%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT188^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 2.89s 1.62s
% Output : Refutation 2.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT188^1 : TPTP v9.2.1. Released v7.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n010.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 06:10:33 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : DAT188^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Data Structures
% 0.19/0.45 % Problem : Lazy lists II 1288
% 0.19/0.45 % Version : [Bla16] axioms : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Fri04] Friedrich (2004), Lazy Lists II
% 0.19/0.45 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.19/0.45 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bla16]
% 0.19/0.45 % Names : llist2__1288.p [Bla16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.67 v8.1.0, 0.50 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 372 ( 123 unt; 68 typ; 0 def)
% 0.19/0.45 % Number of atoms : 791 ( 221 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.19/0.45 % Number of connectives : 4634 ( 76 ~; 14 |; 52 &;4137 @)
% 0.19/0.45 % ( 0 <=>; 355 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 19 ( 8 avg)
% 0.19/0.45 % Number of types : 3 ( 2 usr)
% 0.19/0.45 % Number of type conns : 156 ( 156 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 67 ( 66 usr; 4 con; 0-5 aty)
% 0.19/0.45 % Number of variables : 1043 ( 39 ^; 914 !; 31 ?;1043 :)
% 0.19/0.45 % ( 59 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.19/0.45 % 2016-07-13 14:52:31.804
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 %----Could-be-implicit typings (5)
% 0.19/0.45 thf(ty_t_Coinductive__List_Ollist,type,
% 0.19/0.45 coinductive_llist: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Set_Oset,type,
% 0.19/0.45 set: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Nat_Onat,type,
% 0.19/0.45 nat: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_itself,type,
% 0.19/0.45 itself: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_tf_a,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 %----Explicit typings (63)
% 0.19/0.45 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.19/0.45 bounded_lattice:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_HOL_Otype,type,
% 0.28/0.45 type:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Groups_Ominus,type,
% 0.28/0.45 minus:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.28/0.45 ord:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Otop,type,
% 0.28/0.45 top:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.28/0.45 order:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Groups_Ogroup__add,type,
% 0.28/0.45 group_add:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Lattices_Olattice,type,
% 0.28/0.45 lattice:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Ono__bot,type,
% 0.28/0.45 no_bot:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Ono__top,type,
% 0.28/0.45 no_top:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.28/0.45 linorder:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.28/0.45 preorder:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Oorder__top,type,
% 0.28/0.45 order_top:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Owellorder,type,
% 0.28/0.45 wellorder:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Odense__order,type,
% 0.28/0.45 dense_order:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.28/0.45 semilattice_sup:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.28/0.45 ordered_ab_group_add:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.28/0.45 bounded_lattice_top:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.28/0.45 cancel146912293up_add:
% 0.28/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.28/0.45 coindu328551480prefix:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Coinductive__List_Olappend,type,
% 0.28/0.45 coinductive_lappend:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.28/0.45 coinductive_lfinite:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Coinductive__List_Ollast,type,
% 0.28/0.45 coinductive_llast:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.28/0.45 coinductive_LCons:
% 0.28/0.45 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.28/0.45 coinductive_LNil:
% 0.28/0.45 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.28/0.45 coindu1478340336prefix:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.28/0.45 minus_minus:
% 0.28/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 0.28/0.45 lList2435255213lllsts:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.28/0.45 lList2236698231inlsts:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.28/0.45 lList21916056377ts_rec:
% 0.28/0.45 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinpref,type,
% 0.28/0.45 lList21202317876inpref:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.28/0.45 lList22096119349pslsts:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfliveness,type,
% 0.28/0.45 lList21015763786veness:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 0.28/0.45 lList21612149805nflsts:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsafety,type,
% 0.28/0.45 lList21015939545safety:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsuff,type,
% 0.28/0.45 lList2649413865nfsuff:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 0.28/0.45 lList2370560421utlast:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 0.28/0.45 lList2508575361_ldrop:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oliveness,type,
% 0.28/0.45 lList21805353693veness:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 0.28/0.45 lList2170638824_llast:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 0.28/0.45 lList21232602520length:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 0.28/0.45 lList2281150353e_lrev:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 0.28/0.45 lList22119844313_ltake:
% 0.28/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opfinpref,type,
% 0.28/0.45 lList2467029176inpref:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposliveness,type,
% 0.28/0.45 lList21952340509veness:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.28/0.45 lList21148268032oslsts:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opossafety,type,
% 0.28/0.45 lList292406316safety:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opprefix__closed,type,
% 0.28/0.45 lList21974196564closed:
% 0.28/0.45 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oprefix__closed,type,
% 0.28/0.45 lList21638733016closed:
% 0.28/0.45 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osafety,type,
% 0.28/0.45 lList21350011628safety:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuff,type,
% 0.28/0.45 lList21475143548e_suff:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.28/0.45 sup_sup:
% 0.28/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Nat_OSuc,type,
% 0.28/0.45 suc: nat > nat ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.28/0.45 ord_less:
% 0.28/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.28/0.45 ord_less_eq:
% 0.28/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.28/0.45 top_top:
% 0.28/0.45 !>[A: $tType] : A ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Pure_Otype,type,
% 0.28/0.45 type2:
% 0.28/0.45 !>[A: $tType] : ( itself @ A ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect,type,
% 0.28/0.45 collect:
% 0.28/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member,type,
% 0.28/0.45 member:
% 0.28/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_A,type,
% 0.28/0.45 a2: set @ a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_P,type,
% 0.28/0.45 p: set @ ( coinductive_llist @ a ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_R,type,
% 0.28/0.45 r: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_s,type,
% 0.28/0.45 s: coinductive_llist @ a ).
% 0.28/0.45
% 0.28/0.45 %----Relevant facts (256)
% 0.28/0.45 thf(fact_0_lappT,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lappT
% 0.28/0.45 thf(fact_1_poslivenessI,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ( ! [S2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.28/0.45 => ? [X: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S2 @ X ) @ P ) ) )
% 0.28/0.45 => ( lList21952340509veness @ A @ A2 @ P ) ) ).
% 0.28/0.45
% 0.28/0.45 % poslivenessI
% 0.28/0.45 thf(fact_2_lapp__all__invT,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_all_invT
% 0.28/0.45 thf(fact_3_posliveness__def,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList21952340509veness @ A )
% 0.28/0.45 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ! [X2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList22096119349pslsts @ A @ A3 ) )
% 0.28/0.45 => ? [Y: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % posliveness_def
% 0.28/0.45 thf(fact_4_lappend__assoc,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.28/0.45 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.28/0.45 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lappend_assoc
% 0.28/0.45 thf(fact_5_suff__all,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21475143548e_suff @ A @ A2 @ S ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % suff_all
% 0.28/0.45 thf(fact_6_safetyD,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A ),T: coinductive_llist @ A] :
% 0.28/0.45 ( ( lList21350011628safety @ A @ A2 @ P )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ! [R2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R2 @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 0.28/0.45 => ? [X: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R2 @ X ) @ P ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ T @ P ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % safetyD
% 0.28/0.45 thf(fact_7_safetyE,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ( ( lList21350011628safety @ A @ A2 @ P )
% 0.28/0.45 => ! [X: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ! [Xa: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList21202317876inpref @ A @ A2 @ X ) )
% 0.28/0.45 => ? [Xb: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xb @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xa @ Xb ) @ P ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X @ P ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % safetyE
% 0.28/0.45 thf(fact_8_safetyI,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ( ! [T2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ! [X: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21202317876inpref @ A @ A2 @ T2 ) )
% 0.28/0.45 => ? [Xa: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X @ Xa ) @ P ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ T2 @ P ) ) )
% 0.28/0.45 => ( lList21350011628safety @ A @ A2 @ P ) ) ).
