3 @ X )
% 2.31/1.27 => ~ ( ord_less_eq @ A @ X @ Y4 ) ) ) ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_74_antisym__conv,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [Y4: A,X: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ Y4 @ X )
% 2.31/1.27 => ( ( ord_less_eq @ A @ X @ Y4 )
% 2.31/1.27 = ( X = Y4 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_75_ord__eq__le__trans,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ord @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A,B2: A,C2: A] :
% 2.31/1.27 ( ( A4 = B2 )
% 2.31/1.27 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.31/1.27 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_76_ord__le__eq__trans,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ord @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A,B2: A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 => ( ( B2 = C2 )
% 2.31/1.27 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_77_order__class_Oorder_Oantisym,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A,B2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 => ( ( ord_less_eq @ A @ B2 @ A4 )
% 2.31/1.27 => ( A4 = B2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_78_order__trans,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( preorder @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [X: A,Y4: A,Z3: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ X @ Y4 )
% 2.31/1.27 => ( ( ord_less_eq @ A @ Y4 @ Z3 )
% 2.31/1.27 => ( ord_less_eq @ A @ X @ Z3 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_79_dual__order_Orefl,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_80_linorder__wlog,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( linorder @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [P2: A > A > $o,A4: A,B2: A] :
% 2.31/1.27 ( ! [A5: A,B3: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A5 @ B3 )
% 2.31/1.27 => ( P2 @ A5 @ B3 ) )
% 2.31/1.27 => ( ! [A5: A,B3: A] :
% 2.31/1.27 ( ( P2 @ B3 @ A5 )
% 2.31/1.27 => ( P2 @ A5 @ B3 ) )
% 2.31/1.27 => ( P2 @ A4 @ B2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_81_dual__order_Otrans,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [B2: A,A4: A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ B2 @ A4 )
% 2.31/1.27 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.31/1.27 => ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_82_dual__order_Oantisym,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [B2: A,A4: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ B2 @ A4 )
% 2.31/1.27 => ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 => ( A4 = B2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_83_pref__locally__linear,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,X: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ X )
% 2.31/1.27 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ T @ X )
% 2.31/1.27 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 2.31/1.27 | ( ord_less_eq @ ( coinductive_llist @ A ) @ T @ S ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_84_prefix__closed__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList21638733016closed @ A )
% 2.31/1.27 = ( ^ [A3: set @ ( coinductive_llist @ A )] :
% 2.31/1.27 ! [X2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X2 @ A3 )
% 2.31/1.27 => ! [S3: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ X2 )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ S3 @ A3 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_85_llist__le__anti__sym,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 2.31/1.27 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ T @ S )
% 2.31/1.27 => ( S = T ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_86_finlsts_OLNil__fin,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_87_llist__le__trans,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ R @ S )
% 2.31/1.27 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 2.31/1.27 => ( ord_less_eq @ ( coinductive_llist @ A ) @ R @ T ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_88_llist__le__finT,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ R @ S )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_89_finT__simp,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_90_fin__finite,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_91_lappfin__finT,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_92_lapp__fin__fin__lemma,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_93_finite__lemma,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B4 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B4 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_94_finsubsetall,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_95_top__greatest,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order_top @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ ( top_top @ A ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_96_top_Oextremum__unique,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order_top @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 2.31/1.27 = ( A4
% 2.31/1.27 = ( top_top @ A ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_97_top_Oextremum__uniqueI,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order_top @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 2.31/1.27 => ( A4
% 2.31/1.27 = ( top_top @ A ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_98_lappend__LNil__LNil,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_99_llist__le__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) )
% 2.31/1.27 = ( ^ [S3: coinductive_llist @ A,T3: coinductive_llist @ A] :
% 2.31/1.27 ? [D2: coinductive_llist @ A] :
% 2.31/1.27 ( T3
% 2.31/1.27 = ( coinductive_lappend @ A @ S3 @ D2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_100_finpref__fin,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21202317876inpref @ A @ A2 @ S ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_101_alllsts_OLNil__all,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_102_suff__finpref,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,R: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_103_pprefix__closed__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList21974196564closed @ A )
% 2.31/1.27 = ( ^ [A3: set @ ( coinductive_llist @ A )] :
% 2.31/1.27 ! [X2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X2 @ A3 )
% 2.31/1.27 => ! [S3: coinductive_llist @ A] :
% 2.31/1.27 ( ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ X2 )
% 2.31/1.27 & ( S3
% 2.31/1.27 != ( coinductive_LNil @ A ) ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ S3 @ A3 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_104_livenessE,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A ),S: coinductive_llist @ A] :
% 2.31/1.27 ( ( lList21805353693veness @ A @ A2 @ P2 )
% 2.31/1.27 => ( ! [T2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ~ ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T2 ) @ P2 ) )
% 2.31/1.27 => ~ ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_105_livenessI,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.31/1.27 ( ! [S2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ? [X4: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S2 @ X4 ) @ P2 ) ) )
% 2.31/1.27 => ( lList21805353693veness @ A @ A2 @ P2 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_106_liveness__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList21805353693veness @ A )
% 2.31/1.27 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.31/1.27 ! [X2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.31/1.27 => ? [Y: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_107_suffix__closed__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList2736192599closed @ A )
% 2.31/1.27 = ( ^ [A3: set @ ( coinductive_llist @ A )] :
% 2.31/1.27 ! [X2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X2 @ A3 )
% 2.31/1.27 => ! [S3: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ X2 @ S3 )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ S3 @ A3 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_108_lrev__lappend,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.31/1.27 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_109_LNil__is__lrev__conv,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( ( coinductive_LNil @ A )
% 2.31/1.27 = ( lList2281150353e_lrev @ A @ Xs ) )
% 2.31/1.27 = ( Xs
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_110_lrev__is__LNil__conv,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.31/1.27 = ( coinductive_LNil @ A ) )
% 2.31/1.27 = ( Xs
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_111_top__conj_I2_J,axiom,
% 2.31/1.27 ! [A: $tType,P2: $o,X: A] :
% 2.31/1.27 ( ( P2
% 2.31/1.27 & ( top_top @ ( A > $o ) @ X ) )
% 2.31/1.27 = P2 ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_112_lrev__LNil,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_113_lrevT,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_114_lrev__is__lrev__conv,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.31/1.27 = ( lList2281150353e_lrev @ A @ Ys ) )