% 0.28/0.45
% 0.28/0.45 % safetyI
% 0.28/0.45 thf(fact_9_safety__def,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList21350011628safety @ A )
% 0.28/0.45 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ! [X2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.28/0.45 => ( ! [Y: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21202317876inpref @ A @ A3 @ X2 ) )
% 0.28/0.45 => ? [Z: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P2 ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X2 @ P2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % safety_def
% 0.28/0.45 thf(fact_10_ldropT,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ldropT
% 0.28/0.45 thf(fact_11_alllsts__UNIV,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % alllsts_UNIV
% 0.28/0.45 thf(fact_12_lapp__inf,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( ( coinductive_lappend @ A @ S @ T )
% 0.28/0.45 = S ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_inf
% 0.28/0.45 thf(fact_13_livenessE,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A ),S: coinductive_llist @ A] :
% 0.28/0.45 ( ( lList21805353693veness @ A @ A2 @ P )
% 0.28/0.45 => ( ! [T2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ~ ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T2 ) @ P ) )
% 0.28/0.45 => ~ ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % livenessE
% 0.28/0.45 thf(fact_14_livenessI,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ( ! [S2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ? [X: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S2 @ X ) @ P ) ) )
% 0.28/0.45 => ( lList21805353693veness @ A @ A2 @ P ) ) ).
% 0.28/0.45
% 0.28/0.45 % livenessI
% 0.28/0.45 thf(fact_15_liveness__def,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList21805353693veness @ A )
% 0.28/0.45 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ! [X2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.28/0.45 => ? [Y: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % liveness_def
% 0.28/0.45 thf(fact_16_lapp__fin__fin__iff,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_fin_fin_iff
% 0.28/0.45 thf(fact_17_same__lappend__eq,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( ( coinductive_lappend @ A @ R @ S )
% 0.28/0.45 = ( coinductive_lappend @ A @ R @ T ) )
% 0.28/0.45 = ( S = T ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % same_lappend_eq
% 0.28/0.45 thf(fact_18_notfin__inf,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A] :
% 0.28/0.45 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.28/0.45 = ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % notfin_inf
% 0.28/0.45 thf(fact_19_notinf__fin,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A] :
% 0.28/0.45 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.28/0.45 = ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % notinf_fin
% 0.28/0.45 thf(fact_20_ldrop__fin__iffT,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ldrop_fin_iffT
% 0.28/0.45 thf(fact_21_ldrop__inf__iffT,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ldrop_inf_iffT
% 0.28/0.45 thf(fact_22_inflstsI,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ~ ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inflstsI
% 0.28/0.45 thf(fact_23_inflstsE,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ~ ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inflstsE
% 0.28/0.45 thf(fact_24_finT__simp,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finT_simp
% 0.28/0.45 thf(fact_25_infT__simp,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % infT_simp
% 0.28/0.45 thf(fact_26_fin__finite,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % fin_finite
% 0.28/0.45 thf(fact_27_ldrop__finT,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ldrop_finT
% 0.28/0.45 thf(fact_28_ldrop__infT,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ldrop_infT
% 0.28/0.45 thf(fact_29_finpref__fin,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21202317876inpref @ A @ A2 @ S ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finpref_fin
% 0.28/0.45 thf(fact_30_suff__finpref,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,R: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % suff_finpref
% 0.28/0.45 thf(fact_31_fin__inf__cases,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A] :
% 0.28/0.45 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % fin_inf_cases
% 0.28/0.45 thf(fact_32_suff__finpref__iff,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 0.28/0.45 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % suff_finpref_iff
% 0.28/0.45 thf(fact_33_lapp__fin__infT,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_fin_infT
% 0.28/0.45 thf(fact_34_lapp__inv2T,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 0.28/0.45 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_inv2T
% 0.28/0.45 thf(fact_35_lapp__infT,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 0.28/0.45 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_infT
% 0.28/0.45 thf(fact_36_app__invT,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % app_invT
% 0.28/0.45 thf(fact_37_alllstsE,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ~ ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % alllstsE
% 0.28/0.45 thf(fact_38_finpref__suff,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finpref_suff
% 0.28/0.45 thf(fact_39_lapp__allT__iff,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.28/0.45 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_allT_iff
% 0.28/0.45 thf(fact_40_lapp__fin__fin__lemma,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_fin_fin_lemma
% 0.28/0.45 thf(fact_41_lappfin__finT,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lappfin_finT
% 0.28/0.45 thf(fact_42_finsubsetall,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finsubsetall
% 0.28/0.45 thf(fact_43_finite__lemma,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ B2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finite_lemma
% 0.28/0.45 thf(fact_44_suff__appE,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) )
% 0.28/0.45 => ~ ! [S2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( T
% 0.28/0.45 != ( coinductive_lappend @ A @ R @ S2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % suff_appE
% 0.28/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.28/0.45 ! [A: $tType,A4: A,P: A > $o] :
% 0.28/0.45 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.28/0.45 = ( P @ A4 ) ) ).
% 0.28/0.45
% 0.28/0.45 % mem_Collect_eq
% 0.28/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] :
% 0.28/0.45 ( ( collect @ A
% 0.28/0.45 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.28/0.45 = A2 ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_mem_eq
% 0.28/0.45 thf(fact_47_Collect__cong,axiom,
% 0.28/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.45 ( ! [X4: A] :
% 0.28/0.45 ( ( P @ X4 )
% 0.28/0.45 = ( Q @ X4 ) )
% 0.28/0.45 => ( ( collect @ A @ P )
% 0.28/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_cong
% 0.28/0.45 thf(fact_48_ext,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.28/0.45 ( ! [X4: A] :
% 0.28/0.45 ( ( F @ X4 )
% 0.28/0.45 = ( G @ X4 ) )
% 0.28/0.45 => ( F = G ) ) ).
% 0.28/0.45
% 0.28/0.45 % ext
% 0.28/0.45 thf(fact_49_infsubsetall,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % infsubsetall
% 0.28/0.45 thf(fact_50_infsafety__def,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList21015939545safety @ A )
% 0.28/0.45 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ! [X2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.28/0.45 => ( ! [Y: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21202317876inpref @ A @ A3 @ X2 ) )
% 0.28/0.45 => ? [Z: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P2 ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X2 @ P2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % infsafety_def
% 0.28/0.45 thf(fact_51_infliveness__def,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList21015763786veness @ A )
% 0.28/0.45 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ! [X2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.28/0.45 => ? [Y: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % infliveness_def
% 0.28/0.45 thf(fact_52_safety__prefix__closed,axiom,
% 0.28/0.45 ! [A: $tType,P: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ( ( lList21350011628safety @ A @ ( top_top @ ( set @ A ) ) @ P )
% 0.28/0.45 => ( lList21638733016closed @ A @ P ) ) ).
% 0.28/0.45
% 0.28/0.45 % safety_prefix_closed
% 0.28/0.45 thf(fact_53_infsuff__finpref__iff,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21202317876inpref @ A @ A2 @ R ) )
% 0.28/0.45 = ( member @ ( coinductive_llist @ A ) @ R @ ( lList2649413865nfsuff @ A @ A2 @ T ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % infsuff_finpref_iff
% 0.28/0.45 thf(fact_54_UNIV__I,axiom,
% 0.28/0.45 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % UNIV_I
% 0.28/0.45 thf(fact_55_iso__tuple__UNIV__I,axiom,
% 0.28/0.45 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % iso_tuple_UNIV_I
% 0.28/0.45 thf(fact_56_top__apply,axiom,
% 0.28/0.45 ! [C: $tType,D: $tType] :
% 0.28/0.45 ( ( top @ C @ ( type2 @ C ) )
% 0.28/0.45 => ( ( top_top @ ( D > C ) )
% 0.28/0.45 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % top_apply
% 0.28/0.45 thf(fact_57_lrev__lappend,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.28/0.45 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lrev_lappend
% 0.28/0.45 thf(fact_58_infsuff__appE,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) )
% 0.28/0.45 => ~ ! [S2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( T
% 0.28/0.45 != ( coinductive_lappend @ A @ R @ S2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % infsuff_appE
% 0.28/0.45 thf(fact_59_lapp__suff__llength,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( lList2508575361_ldrop @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 0.28/0.45 = S ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_suff_llength
% 0.28/0.45 thf(fact_60_lrevT,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lrevT
% 0.28/0.45 thf(fact_61_lrev__is__lrev__conv,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.28/0.45 = ( lList2281150353e_lrev @ A @ Ys ) )
% 0.28/0.45 = ( Xs = Ys ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lrev_is_lrev_conv
% 0.28/0.45 thf(fact_62_lrev__lrev__ident,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 0.28/0.45 = Xs ) ) ).
% 0.28/0.45
% 0.28/0.45 % lrev_lrev_ident
% 0.28/0.45 thf(fact_63_top__set__def,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( top_top @ ( set @ A ) )
% 0.28/0.45 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % top_set_def
% 0.28/0.45 thf(fact_64_infsuff__inf,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2649413865nfsuff @ A @ A2 @ S ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % infsuff_inf
% 0.28/0.45 thf(fact_65_UNIV__witness,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ? [X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % UNIV_witness
% 0.28/0.45 thf(fact_66_UNIV__eq__I,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] :
% 0.28/0.45 ( ! [X4: A] : ( member @ A @ X4 @ A2 )
% 0.28/0.45 => ( ( top_top @ ( set @ A ) )
% 0.28/0.45 = A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % UNIV_eq_I
% 0.28/0.45 thf(fact_67_infsuff__finpref,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,R: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % infsuff_finpref
% 0.28/0.45 thf(fact_68_finpref__infsuff,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finpref_infsuff
% 0.28/0.45 thf(fact_69_ltake__lappend__llength,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 0.28/0.45 = R ) ) ).
% 0.28/0.45
% 0.28/0.45 % ltake_lappend_llength
% 0.28/0.45 thf(fact_70_llength__take,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 0.28/0.45 = I ) ) ).
% 0.28/0.45
% 0.28/0.45 % llength_take
% 0.28/0.45 thf(fact_71_take__fin,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % take_fin
% 0.28/0.45 thf(fact_72_ltake__fin,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ltake_fin
% 0.28/0.45 thf(fact_73_inflsts__def,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList21612149805nflsts @ A )
% 0.28/0.45 = ( ^ [A3: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A3 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inflsts_def
% 0.28/0.45 thf(fact_74_lrev__is__LNil__conv,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( Xs
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lrev_is_LNil_conv
% 0.28/0.45 thf(fact_75_LNil__is__lrev__conv,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( ( coinductive_LNil @ A )
% 0.28/0.45 = ( lList2281150353e_lrev @ A @ Xs ) )
% 0.28/0.45 = ( Xs
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LNil_is_lrev_conv
% 0.28/0.45 thf(fact_76_Diff__idemp,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 0.28/0.45 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % Diff_idemp
% 0.28/0.45 thf(fact_77_Diff__iff,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 = ( ( member @ A @ C2 @ A2 )
% 0.28/0.45 & ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Diff_iff
% 0.28/0.45 thf(fact_78_DiffI,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ A2 )
% 0.28/0.45 => ( ~ ( member @ A @ C2 @ B2 )
% 0.28/0.45 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % DiffI
% 0.28/0.45 thf(fact_79_top1I,axiom,
% 0.28/0.45 ! [A: $tType,X3: A] : ( top_top @ ( A > $o ) @ X3 ) ).
% 0.28/0.45
% 0.28/0.45 % top1I
% 0.28/0.45 thf(fact_80_lappend__eq__LNil__iff,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.45 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( ( Xs
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 & ( Ys
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lappend_eq_LNil_iff
% 0.28/0.45 thf(fact_81_LNil__eq__lappend__iff,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.45 ( ( ( coinductive_LNil @ A )
% 0.28/0.45 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.28/0.45 = ( ( Xs
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 & ( Ys
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LNil_eq_lappend_iff
% 0.28/0.45 thf(fact_82_lappend__LNil2,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.45 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.28/0.45 = Xs ) ).
% 0.28/0.45
% 0.28/0.45 % lappend_LNil2
% 0.28/0.45 thf(fact_83_lappend__code_I1_J,axiom,
% 0.28/0.45 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.28/0.45 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.28/0.45 = Ys ) ).
% 0.28/0.45
% 0.28/0.45 % lappend_code(1)
% 0.28/0.45 thf(fact_84_lappend__is__LNil__conv,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( ( coinductive_lappend @ A @ S @ T )
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( ( S
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 & ( T
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lappend_is_LNil_conv
% 0.28/0.45 thf(fact_85_LNil__is__lappend__conv,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( ( coinductive_LNil @ A )
% 0.28/0.45 = ( coinductive_lappend @ A @ S @ T ) )
% 0.28/0.45 = ( ( S
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 & ( T
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LNil_is_lappend_conv
% 0.28/0.45 thf(fact_86_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 0.28/0.45 ! [A: $tType,I: nat] :
% 0.28/0.45 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % LList2_Mirabelle_hamjzmohle.ldrop_LNil
% 0.28/0.45 thf(fact_87_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 0.28/0.45 ! [A: $tType,I: nat] :
% 0.28/0.45 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % LList2_Mirabelle_hamjzmohle.ltake_LNil
% 0.28/0.45 thf(fact_88_lrev__LNil,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % lrev_LNil
% 0.28/0.45 thf(fact_89_LNil__suff,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList21475143548e_suff @ A @ A2 @ S ) )
% 0.28/0.45 = ( S
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LNil_suff
% 0.28/0.45 thf(fact_90_fpslsts__iff,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.28/0.45 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 & ( S
% 0.28/0.45 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % fpslsts_iff
% 0.28/0.45 thf(fact_91_suff__LNil,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] :
% 0.28/0.45 ( ( lList21475143548e_suff @ A @ A2 @ ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % suff_LNil
% 0.28/0.45 thf(fact_92_infsuff__LNil,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] :
% 0.28/0.45 ( ( lList2649413865nfsuff @ A @ A2 @ ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( lList21612149805nflsts @ A @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % infsuff_LNil
% 0.28/0.45 thf(fact_93_DiffD2,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 => ~ ( member @ A @ C2 @ B2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % DiffD2
% 0.28/0.45 thf(fact_94_DiffD1,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 => ( member @ A @ C2 @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % DiffD1
% 0.28/0.45 thf(fact_95_DiffE,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 => ~ ( ( member @ A @ C2 @ A2 )
% 0.28/0.45 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % DiffE
% 0.28/0.45 thf(fact_96_lappend__LNil__LNil,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % lappend_LNil_LNil
% 0.28/0.45 thf(fact_97_finlsts_OLNil__fin,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts.LNil_fin
% 0.28/0.45 thf(fact_98_alllsts_OLNil__all,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % alllsts.LNil_all
% 0.28/0.45 thf(fact_99_drop__nonLNil,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.28/0.45 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 0.28/0.45 != ( coinductive_LNil @ A ) )
% 0.28/0.45 => ( T
% 0.28/0.45 != ( coinductive_LNil @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % drop_nonLNil
% 0.28/0.45 thf(fact_100_llength__drop__take,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.28/0.45 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 0.28/0.45 != ( coinductive_LNil @ A ) )
% 0.28/0.45 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 0.28/0.45 = I ) ) ).