% 2.31/1.27 = ( Xs = Ys ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_115_lrev__lrev__ident,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 2.31/1.27 = Xs ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_116_finlsts__mono,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList2236698231inlsts @ A @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_117_alllsts__mono,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A2 ) @ ( lList2435255213lllsts @ A @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_118_fpslsts__mono,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList22096119349pslsts @ A @ A2 ) @ ( lList22096119349pslsts @ A @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_119_poslsts__mono,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21148268032oslsts @ A @ A2 ) @ ( lList21148268032oslsts @ A @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_120_subset__UNIV,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_121_finpref__mono2,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 2.31/1.27 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21202317876inpref @ A @ A2 @ S ) @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_122_suff__mono2,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 2.31/1.27 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21475143548e_suff @ A @ A2 @ T ) @ ( lList21475143548e_suff @ A @ A2 @ S ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_123_top__conj_I1_J,axiom,
% 2.31/1.27 ! [A: $tType,X: A,P2: $o] :
% 2.31/1.27 ( ( ( top_top @ ( A > $o ) @ X )
% 2.31/1.27 & P2 )
% 2.31/1.27 = P2 ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_124_lrev__LCons,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.31/1.27 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_125_take__fin,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_126_infsuff__finpref,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,R: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_127_ltake__fin,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_128_lbutlast__LNil,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_129_subsetI,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ! [X3: A] :
% 2.31/1.27 ( ( member @ A @ X3 @ A2 )
% 2.31/1.27 => ( member @ A @ X3 @ B4 ) )
% 2.31/1.27 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_130_subset__antisym,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A2 )
% 2.31/1.27 => ( A2 = B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_131_llist_Oinject,axiom,
% 2.31/1.27 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.31/1.27 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 2.31/1.27 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.31/1.27 = ( ( X21 = Y21 )
% 2.31/1.27 & ( X22 = Y22 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_132_lappend__code_I2_J,axiom,
% 2.31/1.27 ! [A: $tType,Xa2: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.31/1.27 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa2 @ X ) @ Ys )
% 2.31/1.27 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_133_LConsE,axiom,
% 2.31/1.27 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 = ( ( member @ A @ X @ A2 )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_134_le__LCons,axiom,
% 2.31/1.27 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 2.31/1.27 = ( ( X = Y4 )
% 2.31/1.27 & ( ord_less_eq @ ( coinductive_llist @ A ) @ Xs @ Ys ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_135_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 2.31/1.27 ! [A: $tType,I: nat] :
% 2.31/1.27 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_136_lbutlast__LCons,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( ( R
% 2.31/1.27 = ( coinductive_LNil @ A ) )
% 2.31/1.27 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.31/1.27 = ( coinductive_LNil @ A ) ) )
% 2.31/1.27 & ( ( R
% 2.31/1.27 != ( coinductive_LNil @ A ) )
% 2.31/1.27 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.31/1.27 = ( coinductive_LCons @ A @ A4 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_137_lbutlast__snoc,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( lList2370560421utlast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 2.31/1.27 = Xs ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_138_set__mp,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A,X: A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ( member @ A @ X @ A2 )
% 2.31/1.27 => ( member @ A @ X @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_139_in__mono,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A,X: A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ( member @ A @ X @ A2 )
% 2.31/1.27 => ( member @ A @ X @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_140_subsetD,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ( member @ A @ C2 @ A2 )
% 2.31/1.27 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_141_subsetCE,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ( member @ A @ C2 @ A2 )
% 2.31/1.27 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_142_equalityE,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( A2 = B4 )
% 2.31/1.27 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_143_subset__eq,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) )
% 2.31/1.27 = ( ^ [A3: set @ A,B5: set @ A] :
% 2.31/1.27 ! [X2: A] :
% 2.31/1.27 ( ( member @ A @ X2 @ A3 )
% 2.31/1.27 => ( member @ A @ X2 @ B5 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_144_equalityD1,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( A2 = B4 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_145_equalityD2,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( A2 = B4 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_146_set__rev__mp,axiom,
% 2.31/1.27 ! [A: $tType,X: A,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( member @ A @ X @ A2 )
% 2.31/1.27 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( member @ A @ X @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_147_subset__iff,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) )
% 2.31/1.27 = ( ^ [A3: set @ A,B5: set @ A] :
% 2.31/1.27 ! [T3: A] :
% 2.31/1.27 ( ( member @ A @ T3 @ A3 )
% 2.31/1.27 => ( member @ A @ T3 @ B5 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_148_rev__subsetD,axiom,
% 2.31/1.27 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( member @ A @ C2 @ A2 )
% 2.31/1.27 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_149_subset__refl,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_150_Collect__mono,axiom,
% 2.31/1.27 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.31/1.27 ( ! [X3: A] :
% 2.31/1.27 ( ( P2 @ X3 )
% 2.31/1.27 => ( Q @ X3 ) )
% 2.31/1.27 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_151_subset__trans,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A,C3: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_152_set__eq__subset,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ^ [Y3: set @ A,Z2: set @ A] : ( Y3 = Z2 ) )
% 2.31/1.27 = ( ^ [A3: set @ A,B5: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 2.31/1.27 & ( ord_less_eq @ ( set @ A ) @ B5 @ A3 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_153_contra__subsetD,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ~ ( member @ A @ C2 @ B4 )
% 2.31/1.27 => ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_154_Collect__mono__iff,axiom,
% 2.31/1.27 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) )
% 2.31/1.27 = ( ! [X2: A] :
% 2.31/1.27 ( ( P2 @ X2 )
% 2.31/1.27 => ( Q @ X2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_155_llistE,axiom,
% 2.31/1.27 ! [A: $tType,Y4: coinductive_llist @ A] :
% 2.31/1.27 ( ( Y4
% 2.31/1.27 != ( coinductive_LNil @ A ) )
% 2.31/1.27 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 2.31/1.27 ( Y4
% 2.31/1.27 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_156_neq__LNil__conv,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.31/1.27 ( ( Xs
% 2.31/1.27 != ( coinductive_LNil @ A ) )
% 2.31/1.27 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 2.31/1.27 ( Xs
% 2.31/1.27 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_157_llist_Odistinct_I1_J,axiom,
% 2.31/1.27 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 2.31/1.27 ( ( coinductive_LNil @ A )
% 2.31/1.27 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_158_finlsts_OLCons__fin,axiom,
% 2.31/1.27 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ A @ A4 @ A2 )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_159_alllsts_OLCons__all,axiom,
% 2.31/1.27 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ A @ A4 @ A2 )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_160_lappend__snocL1__conv__LCons2,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 2.31/1.27 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.31/1.27 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_161_finlsts_Oinducts,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P2: ( coinductive_llist @ A ) > $o] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( P2 @ ( coinductive_LNil @ A ) )
% 2.31/1.27 => ( ! [L2: coinductive_llist @ A,A5: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( P2 @ L2 )
% 2.31/1.27 => ( ( member @ A @ A5 @ A2 )
% 2.31/1.27 => ( P2 @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 2.31/1.27 => ( P2 @ X ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_162_finlsts__induct,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P2: ( coinductive_llist @ A ) > $o] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ! [L2: coinductive_llist @ A] :
% 2.31/1.27 ( ( L2
% 2.31/1.27 = ( coinductive_LNil @ A ) )