% 0.28/0.45
% 0.28/0.45 % llength_drop_take
% 0.28/0.45 thf(fact_101_ltake__ldrop__id,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,I: nat] :
% 0.28/0.45 ( ( coinductive_lappend @ A @ ( lList22119844313_ltake @ A @ X3 @ I ) @ ( lList2508575361_ldrop @ A @ X3 @ I ) )
% 0.28/0.45 = X3 ) ).
% 0.28/0.45
% 0.28/0.45 % ltake_ldrop_id
% 0.28/0.45 thf(fact_102_pfinpref__iff,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2467029176inpref @ A @ A2 @ S ) )
% 0.28/0.45 = ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21202317876inpref @ A @ A2 @ S ) )
% 0.28/0.45 & ( X3
% 0.28/0.45 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % pfinpref_iff
% 0.28/0.45 thf(fact_103_minus__apply,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( minus @ B @ ( type2 @ B ) )
% 0.28/0.45 => ( ( minus_minus @ ( A > B ) )
% 0.28/0.45 = ( ^ [A3: A > B,B3: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B3 @ X2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % minus_apply
% 0.28/0.45 thf(fact_104_top__empty__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( top_top @ ( A > $o ) )
% 0.28/0.45 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % top_empty_eq
% 0.28/0.45 thf(fact_105_poslsts__iff,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.28/0.45 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( S
% 0.28/0.45 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % poslsts_iff
% 0.28/0.45 thf(fact_106_poslsts__UNIV,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 = ( S
% 0.28/0.45 != ( coinductive_LNil @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % poslsts_UNIV
% 0.28/0.45 thf(fact_107_lrev__LCons,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.28/0.45 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lrev_LCons
% 0.28/0.45 thf(fact_108_llist_Oinject,axiom,
% 0.28/0.45 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.28/0.45 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.28/0.45 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.28/0.45 = ( ( X21 = Y21 )
% 0.28/0.45 & ( X22 = Y22 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % llist.inject
% 0.28/0.45 thf(fact_109_lappend__code_I2_J,axiom,
% 0.28/0.45 ! [A: $tType,Xa2: A,X3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.45 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa2 @ X3 ) @ Ys )
% 0.28/0.45 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_lappend @ A @ X3 @ Ys ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lappend_code(2)
% 0.28/0.45 thf(fact_110_LConsE,axiom,
% 0.28/0.45 ! [A: $tType,X3: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X3 @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 = ( ( member @ A @ X3 @ A2 )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LConsE
% 0.28/0.45 thf(fact_111_llist_Odistinct_I1_J,axiom,
% 0.28/0.45 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.28/0.45 ( ( coinductive_LNil @ A )
% 0.28/0.45 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.28/0.45
% 0.28/0.45 % llist.distinct(1)
% 0.28/0.45 thf(fact_112_neq__LNil__conv,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.45 ( ( Xs
% 0.28/0.45 != ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.28/0.45 ( Xs
% 0.28/0.45 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % neq_LNil_conv
% 0.28/0.45 thf(fact_113_llistE,axiom,
% 0.28/0.45 ! [A: $tType,Y2: coinductive_llist @ A] :
% 0.28/0.45 ( ( Y2
% 0.28/0.45 != ( coinductive_LNil @ A ) )
% 0.28/0.45 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.28/0.45 ( Y2
% 0.28/0.45 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % llistE
% 0.28/0.45 thf(fact_114_finlsts_OLCons__fin,axiom,
% 0.28/0.45 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ A @ A4 @ A2 )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts.LCons_fin
% 0.28/0.45 thf(fact_115_alllsts_OLCons__all,axiom,
% 0.28/0.45 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ A @ A4 @ A2 )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % alllsts.LCons_all
% 0.28/0.45 thf(fact_116_inflsts__cases,axiom,
% 0.28/0.45 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.45 => ( S
% 0.28/0.45 != ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inflsts_cases
% 0.28/0.45 thf(fact_117_inflstsI2,axiom,
% 0.28/0.45 ! [A: $tType,A4: A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ A @ A4 @ A2 )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inflstsI2
% 0.28/0.45 thf(fact_118_lappend__snocL1__conv__LCons2,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Y2: A,Ys: coinductive_llist @ A] :
% 0.28/0.45 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y2 @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.28/0.45 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y2 @ Ys ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lappend_snocL1_conv_LCons2
% 0.28/0.45 thf(fact_119_finlsts_Ocases,axiom,
% 0.28/0.45 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( A4
% 0.28/0.45 != ( coinductive_LNil @ A ) )
% 0.28/0.45 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 0.28/0.45 ( ( A4
% 0.28/0.45 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts.cases
% 0.28/0.45 thf(fact_120_finlsts_Osimps,axiom,
% 0.28/0.45 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 = ( ( A4
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 | ? [L3: coinductive_llist @ A,A6: A] :
% 0.28/0.45 ( ( A4
% 0.28/0.45 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts.simps
% 0.28/0.45 thf(fact_121_finlsts__induct,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ! [L2: coinductive_llist @ A] :
% 0.28/0.45 ( ( L2
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 => ( P @ L2 ) )
% 0.28/0.45 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( P @ L2 )
% 0.28/0.45 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.45 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 0.28/0.45 => ( P @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts_induct
% 0.28/0.45 thf(fact_122_finlsts_Oinducts,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.28/0.45 => ( ! [L2: coinductive_llist @ A,A5: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( P @ L2 )
% 0.28/0.45 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.45 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 0.28/0.45 => ( P @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts.inducts
% 0.28/0.45 thf(fact_123_alllsts_Ocoinduct,axiom,
% 0.28/0.45 ! [A: $tType,X5: ( coinductive_llist @ A ) > $o,X3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( X5 @ X3 )
% 0.28/0.45 => ( ! [X4: coinductive_llist @ A] :
% 0.28/0.45 ( ( X5 @ X4 )
% 0.28/0.45 => ( ( X4
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 | ? [L4: coinductive_llist @ A,A7: A] :
% 0.28/0.45 ( ( X4
% 0.28/0.45 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 0.28/0.45 & ( ( X5 @ L4 )
% 0.28/0.45 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.28/0.45 & ( member @ A @ A7 @ A2 ) ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % alllsts.coinduct
% 0.28/0.45 thf(fact_124_alllsts_Osimps,axiom,
% 0.28/0.45 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 = ( ( A4
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 | ? [L3: coinductive_llist @ A,A6: A] :
% 0.28/0.45 ( ( A4
% 0.28/0.45 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % alllsts.simps
% 0.28/0.45 thf(fact_125_alllsts_Ocases,axiom,
% 0.28/0.45 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ( ( A4
% 0.28/0.45 != ( coinductive_LNil @ A ) )
% 0.28/0.45 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 0.28/0.45 ( ( A4
% 0.28/0.45 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % alllsts.cases
% 0.28/0.45 thf(fact_126_fps__induct,axiom,
% 0.28/0.45 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.28/0.45 => ( ! [A5: A] :
% 0.28/0.45 ( ( member @ A @ A5 @ A2 )
% 0.28/0.45 => ( P @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) )
% 0.28/0.45 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.28/0.45 => ( ( P @ L2 )
% 0.28/0.45 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.45 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 0.28/0.45 => ( P @ L ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % fps_induct
% 0.28/0.45 thf(fact_127_fpslsts__cases,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.28/0.45 => ~ ! [A5: A,Rs: coinductive_llist @ A] :
% 0.28/0.45 ( ( R
% 0.28/0.45 = ( coinductive_LCons @ A @ A5 @ Rs ) )
% 0.28/0.45 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.45 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % fpslsts_cases
% 0.28/0.45 thf(fact_128_finlsts__rev__cases,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( T
% 0.28/0.45 != ( coinductive_LNil @ A ) )
% 0.28/0.45 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.45 => ( T
% 0.28/0.45 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts_rev_cases
% 0.28/0.45 thf(fact_129_lrev__induct,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.28/0.45 => ( ! [X4: A,Xs3: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( P @ Xs3 )
% 0.28/0.45 => ( ( member @ A @ X4 @ A2 )
% 0.28/0.45 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X4 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 0.28/0.45 => ( P @ Xs ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lrev_induct
% 0.28/0.45 thf(fact_130_fun__diff__def,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( minus @ B @ ( type2 @ B ) )
% 0.28/0.45 => ( ( minus_minus @ ( A > B ) )
% 0.28/0.45 = ( ^ [A3: A > B,B3: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B3 @ X2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % fun_diff_def
% 0.28/0.45 thf(fact_131_lbutlast__snoc,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X3: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( lList2370560421utlast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) )
% 0.28/0.45 = Xs ) ) ).
% 0.28/0.45
% 0.28/0.45 % lbutlast_snoc
% 0.28/0.45 thf(fact_132_possafetyD,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A ),T: coinductive_llist @ A] :
% 0.28/0.45 ( ( lList292406316safety @ A @ A2 @ P )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.28/0.45 => ( ! [R2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R2 @ ( lList2467029176inpref @ A @ A2 @ T ) )
% 0.28/0.45 => ? [X: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R2 @ X ) @ P ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ T @ P ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % possafetyD
% 0.28/0.45 thf(fact_133_possafetyE,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ( ( lList292406316safety @ A @ A2 @ P )
% 0.28/0.45 => ! [X: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.28/0.45 => ( ! [Xa: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2467029176inpref @ A @ A2 @ X ) )
% 0.28/0.45 => ? [Xb: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xb @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xa @ Xb ) @ P ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X @ P ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % possafetyE
% 0.28/0.45 thf(fact_134_possafetyI,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ( ! [T2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.28/0.45 => ( ! [X: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2467029176inpref @ A @ A2 @ T2 ) )
% 0.28/0.45 => ? [Xa: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X @ Xa ) @ P ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ T2 @ P ) ) )
% 0.28/0.45 => ( lList292406316safety @ A @ A2 @ P ) ) ).
% 0.28/0.45
% 0.28/0.45 % possafetyI
% 0.28/0.45 thf(fact_135_possafety__def,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList292406316safety @ A )
% 0.28/0.45 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ! [X2: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList21148268032oslsts @ A @ A3 ) )
% 0.28/0.45 => ( ! [Y: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2467029176inpref @ A @ A3 @ X2 ) )
% 0.28/0.45 => ? [Z: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.28/0.45 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P2 ) ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ X2 @ P2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % possafety_def
% 0.28/0.45 thf(fact_136_lbutlast__LNil,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % lbutlast_LNil
% 0.28/0.45 thf(fact_137_lbutlast__LCons,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( ( R
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.28/0.45 = ( coinductive_LNil @ A ) ) )
% 0.28/0.45 & ( ( R
% 0.28/0.45 != ( coinductive_LNil @ A ) )
% 0.28/0.45 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.28/0.45 = ( coinductive_LCons @ A @ A4 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lbutlast_LCons
% 0.28/0.45 thf(fact_138_llast__snoc,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X3: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) )
% 0.28/0.45 = X3 ) ) ).
% 0.28/0.45
% 0.28/0.45 % llast_snoc
% 0.28/0.45 thf(fact_139_LList2__Mirabelle__hamjzmohle_Ollast__lappend,axiom,
% 0.28/0.45 ! [A: $tType,X3: coinductive_llist @ A,Y2: coinductive_llist @ A,A4: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ Y2 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ X3 @ ( coinductive_LCons @ A @ A4 @ Y2 ) ) )
% 0.28/0.45 = ( lList2170638824_llast @ A @ ( coinductive_LCons @ A @ A4 @ Y2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LList2_Mirabelle_hamjzmohle.llast_lappend
% 0.28/0.45 thf(fact_140_lbutlast__lapp__llast,axiom,
% 0.28/0.45 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.28/0.45 => ( L
% 0.28/0.45 = ( coinductive_lappend @ A @ ( lList2370560421utlast @ A @ L ) @ ( coinductive_LCons @ A @ ( lList2170638824_llast @ A @ L ) @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lbutlast_lapp_llast
% 0.28/0.45 thf(fact_141_possafety__pprefix__closed,axiom,
% 0.28/0.45 ! [A: $tType,P: set @ ( coinductive_llist @ A )] :
% 0.28/0.45 ( ( lList292406316safety @ A @ ( top_top @ ( set @ A ) ) @ P )
% 0.28/0.45 => ( lList21974196564closed @ A @ P ) ) ).
% 0.28/0.45
% 0.28/0.45 % possafety_pprefix_closed
% 0.28/0.45 thf(fact_142_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 0.28/0.45 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A4: B] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 0.28/0.45 => ( ( ( R
% 0.28/0.45 = ( coinductive_LNil @ B ) )
% 0.28/0.45 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 0.28/0.45 = A4 ) )
% 0.28/0.45 & ( ( R
% 0.28/0.45 != ( coinductive_LNil @ B ) )
% 0.28/0.45 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 0.28/0.45 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LList2_Mirabelle_hamjzmohle.llast_LCons
% 0.28/0.45 thf(fact_143_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Y2: A,Ys: coinductive_llist @ A] :
% 0.28/0.45 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y2 @ Ys ) )
% 0.28/0.45 = ( ( Xs
% 0.28/0.45 = ( coinductive_LNil @ A ) )
% 0.28/0.45 | ? [Xs2: coinductive_llist @ A] :
% 0.28/0.45 ( ( Xs
% 0.28/0.45 = ( coinductive_LCons @ A @ Y2 @ Xs2 ) )
% 0.28/0.45 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.28/0.45 thf(fact_144_top__conj_I1_J,axiom,
% 0.28/0.45 ! [A: $tType,X3: A,P: $o] :
% 0.28/0.45 ( ( ( top_top @ ( A > $o ) @ X3 )
% 0.28/0.45 & P )
% 0.28/0.45 = P ) ).
% 0.28/0.45
% 0.28/0.45 % top_conj(1)
% 0.28/0.45 thf(fact_145_top__conj_I2_J,axiom,
% 0.28/0.45 ! [A: $tType,P: $o,X3: A] :
% 0.28/0.45 ( ( P
% 0.28/0.45 & ( top_top @ ( A > $o ) @ X3 ) )
% 0.28/0.45 = P ) ).
% 0.28/0.45
% 0.28/0.45 % top_conj(2)
% 0.28/0.45 thf(fact_146_lstrict__prefix__code_I2_J,axiom,
% 0.28/0.45 ! [B: $tType,Y2: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y2 @ Ys ) ) ).
% 0.28/0.45
% 0.28/0.45 % lstrict_prefix_code(2)
% 0.28/0.45 thf(fact_147_lstrict__prefix__code_I4_J,axiom,
% 0.28/0.45 ! [B: $tType,X3: B,Xs: coinductive_llist @ B,Y2: B,Ys: coinductive_llist @ B] :
% 0.28/0.45 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X3 @ Xs ) @ ( coinductive_LCons @ B @ Y2 @ Ys ) )
% 0.28/0.45 = ( ( X3 = Y2 )
% 0.28/0.45 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % lstrict_prefix_code(4)
% 0.28/0.45 thf(fact_148_lstrict__prefix__code_I1_J,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % lstrict_prefix_code(1)
% 0.28/0.45 thf(fact_149_lstrict__prefix__code_I3_J,axiom,
% 0.28/0.45 ! [B: $tType,X3: B,Xs: coinductive_llist @ B] :
% 0.28/0.45 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X3 @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.28/0.45
% 0.28/0.45 % lstrict_prefix_code(3)
% 0.28/0.45 thf(fact_150_llist__less__induct,axiom,
% 0.28/0.45 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.28/0.45 ( ! [Xs3: coinductive_llist @ A] :
% 0.28/0.45 ( ! [Ys2: coinductive_llist @ A] :
% 0.28/0.45 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.28/0.45 => ( P @ Ys2 ) )
% 0.28/0.45 => ( P @ Xs3 ) )
% 0.28/0.45 => ( P @ Xs ) ) ).