% 2.31/1.27 => ( P2 @ L2 ) )
% 2.31/1.27 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( P2 @ L2 )
% 2.31/1.27 => ( ( member @ A @ A5 @ A2 )
% 2.31/1.27 => ( P2 @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 2.31/1.27 => ( P2 @ X ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_163_finlsts_Osimps,axiom,
% 2.31/1.27 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 = ( ( A4
% 2.31/1.27 = ( coinductive_LNil @ A ) )
% 2.31/1.27 | ? [L3: coinductive_llist @ A,A6: A] :
% 2.31/1.27 ( ( A4
% 2.31/1.27 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_164_finlsts_Ocases,axiom,
% 2.31/1.27 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( A4
% 2.31/1.27 != ( coinductive_LNil @ A ) )
% 2.31/1.27 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 2.31/1.27 ( ( A4
% 2.31/1.27 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_165_alllsts_Ocases,axiom,
% 2.31/1.27 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ( ( A4
% 2.31/1.27 != ( coinductive_LNil @ A ) )
% 2.31/1.27 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 2.31/1.27 ( ( A4
% 2.31/1.27 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_166_alllsts_Osimps,axiom,
% 2.31/1.27 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 = ( ( A4
% 2.31/1.27 = ( coinductive_LNil @ A ) )
% 2.31/1.27 | ? [L3: coinductive_llist @ A,A6: A] :
% 2.31/1.27 ( ( A4
% 2.31/1.27 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_167_alllsts_Ocoinduct,axiom,
% 2.31/1.27 ! [A: $tType,X5: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( X5 @ X )
% 2.31/1.27 => ( ! [X3: coinductive_llist @ A] :
% 2.31/1.27 ( ( X5 @ X3 )
% 2.31/1.27 => ( ( X3
% 2.31/1.27 = ( coinductive_LNil @ A ) )
% 2.31/1.27 | ? [L4: coinductive_llist @ A,A7: A] :
% 2.31/1.27 ( ( X3
% 2.31/1.27 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 2.31/1.27 & ( ( X5 @ L4 )
% 2.31/1.27 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.31/1.27 & ( member @ A @ A7 @ A2 ) ) ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_168_not__LCons__le__LNil,axiom,
% 2.31/1.27 ! [A: $tType,A4: A,L: coinductive_llist @ A] :
% 2.31/1.27 ~ ( ord_less_eq @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( coinductive_LNil @ A ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_169_fps__induct,axiom,
% 2.31/1.27 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,P2: ( coinductive_llist @ A ) > $o] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.31/1.27 => ( ! [A5: A] :
% 2.31/1.27 ( ( member @ A @ A5 @ A2 )
% 2.31/1.27 => ( P2 @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) )
% 2.31/1.27 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.31/1.27 => ( ( P2 @ L2 )
% 2.31/1.27 => ( ( member @ A @ A5 @ A2 )
% 2.31/1.27 => ( P2 @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 2.31/1.27 => ( P2 @ L ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_170_fpslsts__cases,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.31/1.27 => ~ ! [A5: A,Rs: coinductive_llist @ A] :
% 2.31/1.27 ( ( R
% 2.31/1.27 = ( coinductive_LCons @ A @ A5 @ Rs ) )
% 2.31/1.27 => ( ( member @ A @ A5 @ A2 )
% 2.31/1.27 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_171_infsuff__mono2,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 2.31/1.27 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2649413865nfsuff @ A @ A2 @ T ) @ ( lList2649413865nfsuff @ A @ A2 @ S ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_172_lrev__induct,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,P2: ( coinductive_llist @ A ) > $o] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( P2 @ ( coinductive_LNil @ A ) )
% 2.31/1.27 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( P2 @ Xs3 )
% 2.31/1.27 => ( ( member @ A @ X3 @ A2 )
% 2.31/1.27 => ( P2 @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 2.31/1.27 => ( P2 @ Xs ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_173_finlsts__rev__cases,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( T
% 2.31/1.27 != ( coinductive_LNil @ A ) )
% 2.31/1.27 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ A @ A5 @ A2 )
% 2.31/1.27 => ( T
% 2.31/1.27 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_174_llast__snoc,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 2.31/1.27 = X ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_175_LList2__Mirabelle__hamjzmohle_Ollast__lappend,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,Y4: coinductive_llist @ A,A4: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ Y4 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ X @ ( coinductive_LCons @ A @ A4 @ Y4 ) ) )
% 2.31/1.27 = ( lList2170638824_llast @ A @ ( coinductive_LCons @ A @ A4 @ Y4 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_176_lbutlast__lapp__llast,axiom,
% 2.31/1.27 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.31/1.27 => ( L
% 2.31/1.27 = ( coinductive_lappend @ A @ ( lList2370560421utlast @ A @ L ) @ ( coinductive_LCons @ A @ ( lList2170638824_llast @ A @ L ) @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_177_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 2.31/1.27 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A4: B] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 2.31/1.27 => ( ( ( R
% 2.31/1.27 = ( coinductive_LNil @ B ) )
% 2.31/1.27 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 2.31/1.27 = A4 ) )
% 2.31/1.27 & ( ( R
% 2.31/1.27 != ( coinductive_LNil @ B ) )
% 2.31/1.27 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 2.31/1.27 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_178_ltake__lappend__llength,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 2.31/1.27 = R ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_179_infsuff__finpref__iff,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21202317876inpref @ A @ A2 @ R ) )
% 2.31/1.27 = ( member @ ( coinductive_llist @ A ) @ R @ ( lList2649413865nfsuff @ A @ A2 @ T ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_180_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 2.31/1.27 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 2.31/1.27 = ( ( Xs
% 2.31/1.27 = ( coinductive_LNil @ A ) )
% 2.31/1.27 | ? [Xs2: coinductive_llist @ A] :
% 2.31/1.27 ( ( Xs
% 2.31/1.27 = ( coinductive_LCons @ A @ Y4 @ Xs2 ) )
% 2.31/1.27 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_181_lapp__inf,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( coinductive_lappend @ A @ S @ T )
% 2.31/1.27 = S ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_182_notfin__inf,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A] :
% 2.31/1.27 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.31/1.27 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_183_notinf__fin,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A] :
% 2.31/1.27 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.31/1.27 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_184_infsuff__LNil,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A] :
% 2.31/1.27 ( ( lList2649413865nfsuff @ A @ A2 @ ( coinductive_LNil @ A ) )
% 2.31/1.27 = ( lList21612149805nflsts @ A @ A2 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_185_llength__take,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 2.31/1.27 = I ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_186_inflstsI,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_187_infsuff__inf,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2649413865nfsuff @ A @ A2 @ S ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_188_infT__simp,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_189_llist__inf__le,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 2.31/1.27 = ( S = T ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_190_infsubsetall,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_191_inflstsI2,axiom,
% 2.31/1.27 ! [A: $tType,A4: A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ A @ A4 @ A2 )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_192_inflsts__cases,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ A @ A5 @ A2 )
% 2.31/1.27 => ( S
% 2.31/1.27 != ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_193_fin__inf__cases,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A] :
% 2.31/1.27 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_194_lapp__fin__infT,axiom,
% 2.31/1.27 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_195_lapp__inv2T,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 2.31/1.27 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_196_lapp__infT,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 2.31/1.27 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_197_app__invT,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_198_alllstsE,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_199_prefix__lemma,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,Y4: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ Y4 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ! [S2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S2 @ X )
% 2.31/1.27 => ( ord_less_eq @ ( coinductive_llist @ A ) @ S2 @ Y4 ) ) )
% 2.31/1.27 => ( X = Y4 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_200_inf__neqE,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,Y4: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ Y4 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( ( X != Y4 )