% 0.28/0.45
% 0.28/0.45 % llist_less_induct
% 0.28/0.45 thf(fact_151_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.45 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.28/0.45 = ( Xs
% 0.28/0.45 = ( coinductive_LNil @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.28/0.45 thf(fact_152_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.28/0.45 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.28/0.45
% 0.28/0.45 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.28/0.45 thf(fact_153_finlsts__rec__LCons__def,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.28/0.45 ( ( F
% 0.28/0.45 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( F @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.28/0.45 = ( D2 @ A4 @ R @ ( F @ R ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts_rec_LCons_def
% 0.28/0.45 thf(fact_154_finlsts__rec__LCons,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,A4: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.28/0.45 = ( D2 @ A4 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ R ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts_rec_LCons
% 0.28/0.45 thf(fact_155_LList2__Mirabelle__hamjzmohle_Ollength__LCons,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( lList21232602520length @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.28/0.45 = ( suc @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LList2_Mirabelle_hamjzmohle.llength_LCons
% 0.28/0.45 thf(fact_156_finlsts__rec__LNil__def,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 0.28/0.45 ( ( F
% 0.28/0.45 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.28/0.45 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.28/0.45 = C2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts_rec_LNil_def
% 0.28/0.45 thf(fact_157_finlsts__rec__LNil,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType,C2: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 0.28/0.45 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D2 @ ( coinductive_LNil @ B ) )
% 0.28/0.45 = C2 ) ).
% 0.28/0.45
% 0.28/0.45 % finlsts_rec_LNil
% 0.28/0.45 thf(fact_158_ltake__LCons__Suc,axiom,
% 0.28/0.45 ! [A: $tType,A4: A,L: coinductive_llist @ A,I: nat] :
% 0.28/0.45 ( ( lList22119844313_ltake @ A @ ( coinductive_LCons @ A @ A4 @ L ) @ ( suc @ I ) )
% 0.28/0.45 = ( coinductive_LCons @ A @ A4 @ ( lList22119844313_ltake @ A @ L @ I ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ltake_LCons_Suc
% 0.28/0.45 thf(fact_159_llast__singleton,axiom,
% 0.28/0.45 ! [A: $tType,X3: A] :
% 0.28/0.45 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) )
% 0.28/0.45 = X3 ) ).
% 0.28/0.45
% 0.28/0.45 % llast_singleton
% 0.28/0.45 thf(fact_160_take__inf__less,axiom,
% 0.28/0.45 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.45 => ( ord_less @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ T ) ) ).
% 0.28/0.45
% 0.28/0.45 % take_inf_less
% 0.28/0.45 thf(fact_161_fin__Un__inf,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.45 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % fin_Un_inf
% 0.28/0.45 thf(fact_162_sup_Oright__idem,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A] :
% 0.28/0.45 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B4 ) @ B4 )
% 0.28/0.45 = ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.right_idem
% 0.28/0.45 thf(fact_163_sup__left__idem,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( sup_sup @ A @ X3 @ Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_left_idem
% 0.28/0.45 thf(fact_164_sup_Oleft__idem,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A] :
% 0.28/0.45 ( ( sup_sup @ A @ A4 @ ( sup_sup @ A @ A4 @ B4 ) )
% 0.28/0.45 = ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.left_idem
% 0.28/0.45 thf(fact_165_sup__idem,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ( ( sup_sup @ A @ X3 @ X3 )
% 0.28/0.45 = X3 ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_idem
% 0.28/0.45 thf(fact_166_sup_Oidem,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A] :
% 0.28/0.45 ( ( sup_sup @ A @ A4 @ A4 )
% 0.28/0.45 = A4 ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.idem
% 0.28/0.45 thf(fact_167_sup__apply,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.28/0.45 => ( ( sup_sup @ ( A > B ) )
% 0.28/0.45 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_apply
% 0.28/0.45 thf(fact_168_Un__iff,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 = ( ( member @ A @ C2 @ A2 )
% 0.28/0.45 | ( member @ A @ C2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_iff
% 0.28/0.45 thf(fact_169_UnCI,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.28/0.45 ( ( ~ ( member @ A @ C2 @ B2 )
% 0.28/0.45 => ( member @ A @ C2 @ A2 ) )
% 0.28/0.45 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % UnCI
% 0.28/0.45 thf(fact_170_sup__top__right,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ( ( sup_sup @ A @ X3 @ ( top_top @ A ) )
% 0.28/0.45 = ( top_top @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_top_right
% 0.28/0.45 thf(fact_171_sup__top__left,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ( ( sup_sup @ A @ ( top_top @ A ) @ X3 )
% 0.28/0.45 = ( top_top @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_top_left
% 0.28/0.45 thf(fact_172_Un__Diff__cancel,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 0.28/0.45 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_Diff_cancel
% 0.28/0.45 thf(fact_173_Un__Diff__cancel2,axiom,
% 0.28/0.45 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) @ A2 )
% 0.28/0.45 = ( sup_sup @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_Diff_cancel2
% 0.28/0.45 thf(fact_174_llast__LCons2,axiom,
% 0.28/0.45 ! [A: $tType,X3: A,Y2: A,Xs: coinductive_llist @ A] :
% 0.28/0.45 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LCons @ A @ Y2 @ Xs ) ) )
% 0.28/0.45 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y2 @ Xs ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % llast_LCons2
% 0.28/0.45 thf(fact_175_less__LCons,axiom,
% 0.28/0.45 ! [A: $tType,A4: A,R: coinductive_llist @ A,B4: A,T: coinductive_llist @ A] :
% 0.28/0.45 ( ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ R ) @ ( coinductive_LCons @ A @ B4 @ T ) )
% 0.28/0.45 = ( ( A4 = B4 )
% 0.28/0.45 & ( ord_less @ ( coinductive_llist @ A ) @ R @ T ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_LCons
% 0.28/0.45 thf(fact_176_llist__less__finT,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.45 ( ( ord_less @ ( coinductive_llist @ A ) @ R @ S )
% 0.28/0.45 => ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % llist_less_finT
% 0.28/0.45 thf(fact_177_LNil__less__LCons,axiom,
% 0.28/0.45 ! [A: $tType,A4: A,T: coinductive_llist @ A] : ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) ) ).