% 2.31/1.27 => ~ ! [S2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S2 @ X )
% 2.31/1.27 => ( ord_less_eq @ ( coinductive_llist @ A ) @ S2 @ Y4 ) ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_201_inflsts__mono,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21612149805nflsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_202_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_203_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.31/1.27 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.31/1.27 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.31/1.27 = ( Xs
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_204_finpref__infsuff,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_205_inflstsE,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_206_lapp__allT__iff,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.31/1.27 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_207_infsuff__appE,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) )
% 2.31/1.27 => ~ ! [S2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( T
% 2.31/1.27 != ( coinductive_lappend @ A @ R @ S2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_208_infsafety__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList21015939545safety @ A )
% 2.31/1.27 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.31/1.27 ! [X2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.31/1.27 => ( ! [Y: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21202317876inpref @ A @ A3 @ X2 ) )
% 2.31/1.27 => ? [Z: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P ) ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ X2 @ P ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_209_infliveness__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList21015763786veness @ A )
% 2.31/1.27 = ( ^ [A3: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.31/1.27 ! [X2: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.31/1.27 => ? [Y: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_210_llength__drop__take,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.31/1.27 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 2.31/1.27 != ( coinductive_LNil @ A ) )
% 2.31/1.27 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 2.31/1.27 = I ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_211_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 2.31/1.27 ! [A: $tType,I: nat] :
% 2.31/1.27 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_212_ldrop__fin__iffT,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_213_ldrop__inf__iffT,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_214_ldrop__infT,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_215_ldropT,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_216_ldrop__finT,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_217_drop__nonLNil,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.31/1.27 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 2.31/1.27 != ( coinductive_LNil @ A ) )
% 2.31/1.27 => ( T
% 2.31/1.27 != ( coinductive_LNil @ A ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_218_ldrop__LNil__less,axiom,
% 2.31/1.27 ! [A: $tType,J: nat,I: nat,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ nat @ J @ I )
% 2.31/1.27 => ( ( ( lList2508575361_ldrop @ A @ T @ J )
% 2.31/1.27 = ( coinductive_LNil @ A ) )
% 2.31/1.27 => ( ( lList2508575361_ldrop @ A @ T @ I )
% 2.31/1.27 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_219_ltake__ldrop__id,axiom,
% 2.31/1.27 ! [A: $tType,X: coinductive_llist @ A,I: nat] :
% 2.31/1.27 ( ( coinductive_lappend @ A @ ( lList22119844313_ltake @ A @ X @ I ) @ ( lList2508575361_ldrop @ A @ X @ I ) )
% 2.31/1.27 = X ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_220_lapp__suff__llength,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( lList2508575361_ldrop @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 2.31/1.27 = S ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_221_lstrict__prefix__code_I3_J,axiom,
% 2.31/1.27 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.31/1.27 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_222_lstrict__prefix__code_I2_J,axiom,
% 2.31/1.27 ! [B: $tType,Y4: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y4 @ Ys ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_223_lstrict__prefix__code_I4_J,axiom,
% 2.31/1.27 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y4: B,Ys: coinductive_llist @ B] :
% 2.31/1.27 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y4 @ Ys ) )
% 2.31/1.27 = ( ( X = Y4 )
% 2.31/1.27 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_224_lstrict__prefix__code_I1_J,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_225_llist__less__induct,axiom,
% 2.31/1.27 ! [A: $tType,P2: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.31/1.27 ( ! [Xs3: coinductive_llist @ A] :
% 2.31/1.27 ( ! [Ys2: coinductive_llist @ A] :
% 2.31/1.27 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 2.31/1.27 => ( P2 @ Ys2 ) )
% 2.31/1.27 => ( P2 @ Xs3 ) )
% 2.31/1.27 => ( P2 @ Xs ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_226_finlsts__rec__LCons,axiom,
% 2.31/1.27 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C2: B,D3: A > ( coinductive_llist @ A ) > B > B,A4: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D3 @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.31/1.27 = ( D3 @ A4 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D3 @ R ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_227_finlsts__rec__LCons__def,axiom,
% 2.31/1.27 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D3: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.31/1.27 ( ( F
% 2.31/1.27 = ( lList21916056377ts_rec @ B @ A @ C2 @ D3 ) )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( F @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.31/1.27 = ( D3 @ A4 @ R @ ( F @ R ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_228_finlsts__rec__LNil__def,axiom,
% 2.31/1.27 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D3: A > ( coinductive_llist @ A ) > B > B] :
% 2.31/1.27 ( ( F
% 2.31/1.27 = ( lList21916056377ts_rec @ B @ A @ C2 @ D3 ) )
% 2.31/1.27 => ( ( F @ ( coinductive_LNil @ A ) )
% 2.31/1.27 = C2 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_229_finlsts__rec__LNil,axiom,
% 2.31/1.27 ! [B: $tType,A: $tType,C2: A,D3: B > ( coinductive_llist @ B ) > A > A] :
% 2.31/1.27 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D3 @ ( coinductive_LNil @ B ) )
% 2.31/1.27 = C2 ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_230_inflsts__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( lList21612149805nflsts @ A )
% 2.31/1.27 = ( ^ [A3: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A3 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_231_LList2__Mirabelle__hamjzmohle_Ollength__LCons,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( ( lList21232602520length @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.31/1.27 = ( suc @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_232_DiffI,axiom,
% 2.31/1.27 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( member @ A @ C2 @ A2 )
% 2.31/1.27 => ( ~ ( member @ A @ C2 @ B4 )
% 2.31/1.27 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_233_Diff__iff,axiom,
% 2.31/1.27 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) )
% 2.31/1.27 = ( ( member @ A @ C2 @ A2 )
% 2.31/1.27 & ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_234_Diff__idemp,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) @ B4 )
% 2.31/1.27 = ( minus_minus @ ( set @ A ) @ A2 @ B4 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_235_ltake__LCons__Suc,axiom,
% 2.31/1.27 ! [A: $tType,A4: A,L: coinductive_llist @ A,I: nat] :
% 2.31/1.27 ( ( lList22119844313_ltake @ A @ ( coinductive_LCons @ A @ A4 @ L ) @ ( suc @ I ) )
% 2.31/1.27 = ( coinductive_LCons @ A @ A4 @ ( lList22119844313_ltake @ A @ L @ I ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_236_DiffE,axiom,
% 2.31/1.27 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) )
% 2.31/1.27 => ~ ( ( member @ A @ C2 @ A2 )
% 2.31/1.27 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_237_DiffD1,axiom,
% 2.31/1.27 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) )
% 2.31/1.27 => ( member @ A @ C2 @ A2 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_238_DiffD2,axiom,
% 2.31/1.27 ! [A: $tType,C2: A,A2: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) )
% 2.31/1.27 => ~ ( member @ A @ C2 @ B4 ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_239_Diff__mono,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,C3: set @ A,D4: set @ A,B4: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C3 )
% 2.31/1.27 => ( ( ord_less_eq @ ( set @ A ) @ D4 @ B4 )
% 2.31/1.27 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) @ ( minus_minus @ ( set @ A ) @ C3 @ D4 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_240_Diff__subset,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B4 ) @ A2 ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_241_double__diff,axiom,
% 2.31/1.27 ! [A: $tType,A2: set @ A,B4: set @ A,C3: set @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 2.31/1.27 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 2.31/1.27 => ( ( minus_minus @ ( set @ A ) @ B4 @ ( minus_minus @ ( set @ A ) @ C3 @ A2 ) )
% 2.31/1.27 = A2 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_242_lift__Suc__antimono__le,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [F: nat > A,N: nat,N2: nat] :
% 2.31/1.27 ( ! [N3: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 2.31/1.27 => ( ( ord_less_eq @ nat @ N @ N2 )
% 2.31/1.27 => ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ N ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_243_lift__Suc__mono__le,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( order @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [F: nat > A,N: nat,N2: nat] :
% 2.31/1.27 ( ! [N3: nat] : ( ord_less_eq @ A @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 2.31/1.27 => ( ( ord_less_eq @ nat @ N @ N2 )
% 2.31/1.27 => ( ord_less_eq @ A @ ( F @ N ) @ ( F @ N2 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_244_diff__mono,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A,B2: A,D3: A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 => ( ( ord_less_eq @ A @ D3 @ C2 )
% 2.31/1.27 => ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B2 @ D3 ) ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_245_diff__left__mono,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [B2: A,A4: A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ B2 @ A4 )
% 2.31/1.27 => ( ord_less_eq @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_246_diff__eq__diff__less__eq,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A,B2: A,C2: A,D3: A] :
% 2.31/1.27 ( ( ( minus_minus @ A @ A4 @ B2 )
% 2.31/1.27 = ( minus_minus @ A @ C2 @ D3 ) )
% 2.31/1.27 => ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 = ( ord_less_eq @ A @ C2 @ D3 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_247_diff__right__mono,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.31/1.27 => ! [A4: A,B2: A,C2: A] :
% 2.31/1.27 ( ( ord_less_eq @ A @ A4 @ B2 )
% 2.31/1.27 => ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B2 @ C2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_248_llast__singleton,axiom,
% 2.31/1.27 ! [A: $tType,X: A] :
% 2.31/1.27 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 2.31/1.27 = X ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_249_take__inf__less,axiom,
% 2.31/1.27 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.31/1.27 => ( ord_less @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ T ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_250_llast__LCons2,axiom,
% 2.31/1.27 ! [A: $tType,X: A,Y4: A,Xs: coinductive_llist @ A] :
% 2.31/1.27 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y4 @ Xs ) ) )
% 2.31/1.27 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y4 @ Xs ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_251_less__LCons,axiom,
% 2.31/1.27 ! [A: $tType,A4: A,R: coinductive_llist @ A,B2: A,T: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ R ) @ ( coinductive_LCons @ A @ B2 @ T ) )
% 2.31/1.27 = ( ( A4 = B2 )
% 2.31/1.27 & ( ord_less @ ( coinductive_llist @ A ) @ R @ T ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_252_llist__less__finT,axiom,
% 2.31/1.27 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.31/1.27 ( ( ord_less @ ( coinductive_llist @ A ) @ R @ S )
% 2.31/1.27 => ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.31/1.27 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_253_LNil__less__LCons,axiom,
% 2.31/1.27 ! [A: $tType,A4: A,T: coinductive_llist @ A] : ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_254_llist__less__def,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ord_less @ ( coinductive_llist @ A ) )
% 2.31/1.27 = ( ^ [S3: coinductive_llist @ A,T3: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ T3 )
% 2.31/1.27 & ( S3 != T3 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(fact_255_llist__less__le__not__le,axiom,
% 2.31/1.27 ! [A: $tType] :
% 2.31/1.27 ( ( ord_less @ ( coinductive_llist @ A ) )
% 2.31/1.27 = ( ^ [S3: coinductive_llist @ A,T3: coinductive_llist @ A] :
% 2.31/1.27 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ T3 )
% 2.31/1.27 & ~ ( ord_less_eq @ ( coinductive_llist @ A ) @ T3 @ S3 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 2.31/1.27 ! [A8: $tType,A9: $tType] :
% 2.31/1.27 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 2.31/1.27 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.31/1.27 ! [A8: $tType,A9: $tType] :
% 2.31/1.27 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 2.31/1.27 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.31/1.27 ! [A8: $tType,A9: $tType] :
% 2.31/1.27 ( ( order @ A9 @ ( type2 @ A9 ) )
% 2.31/1.27 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_fun___Orderings_Otop,axiom,
% 2.31/1.27 ! [A8: $tType,A9: $tType] :
% 2.31/1.27 ( ( top @ A9 @ ( type2 @ A9 ) )
% 2.31/1.27 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_fun___Orderings_Oord,axiom,
% 2.31/1.27 ! [A8: $tType,A9: $tType] :
% 2.31/1.27 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 2.31/1.27 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 2.31/1.27 preorder @ nat @ ( type2 @ nat ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.31/1.27 linorder @ nat @ ( type2 @ nat ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 2.31/1.27 order @ nat @ ( type2 @ nat ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 2.31/1.27 ord @ nat @ ( type2 @ nat ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Set_Oset___Orderings_Oorder__top_4,axiom,
% 2.31/1.27 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 2.31/1.27 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 2.31/1.27 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Set_Oset___Orderings_Otop_7,axiom,
% 2.31/1.27 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Set_Oset___Orderings_Oord_8,axiom,
% 2.31/1.27 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_HOL_Obool___Orderings_Oorder__top_9,axiom,
% 2.31/1.27 order_top @ $o @ ( type2 @ $o ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_HOL_Obool___Orderings_Opreorder_10,axiom,
% 2.31/1.27 preorder @ $o @ ( type2 @ $o ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_HOL_Obool___Orderings_Olinorder_11,axiom,
% 2.31/1.27 linorder @ $o @ ( type2 @ $o ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_HOL_Obool___Orderings_Oorder_12,axiom,
% 2.31/1.27 order @ $o @ ( type2 @ $o ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_HOL_Obool___Orderings_Otop_13,axiom,
% 2.31/1.27 top @ $o @ ( type2 @ $o ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_HOL_Obool___Orderings_Oord_14,axiom,
% 2.31/1.27 ord @ $o @ ( type2 @ $o ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_15,axiom,
% 2.31/1.27 ! [A8: $tType] : ( preorder @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_16,axiom,
% 2.31/1.27 ! [A8: $tType] : ( order @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_17,axiom,
% 2.31/1.27 ! [A8: $tType] : ( ord @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.31/1.27
% 2.31/1.27 thf(conj_0,conjecture,
% 2.31/1.27 ? [X4: coinductive_llist @ a] :
% 2.31/1.27 ( ( member @ ( coinductive_llist @ a ) @ X4 @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
% 2.31/1.27 & ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ X4 ) @ p ) ) ).
% 2.31/1.27 ------------------------
% 2.40/1.30 % (10367)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/2Mi)
% 2.40/1.30 % (10366)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_10143 for (2999ds/27Mi)
% 2.40/1.30 % (10370)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/18Mi)
% 2.40/1.30 % (10367)Instruction limit reached!
% 2.40/1.30 % (10367)------------------------------
% 2.40/1.30 % (10367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.30 % (10367)Termination reason: Unknown
% 2.40/1.30 % (10367)Termination phase: shuffling
% 2.40/1.30
% 2.40/1.30 % (10367)Memory used [KB]: 1407
% 2.40/1.30 % (10367)Time elapsed: 0.003 s
% 2.40/1.30 % (10367)Instructions burned: 3 (million)
% 2.40/1.30 % (10367)------------------------------
% 2.40/1.30 % (10367)------------------------------
% 2.40/1.31 % (10365)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_10143 for (2999ds/4Mi)
% 2.40/1.31 % (10370)Instruction limit reached!
% 2.40/1.31 % (10370)------------------------------
% 2.40/1.31 % (10370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.31 % (10370)Termination reason: Unknown
% 2.40/1.31 % (10370)Termination phase: shuffling
% 2.40/1.31
% 2.40/1.31 % (10370)Memory used [KB]: 1663
% 2.40/1.31 % (10370)Time elapsed: 0.008 s
% 2.40/1.31 % (10370)Instructions burned: 19 (million)
% 2.40/1.31 % (10370)------------------------------
% 2.40/1.31 % (10370)------------------------------
% 2.40/1.31 % (10364)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/183Mi)
% 2.40/1.31 % (10368)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_10143 for (2999ds/2Mi)
% 2.40/1.31 % (10369)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_10143 for (2999ds/275Mi)
% 2.40/1.31 % (10366)Instruction limit reached!
% 2.40/1.31 % (10366)------------------------------
% 2.40/1.31 % (10366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.31 % (10366)Termination reason: Unknown
% 2.40/1.31 % (10366)Termination phase: Property scanning
% 2.40/1.31
% 2.40/1.31 % (10366)Memory used [KB]: 1791
% 2.40/1.31 % (10366)Time elapsed: 0.011 s
% 2.40/1.31 % (10366)Instructions burned: 27 (million)
% 2.40/1.31 % (10366)------------------------------
% 2.40/1.31 % (10366)------------------------------
% 2.40/1.31 % (10368)Instruction limit reached!