% 0.28/0.45
% 0.28/0.45 % LNil_less_LCons
% 0.28/0.45 thf(fact_178_sup_Ostrict__coboundedI2,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [C2: A,B4: A,A4: A] :
% 0.28/0.45 ( ( ord_less @ A @ C2 @ B4 )
% 0.28/0.45 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_coboundedI2
% 0.28/0.45 thf(fact_179_sup_Ostrict__coboundedI1,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [C2: A,A4: A,B4: A] :
% 0.28/0.45 ( ( ord_less @ A @ C2 @ A4 )
% 0.28/0.45 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_coboundedI1
% 0.28/0.45 thf(fact_180_sup_Ostrict__order__iff,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ( ( ord_less @ A )
% 0.28/0.45 = ( ^ [B5: A,A6: A] :
% 0.28/0.45 ( ( A6
% 0.28/0.45 = ( sup_sup @ A @ A6 @ B5 ) )
% 0.28/0.45 & ( A6 != B5 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_order_iff
% 0.28/0.45 thf(fact_181_sup_Ostrict__boundedE,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [B4: A,C2: A,A4: A] :
% 0.28/0.45 ( ( ord_less @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A4 )
% 0.28/0.45 => ~ ( ( ord_less @ A @ B4 @ A4 )
% 0.28/0.45 => ~ ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_boundedE
% 0.28/0.45 thf(fact_182_sup__left__commute,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A,Z2: A] :
% 0.28/0.45 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) )
% 0.28/0.45 = ( sup_sup @ A @ Y2 @ ( sup_sup @ A @ X3 @ Z2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_left_commute
% 0.28/0.45 thf(fact_183_sup_Oleft__commute,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [B4: A,A4: A,C2: A] :
% 0.28/0.45 ( ( sup_sup @ A @ B4 @ ( sup_sup @ A @ A4 @ C2 ) )
% 0.28/0.45 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.left_commute
% 0.28/0.45 thf(fact_184_sup__commute,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ( ( sup_sup @ A )
% 0.28/0.45 = ( ^ [X2: A,Y: A] : ( sup_sup @ A @ Y @ X2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_commute
% 0.28/0.45 thf(fact_185_sup_Ocommute,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ( ( sup_sup @ A )
% 0.28/0.45 = ( ^ [A6: A,B5: A] : ( sup_sup @ A @ B5 @ A6 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.commute
% 0.28/0.45 thf(fact_186_less__supI2,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,B4: A,A4: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ B4 )
% 0.28/0.45 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_supI2
% 0.28/0.45 thf(fact_187_less__supI1,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,A4: A,B4: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ A4 )
% 0.28/0.45 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_supI1
% 0.28/0.45 thf(fact_188_sup__assoc,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A,Z2: A] :
% 0.28/0.45 ( ( sup_sup @ A @ ( sup_sup @ A @ X3 @ Y2 ) @ Z2 )
% 0.28/0.45 = ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_assoc
% 0.28/0.45 thf(fact_189_sup_Oassoc,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A,C2: A] :
% 0.28/0.45 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B4 ) @ C2 )
% 0.28/0.45 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.assoc
% 0.28/0.45 thf(fact_190_sup__fun__def,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.28/0.45 => ( ( sup_sup @ ( A > B ) )
% 0.28/0.45 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_fun_def
% 0.28/0.45 thf(fact_191_inf__sup__aci_I5_J,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lattice @ A @ ( type2 @ A ) )
% 0.28/0.45 => ( ( sup_sup @ A )
% 0.28/0.45 = ( ^ [X2: A,Y: A] : ( sup_sup @ A @ Y @ X2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(5)
% 0.28/0.45 thf(fact_192_inf__sup__aci_I6_J,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lattice @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A,Z2: A] :
% 0.28/0.45 ( ( sup_sup @ A @ ( sup_sup @ A @ X3 @ Y2 ) @ Z2 )
% 0.28/0.45 = ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(6)
% 0.28/0.45 thf(fact_193_inf__sup__aci_I7_J,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lattice @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A,Z2: A] :
% 0.28/0.45 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) )
% 0.28/0.45 = ( sup_sup @ A @ Y2 @ ( sup_sup @ A @ X3 @ Z2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(7)
% 0.28/0.45 thf(fact_194_inf__sup__aci_I8_J,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( lattice @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( sup_sup @ A @ X3 @ Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(8)
% 0.28/0.45 thf(fact_195_Un__UNIV__right,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.28/0.45 = ( top_top @ ( set @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_UNIV_right
% 0.28/0.45 thf(fact_196_Un__UNIV__left,axiom,
% 0.28/0.45 ! [A: $tType,B2: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.28/0.45 = ( top_top @ ( set @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_UNIV_left
% 0.28/0.45 thf(fact_197_top_Onot__eq__extremum,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A] :
% 0.28/0.45 ( ( A4
% 0.28/0.45 != ( top_top @ A ) )
% 0.28/0.45 = ( ord_less @ A @ A4 @ ( top_top @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.not_eq_extremum
% 0.28/0.45 thf(fact_198_top_Oextremum__strict,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A] :
% 0.28/0.45 ~ ( ord_less @ A @ ( top_top @ A ) @ A4 ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_strict
% 0.28/0.45 thf(fact_199_Un__Diff,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.28/0.45 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.28/0.45 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_Diff
% 0.28/0.45 thf(fact_200_not__less__LNil,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A] :
% 0.28/0.45 ~ ( ord_less @ ( coinductive_llist @ A ) @ R @ ( coinductive_LNil @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % not_less_LNil
% 0.28/0.45 thf(fact_201_dual__order_Ostrict__implies__not__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [B4: A,A4: A] :
% 0.28/0.45 ( ( ord_less @ A @ B4 @ A4 )
% 0.28/0.45 => ( A4 != B4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.strict_implies_not_eq
% 0.28/0.45 thf(fact_202_order_Ostrict__implies__not__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 => ( A4 != B4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.strict_implies_not_eq
% 0.28/0.45 thf(fact_203_not__less__iff__gr__or__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( ( ord_less @ A @ Y2 @ X3 )
% 0.28/0.45 | ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % not_less_iff_gr_or_eq
% 0.28/0.45 thf(fact_204_dual__order_Ostrict__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [B4: A,A4: A,C2: A] :
% 0.28/0.45 ( ( ord_less @ A @ B4 @ A4 )
% 0.28/0.45 => ( ( ord_less @ A @ C2 @ B4 )
% 0.28/0.45 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.strict_trans
% 0.28/0.45 thf(fact_205_less__imp__not__less,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_not_less
% 0.28/0.45 thf(fact_206_order_Ostrict__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A,C2: A] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 => ( ( ord_less @ A @ B4 @ C2 )
% 0.28/0.45 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.strict_trans
% 0.28/0.45 thf(fact_207_dual__order_Oirrefl,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A] :
% 0.28/0.45 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.irrefl
% 0.28/0.45 thf(fact_208_linorder__cases,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( X3 != Y2 )
% 0.28/0.45 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % linorder_cases
% 0.28/0.45 thf(fact_209_less__imp__triv,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A,P: $o] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less @ A @ Y2 @ X3 )
% 0.28/0.45 => P ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_triv
% 0.28/0.45 thf(fact_210_less__imp__not__eq2,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( Y2 != X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_not_eq2
% 0.28/0.45 thf(fact_211_antisym__conv3,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [Y2: A,X3: A] :
% 0.28/0.45 ( ~ ( ord_less @ A @ Y2 @ X3 )
% 0.28/0.45 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv3
% 0.28/0.45 thf(fact_212_less__induct,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [P: A > $o,A4: A] :
% 0.28/0.45 ( ! [X4: A] :
% 0.28/0.45 ( ! [Y3: A] :
% 0.28/0.45 ( ( ord_less @ A @ Y3 @ X4 )
% 0.28/0.45 => ( P @ Y3 ) )
% 0.28/0.45 => ( P @ X4 ) )
% 0.28/0.45 => ( P @ A4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_induct
% 0.28/0.45 thf(fact_213_less__not__sym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_not_sym
% 0.28/0.45 thf(fact_214_less__imp__not__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( X3 != Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_not_eq
% 0.28/0.45 thf(fact_215_dual__order_Oasym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [B4: A,A4: A] :
% 0.28/0.45 ( ( ord_less @ A @ B4 @ A4 )
% 0.28/0.45 => ~ ( ord_less @ A @ A4 @ B4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.asym
% 0.28/0.45 thf(fact_216_ord__less__eq__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A,C2: A] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 => ( ( B4 = C2 )
% 0.28/0.45 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_less_eq_trans
% 0.28/0.45 thf(fact_217_ord__eq__less__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A,C2: A] :
% 0.28/0.45 ( ( A4 = B4 )
% 0.28/0.45 => ( ( ord_less @ A @ B4 @ C2 )
% 0.28/0.45 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_less_trans
% 0.28/0.45 thf(fact_218_less__irrefl,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_irrefl
% 0.28/0.45 thf(fact_219_less__linear,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 | ( X3 = Y2 )
% 0.28/0.45 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_linear
% 0.28/0.45 thf(fact_220_less__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A,Z2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less @ A @ Y2 @ Z2 )
% 0.28/0.45 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_trans
% 0.28/0.45 thf(fact_221_less__asym_H,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 => ~ ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_asym'
% 0.28/0.45 thf(fact_222_less__asym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_asym
% 0.28/0.45 thf(fact_223_less__imp__neq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( X3 != Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_neq
% 0.28/0.45 thf(fact_224_dense,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ? [Z3: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Z3 )
% 0.28/0.45 & ( ord_less @ A @ Z3 @ Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dense
% 0.28/0.45 thf(fact_225_order_Oasym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 => ~ ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.asym
% 0.28/0.45 thf(fact_226_neq__iff,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( X3 != Y2 )
% 0.28/0.45 = ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 | ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % neq_iff
% 0.28/0.45 thf(fact_227_neqE,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( X3 != Y2 )
% 0.28/0.45 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % neqE
% 0.28/0.45 thf(fact_228_gt__ex,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( no_top @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ? [X1: A] : ( ord_less @ A @ X3 @ X1 ) ) ).