% 2.40/1.31 % (10368)------------------------------
% 2.40/1.31 % (10368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.31 % (10368)Termination reason: Unknown
% 2.40/1.31 % (10368)Termination phase: shuffling
% 2.40/1.31
% 2.40/1.31 % (10368)Memory used [KB]: 1407
% 2.40/1.31 % (10368)Time elapsed: 0.004 s
% 2.40/1.31 % (10368)Instructions burned: 3 (million)
% 2.40/1.31 % (10368)------------------------------
% 2.40/1.31 % (10368)------------------------------
% 2.40/1.31 % (10365)Instruction limit reached!
% 2.40/1.31 % (10365)------------------------------
% 2.40/1.31 % (10365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.31 % (10365)Termination reason: Unknown
% 2.40/1.31 % (10365)Termination phase: shuffling
% 2.40/1.31
% 2.40/1.31 % (10365)Memory used [KB]: 1407
% 2.40/1.31 % (10365)Time elapsed: 0.005 s
% 2.40/1.31 % (10365)Instructions burned: 5 (million)
% 2.40/1.31 % (10365)------------------------------
% 2.40/1.31 % (10365)------------------------------
% 2.40/1.31 % (10371)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/3Mi)
% 2.40/1.31 % (10371)Instruction limit reached!
% 2.40/1.31 % (10371)------------------------------
% 2.40/1.31 % (10371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.31 % (10371)Termination reason: Unknown
% 2.40/1.31 % (10371)Termination phase: shuffling
% 2.40/1.31
% 2.40/1.31 % (10371)Memory used [KB]: 1407
% 2.40/1.31 % (10371)Time elapsed: 0.002 s
% 2.40/1.31 % (10371)Instructions burned: 3 (million)
% 2.40/1.31 % (10371)------------------------------
% 2.40/1.31 % (10371)------------------------------
% 2.40/1.32 % (10372)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_10143 for (2999ds/37Mi)
% 2.40/1.32 % (10376)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/7Mi)
% 2.40/1.33 % (10376)Instruction limit reached!
% 2.40/1.33 % (10376)------------------------------
% 2.40/1.33 % (10376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.33 % (10376)Termination reason: Unknown
% 2.40/1.33 % (10376)Termination phase: shuffling
% 2.40/1.33
% 2.40/1.33 % (10376)Memory used [KB]: 1407
% 2.40/1.33 % (10376)Time elapsed: 0.004 s
% 2.40/1.33 % (10376)Instructions burned: 9 (million)
% 2.40/1.33 % (10376)------------------------------
% 2.40/1.33 % (10376)------------------------------
% 2.40/1.33 % (10373)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_10143 for (2999ds/15Mi)
% 2.40/1.33 % (10374)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_10143 for (2999ds/3Mi)
% 2.40/1.33 % (10375)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_10143 for (2999ds/1041Mi)
% 2.40/1.33 % (10374)Instruction limit reached!
% 2.40/1.33 % (10374)------------------------------
% 2.40/1.33 % (10374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.33 % (10374)Termination reason: Unknown
% 2.40/1.33 % (10374)Termination phase: shuffling
% 2.40/1.33
% 2.40/1.33 % (10374)Memory used [KB]: 1407
% 2.40/1.33 % (10374)Time elapsed: 0.004 s
% 2.40/1.33 % (10374)Instructions burned: 3 (million)
% 2.40/1.33 % (10374)------------------------------
% 2.40/1.33 % (10374)------------------------------
% 2.40/1.33 % (10372)Instruction limit reached!
% 2.40/1.33 % (10372)------------------------------
% 2.40/1.33 % (10372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.33 % (10372)Termination reason: Unknown
% 2.40/1.33 % (10372)Termination phase: shuffling
% 2.40/1.33
% 2.40/1.33 % (10372)Memory used [KB]: 2046
% 2.40/1.33 % (10372)Time elapsed: 0.013 s
% 2.40/1.33 % (10372)Instructions burned: 37 (million)
% 2.40/1.33 % (10372)------------------------------
% 2.40/1.33 % (10372)------------------------------
% 2.40/1.34 % (10377)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/16Mi)
% 2.40/1.34 % (10373)Instruction limit reached!
% 2.40/1.34 % (10373)------------------------------
% 2.40/1.34 % (10373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.34 % (10373)Termination reason: Unknown
% 2.40/1.34 % (10373)Termination phase: shuffling
% 2.40/1.34
% 2.40/1.34 % (10373)Memory used [KB]: 1535
% 2.40/1.34 % (10373)Time elapsed: 0.012 s
% 2.40/1.34 % (10373)Instructions burned: 15 (million)
% 2.40/1.34 % (10373)------------------------------
% 2.40/1.34 % (10373)------------------------------
% 2.40/1.34 % (10379)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/3Mi)
% 2.40/1.34 % (10377)Instruction limit reached!
% 2.40/1.34 % (10377)------------------------------
% 2.40/1.34 % (10377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.34 % (10377)Termination reason: Unknown
% 2.40/1.34 % (10377)Termination phase: shuffling
% 2.40/1.34
% 2.40/1.34 % (10377)Memory used [KB]: 1663
% 2.40/1.34 % (10377)Time elapsed: 0.007 s
% 2.40/1.34 % (10377)Instructions burned: 17 (million)
% 2.40/1.34 % (10377)------------------------------
% 2.40/1.34 % (10377)------------------------------
% 2.40/1.34 % (10379)Instruction limit reached!
% 2.40/1.34 % (10379)------------------------------
% 2.40/1.34 % (10379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.34 % (10379)Termination reason: Unknown
% 2.40/1.34 % (10379)Termination phase: shuffling
% 2.40/1.34
% 2.40/1.34 % (10379)Memory used [KB]: 1407
% 2.40/1.34 % (10379)Time elapsed: 0.003 s
% 2.40/1.34 % (10379)Instructions burned: 3 (million)
% 2.40/1.34 % (10379)------------------------------
% 2.40/1.34 % (10379)------------------------------
% 2.40/1.35 % (10378)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/3Mi)
% 2.40/1.35 % (10378)Instruction limit reached!
% 2.40/1.35 % (10378)------------------------------
% 2.40/1.35 % (10378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.35 % (10378)Termination reason: Unknown
% 2.40/1.35 % (10378)Termination phase: shuffling
% 2.40/1.35
% 2.40/1.35 % (10378)Memory used [KB]: 1407
% 2.40/1.35 % (10378)Time elapsed: 0.004 s
% 2.40/1.35 % (10378)Instructions burned: 3 (million)
% 2.40/1.35 % (10378)------------------------------
% 2.40/1.35 % (10378)------------------------------
% 2.40/1.35 % (10381)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/3Mi)
% 2.40/1.35 % (10381)Instruction limit reached!
% 2.40/1.35 % (10381)------------------------------
% 2.40/1.35 % (10381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.35 % (10381)Termination reason: Unknown
% 2.40/1.35 % (10381)Termination phase: shuffling
% 2.40/1.35
% 2.40/1.35 % (10381)Memory used [KB]: 1407
% 2.40/1.35 % (10381)Time elapsed: 0.002 s
% 2.40/1.35 % (10381)Instructions burned: 4 (million)
% 2.40/1.35 % (10381)------------------------------
% 2.40/1.35 % (10381)------------------------------
% 2.40/1.35 % (10369)Refutation not found, incomplete strategy
% 2.40/1.35 % (10369)------------------------------
% 2.40/1.35 % (10369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.35 % (10369)Termination reason: Refutation not found, incomplete strategy
% 2.40/1.35
% 2.40/1.35
% 2.40/1.35 % (10369)Memory used [KB]: 6652
% 2.40/1.35 % (10369)Time elapsed: 0.044 s
% 2.40/1.35 % (10369)Instructions burned: 76 (million)
% 2.40/1.35 % (10369)------------------------------
% 2.40/1.35 % (10369)------------------------------
% 2.40/1.35 % (10382)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/4Mi)
% 2.40/1.35 % (10382)Instruction limit reached!
% 2.40/1.35 % (10382)------------------------------
% 2.40/1.35 % (10382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.35 % (10382)Termination reason: Unknown
% 2.40/1.35 % (10382)Termination phase: shuffling
% 2.40/1.35
% 2.40/1.35 % (10382)Memory used [KB]: 1407
% 2.40/1.35 % (10382)Time elapsed: 0.003 s
% 2.40/1.35 % (10382)Instructions burned: 4 (million)
% 2.40/1.35 % (10382)------------------------------
% 2.40/1.35 % (10382)------------------------------
% 2.40/1.36 % (10380)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/7Mi)
% 2.40/1.36 % (10380)Instruction limit reached!
% 2.40/1.36 % (10380)------------------------------
% 2.40/1.36 % (10380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.36 % (10380)Termination reason: Unknown
% 2.40/1.36 % (10380)Termination phase: shuffling
% 2.40/1.36
% 2.40/1.36 % (10380)Memory used [KB]: 1407
% 2.40/1.36 % (10380)Time elapsed: 0.006 s
% 2.40/1.36 % (10380)Instructions burned: 7 (million)
% 2.40/1.36 % (10380)------------------------------
% 2.40/1.36 % (10380)------------------------------
% 2.40/1.36 % (10384)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/710Mi)
% 2.40/1.36 % (10385)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/6Mi)
% 2.40/1.36 % (10386)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/902Mi)
% 2.40/1.36 % (10385)Instruction limit reached!
% 2.40/1.36 % (10385)------------------------------
% 2.40/1.36 % (10385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.36 % (10385)Termination reason: Unknown
% 2.40/1.36 % (10385)Termination phase: shuffling
% 2.40/1.36
% 2.40/1.36 % (10385)Memory used [KB]: 1407
% 2.40/1.36 % (10385)Time elapsed: 0.004 s
% 2.40/1.36 % (10385)Instructions burned: 6 (million)
% 2.40/1.36 % (10385)------------------------------
% 2.40/1.36 % (10385)------------------------------
% 2.40/1.37 % (10383)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/18Mi)
% 2.40/1.37 % (10388)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/5Mi)
% 2.40/1.37 % (10387)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/21Mi)
% 2.40/1.38 % (10388)Instruction limit reached!
% 2.40/1.38 % (10388)------------------------------
% 2.40/1.38 % (10388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.38 % (10388)Termination reason: Unknown
% 2.40/1.38 % (10388)Termination phase: shuffling
% 2.40/1.38
% 2.40/1.38 % (10388)Memory used [KB]: 1407
% 2.40/1.38 % (10388)Time elapsed: 0.003 s
% 2.40/1.38 % (10388)Instructions burned: 6 (million)
% 2.40/1.38 % (10388)------------------------------
% 2.40/1.38 % (10388)------------------------------
% 2.40/1.38 % (10383)Instruction limit reached!
% 2.40/1.38 % (10383)------------------------------
% 2.40/1.38 % (10383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.38 % (10383)Termination reason: Unknown
% 2.40/1.38 % (10383)Termination phase: shuffling
% 2.40/1.38
% 2.40/1.38 % (10383)Memory used [KB]: 1663
% 2.40/1.38 % (10383)Time elapsed: 0.013 s
% 2.40/1.38 % (10383)Instructions burned: 18 (million)
% 2.40/1.38 % (10383)------------------------------
% 2.40/1.38 % (10383)------------------------------
% 2.40/1.38 % (10387)Instruction limit reached!
% 2.40/1.38 % (10387)------------------------------
% 2.40/1.38 % (10387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.38 % (10387)Termination reason: Unknown
% 2.40/1.38 % (10387)Termination phase: shuffling
% 2.40/1.38
% 2.40/1.38 % (10387)Memory used [KB]: 1663
% 2.40/1.38 % (10387)Time elapsed: 0.010 s
% 2.40/1.38 % (10387)Instructions burned: 22 (million)
% 2.40/1.38 % (10387)------------------------------
% 2.40/1.38 % (10387)------------------------------
% 2.40/1.39 % (10389)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_10143 for (2999ds/6Mi)
% 2.40/1.39 % (10389)Instruction limit reached!
% 2.40/1.39 % (10389)------------------------------
% 2.40/1.39 % (10389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.39 % (10389)Termination reason: Unknown
% 2.40/1.39 % (10389)Termination phase: shuffling
% 2.40/1.39
% 2.40/1.39 % (10389)Memory used [KB]: 1407
% 2.40/1.39 % (10389)Time elapsed: 0.003 s
% 2.40/1.39 % (10389)Instructions burned: 7 (million)
% 2.40/1.39 % (10389)------------------------------
% 2.40/1.39 % (10389)------------------------------
% 2.40/1.39 % (10384)First to succeed.
% 2.40/1.39 % (10384)Refutation found. Thanks to Tanya!
% 2.40/1.39 % SZS status Theorem for DTF2THF_10143
% 2.40/1.39 % SZS output start Proof for DTF2THF_10143
% 2.40/1.39 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.40/1.39 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 2.40/1.39 thf(type_def_8, type, set: ($tType) > $tType).
% 2.40/1.39 thf(type_def_9, type, nat: $tType).
% 2.40/1.39 thf(type_def_10, type, a: $tType).
% 2.40/1.39 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 2.40/1.39 thf(func_def_1, type, set: ($tType) > $tType).
% 2.40/1.39 thf(func_def_2, type, nat: $tType).
% 2.40/1.39 thf(func_def_3, type, itself: ($tType) > $tType).
% 2.40/1.39 thf(func_def_4, type, a: $tType).
% 2.40/1.39 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.40/1.39 thf(func_def_6, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.40/1.39 thf(func_def_7, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.40/1.39 thf(func_def_8, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.40/1.39 thf(func_def_9, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.40/1.39 thf(func_def_10, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.40/1.39 thf(func_def_11, type, order_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.40/1.39 thf(func_def_12, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.40/1.39 thf(func_def_13, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_14, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_15, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.40/1.39 thf(func_def_16, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_17, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_18, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_19, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.40/1.39 thf(func_def_20, type, lList2435255213lllsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_21, type, lList2236698231inlsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_22, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0)).
% 2.40/1.39 thf(func_def_23, type, lList21202317876inpref: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_24, type, lList22096119349pslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_25, type, lList21015763786veness: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_26, type, lList21612149805nflsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_27, type, lList21015939545safety: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_28, type, lList2649413865nfsuff: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_29, type, lList2370560421utlast: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_30, type, lList2508575361_ldrop: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_31, type, lList21805353693veness: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_32, type, lList2170638824_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.40/1.39 thf(func_def_33, type, lList21232602520length: !>[X0: $tType]:(coinductive_llist @ X0 > nat)).
% 2.40/1.39 thf(func_def_34, type, lList2281150353e_lrev: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_35, type, lList22119844313_ltake: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_36, type, lList2467029176inpref: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_37, type, lList21952340509veness: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_38, type, lList21148268032oslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_39, type, lList292406316safety: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_40, type, lList21974196564closed: !>[X0: $tType]:(set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_41, type, lList21638733016closed: !>[X0: $tType]:(set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_42, type, lList21350011628safety: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_43, type, lList21475143548e_suff: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_44, type, lList2736192599closed: !>[X0: $tType]:(set @ coinductive_llist @ X0 > $o)).
% 2.40/1.39 thf(func_def_45, type, suc: nat > nat).
% 2.40/1.39 thf(func_def_46, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.40/1.39 thf(func_def_47, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.40/1.39 thf(func_def_48, type, top_top: !>[X0: $tType]:(X0)).
% 2.40/1.39 thf(func_def_49, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.40/1.39 thf(func_def_50, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.40/1.39 thf(func_def_51, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.40/1.39 thf(func_def_52, type, p: set @ coinductive_llist @ a).
% 2.40/1.39 thf(func_def_53, type, r: coinductive_llist @ a).
% 2.40/1.39 thf(func_def_54, type, s: coinductive_llist @ a).
% 2.40/1.39 thf(func_def_55, type, t: coinductive_llist @ a).
% 2.40/1.39 thf(func_def_56, type, u: coinductive_llist @ a).
% 2.40/1.39 thf(func_def_57, type, v: coinductive_llist @ a).
% 2.40/1.39 thf(func_def_73, type, sK0: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_74, type, sK1: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.40/1.39 thf(func_def_75, type, sK2: coinductive_llist @ a).
% 2.40/1.39 thf(func_def_76, type, sK3: !>[X0: $tType]:(set @ X0 > X0)).
% 2.40/1.39 thf(func_def_77, type, sK4: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_78, type, sK5: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.40/1.39 thf(func_def_79, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.40/1.39 thf(func_def_80, type, sK7: coinductive_llist @ a).
% 2.40/1.39 thf(func_def_81, type, sK8: !>[X0: $tType]:(X0)).
% 2.40/1.39 thf(func_def_82, type, sK9: !>[X0: $tType]:(set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 2.40/1.39 thf(func_def_84, type, ph11: !>[X0: $tType]:(X0)).
% 2.40/1.39 thf(f965,plain,(
% 2.40/1.39 $false),
% 2.40/1.39 inference(trivial_inequality_removal,[status(thm)],[f964])).
% 2.40/1.39 thf(f964,plain,(
% 2.40/1.39 ($true != $true)),
% 2.40/1.39 inference(superposition,[status(thm)],[f933,f913])).
% 2.40/1.39 thf(f913,plain,(
% 2.40/1.39 ($true = (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ (coinductive_lappend @ a @ u @ v)) @ p))),
% 2.40/1.39 inference(definition_unfolding,[status(thm)],[f868,f858])).
% 2.40/1.39 thf(f858,plain,(
% 2.40/1.39 (t = (coinductive_lappend @ a @ r @ (coinductive_lappend @ a @ u @ v)))),
% 2.40/1.39 inference(cnf_transformation,[status(thm)],[f2])).
% 2.40/1.39 thf(f2,axiom,(
% 2.40/1.39 (t = (coinductive_lappend @ a @ r @ (coinductive_lappend @ a @ u @ v)))),
% 2.40/1.39 file('/export/starexec/sandbox2/tmp/tmp.ssc2Uifky4/DTF2THF_10143.p',fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062)).
% 2.40/1.39 thf(f868,plain,(
% 2.40/1.39 ((member @ coinductive_llist @ a @ t @ p) = $true)),
% 2.40/1.39 inference(cnf_transformation,[status(thm)],[f758])).
% 2.40/1.39 thf(f758,plain,(
% 2.40/1.39 ((member @ coinductive_llist @ a @ t @ p) = $true)),
% 2.40/1.39 inference(fool_elimination,[status(thm)],[f757])).
% 2.40/1.39 thf(f757,plain,(
% 2.40/1.39 (member @ coinductive_llist @ a @ t @ p)),
% 2.40/1.39 inference(rectify,[status(thm)],[f1])).
% 2.40/1.39 thf(f1,axiom,(
% 2.40/1.39 (member @ coinductive_llist @ a @ t @ p)),
% 2.40/1.39 file('/export/starexec/sandbox2/tmp/tmp.ssc2Uifky4/DTF2THF_10143.p',fact_0_tP)).
% 2.40/1.39 thf(f933,plain,(
% 2.40/1.39 ( ! [X0 : coinductive_llist @ a] : (($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p))) )),
% 2.40/1.39 inference(subsumption_resolution,[status(thm)],[f857,f884])).
% 2.40/1.39 thf(f884,plain,(
% 2.40/1.39 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0)))) )),
% 2.40/1.39 inference(cnf_transformation,[status(thm)],[f456])).
% 2.40/1.39 thf(f456,plain,(
% 2.40/1.39 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0)))),
% 2.40/1.39 inference(fool_elimination,[status(thm)],[f455])).
% 2.40/1.39 thf(f455,plain,(
% 2.40/1.39 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))),
% 2.40/1.39 inference(rectify,[status(thm)],[f6])).
% 2.40/1.39 thf(f6,axiom,(
% 2.40/1.39 ! [X0 : $tType,X3 : coinductive_llist @ X0] : (member @ coinductive_llist @ X0 @ X3 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))),
% 2.40/1.39 file('/export/starexec/sandbox2/tmp/tmp.ssc2Uifky4/DTF2THF_10143.p',fact_5_alllsts__UNIV)).
% 2.40/1.39 thf(f857,plain,(
% 2.40/1.39 ( ! [X0 : coinductive_llist @ a] : (($true != (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a))) | ($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p))) )),
% 2.40/1.39 inference(cnf_transformation,[status(thm)],[f792])).
% 2.40/1.39 thf(f792,plain,(
% 2.40/1.39 ! [X0 : coinductive_llist @ a] : (($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p)) | ($true != (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a))))),
% 2.40/1.39 inference(ennf_transformation,[status(thm)],[f494])).
% 2.40/1.39 thf(f494,plain,(
% 2.40/1.39 ~? [X0 : coinductive_llist @ a] : (($true = (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a))) & ($true = (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p)))),
% 2.40/1.39 inference(fool_elimination,[status(thm)],[f493])).
% 2.40/1.39 thf(f493,plain,(
% 2.40/1.39 ~? [X0 : coinductive_llist @ a] : ((member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p))),
% 2.40/1.39 inference(rectify,[status(thm)],[f281])).
% 2.40/1.39 thf(f281,negated_conjecture,(
% 2.40/1.39 ~? [X21 : coinductive_llist @ a] : ((member @ coinductive_llist @ a @ X21 @ (lList2435255213lllsts @ a @ top_top @ set @ a)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X21) @ p))),
% 2.40/1.39 inference(negated_conjecture,[status(cth)],[f280])).
% 2.40/1.39 thf(f280,conjecture,(
% 2.40/1.39 ? [X21 : coinductive_llist @ a] : ((member @ coinductive_llist @ a @ X21 @ (lList2435255213lllsts @ a @ top_top @ set @ a)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X21) @ p))),
% 2.40/1.39 file('/export/starexec/sandbox2/tmp/tmp.ssc2Uifky4/DTF2THF_10143.p',conj_0)).
% 2.40/1.39 % SZS output end Proof for DTF2THF_10143
% 2.40/1.39 % (10384)------------------------------
% 2.40/1.39 % (10384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.39 % (10384)Termination reason: Refutation
% 2.40/1.39
% 2.40/1.39 % (10384)Memory used [KB]: 6652
% 2.40/1.39 % (10384)Time elapsed: 0.028 s
% 2.40/1.39 % (10384)Instructions burned: 83 (million)
% 2.40/1.39 % (10384)------------------------------
% 2.40/1.39 % (10384)------------------------------
% 2.40/1.39 % (10363)Success in time 0.11 s
%------------------------------------------------------------------------------