% 0.28/0.45
% 0.28/0.45 % gt_ex
% 0.28/0.45 thf(fact_229_lt__ex,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ? [Y4: A] : ( ord_less @ A @ Y4 @ X3 ) ) ).
% 0.28/0.45
% 0.28/0.45 % lt_ex
% 0.28/0.45 thf(fact_230_order__less__subst2,axiom,
% 0.28/0.45 ! [A: $tType,C: $tType] :
% 0.28/0.45 ( ( ( order @ C @ ( type2 @ C ) )
% 0.28/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.28/0.45 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 => ( ( ord_less @ C @ ( F @ B4 ) @ C2 )
% 0.28/0.45 => ( ! [X4: A,Y4: A] :
% 0.28/0.45 ( ( ord_less @ A @ X4 @ Y4 )
% 0.28/0.45 => ( ord_less @ C @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_less_subst2
% 0.28/0.45 thf(fact_231_order__less__subst1,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( order @ B @ ( type2 @ B ) )
% 0.28/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.28/0.45 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ ( F @ B4 ) )
% 0.28/0.45 => ( ( ord_less @ B @ B4 @ C2 )
% 0.28/0.45 => ( ! [X4: B,Y4: B] :
% 0.28/0.45 ( ( ord_less @ B @ X4 @ Y4 )
% 0.28/0.45 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_less_subst1
% 0.28/0.45 thf(fact_232_ord__less__eq__subst,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.28/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.28/0.45 => ! [A4: A,B4: A,F: A > B,C2: B] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 => ( ( ( F @ B4 )
% 0.28/0.45 = C2 )
% 0.28/0.45 => ( ! [X4: A,Y4: A] :
% 0.28/0.45 ( ( ord_less @ A @ X4 @ Y4 )
% 0.28/0.45 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_less_eq_subst
% 0.28/0.45 thf(fact_233_ord__eq__less__subst,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.28/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.28/0.45 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.28/0.45 ( ( A4
% 0.28/0.45 = ( F @ B4 ) )
% 0.28/0.45 => ( ( ord_less @ B @ B4 @ C2 )
% 0.28/0.45 => ( ! [X4: B,Y4: B] :
% 0.28/0.45 ( ( ord_less @ B @ X4 @ Y4 )
% 0.28/0.45 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_less_subst
% 0.28/0.45 thf(fact_234_Un__left__commute,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.28/0.45 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_left_commute
% 0.28/0.45 thf(fact_235_Un__left__absorb,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_left_absorb
% 0.28/0.45 thf(fact_236_Un__commute,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) )
% 0.28/0.45 = ( ^ [A3: set @ A,B3: set @ A] : ( sup_sup @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_commute
% 0.28/0.45 thf(fact_237_Un__absorb,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.28/0.45 = A2 ) ).
% 0.28/0.45
% 0.28/0.45 % Un_absorb
% 0.28/0.45 thf(fact_238_Un__assoc,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.28/0.45 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.28/0.45 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_assoc
% 0.28/0.45 thf(fact_239_ball__Un,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.28/0.45 ( ( ! [X2: A] :
% 0.28/0.45 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 => ( P @ X2 ) ) )
% 0.28/0.45 = ( ! [X2: A] :
% 0.28/0.45 ( ( member @ A @ X2 @ A2 )
% 0.28/0.45 => ( P @ X2 ) )
% 0.28/0.45 & ! [X2: A] :
% 0.28/0.45 ( ( member @ A @ X2 @ B2 )
% 0.28/0.45 => ( P @ X2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ball_Un
% 0.28/0.45 thf(fact_240_bex__Un,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.28/0.45 ( ( ? [X2: A] :
% 0.28/0.45 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 & ( P @ X2 ) ) )
% 0.28/0.45 = ( ? [X2: A] :
% 0.28/0.45 ( ( member @ A @ X2 @ A2 )
% 0.28/0.45 & ( P @ X2 ) )
% 0.28/0.45 | ? [X2: A] :
% 0.28/0.45 ( ( member @ A @ X2 @ B2 )
% 0.28/0.45 & ( P @ X2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % bex_Un
% 0.28/0.45 thf(fact_241_UnI2,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ B2 )
% 0.28/0.45 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % UnI2
% 0.28/0.45 thf(fact_242_UnI1,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ A2 )
% 0.28/0.45 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % UnI1
% 0.28/0.45 thf(fact_243_UnE,axiom,
% 0.28/0.45 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.45 => ( ~ ( member @ A @ C2 @ A2 )
% 0.28/0.45 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % UnE
% 0.28/0.45 thf(fact_244_diff__strict__mono,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A,D2: A,C2: A] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 => ( ( ord_less @ A @ D2 @ C2 )
% 0.28/0.45 => ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B4 @ D2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_strict_mono
% 0.28/0.45 thf(fact_245_diff__eq__diff__less,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A,C2: A,D2: A] :
% 0.28/0.45 ( ( ( minus_minus @ A @ A4 @ B4 )
% 0.28/0.45 = ( minus_minus @ A @ C2 @ D2 ) )
% 0.28/0.45 => ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.45 = ( ord_less @ A @ C2 @ D2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_eq_diff_less
% 0.28/0.45 thf(fact_246_diff__strict__left__mono,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [B4: A,A4: A,C2: A] :
% 0.28/0.45 ( ( ord_less @ A @ B4 @ A4 )
% 0.28/0.45 => ( ord_less @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_strict_left_mono
% 0.28/0.45 thf(fact_247_LList2__Mirabelle__hamjzmohle_Ollength__mono,axiom,
% 0.28/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.45 => ( ( ord_less @ ( coinductive_llist @ A ) @ S @ R )
% 0.28/0.45 => ( ord_less @ nat @ ( lList21232602520length @ A @ S ) @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % LList2_Mirabelle_hamjzmohle.llength_mono
% 0.28/0.45 thf(fact_248_psubset__imp__ex__mem,axiom,
% 0.28/0.45 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.28/0.45 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.28/0.45 => ? [B6: A] : ( member @ A @ B6 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % psubset_imp_ex_mem
% 0.28/0.45 thf(fact_249_diff__right__commute,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,C2: A,B4: A] :
% 0.28/0.45 ( ( minus_minus @ A @ ( minus_minus @ A @ A4 @ C2 ) @ B4 )
% 0.28/0.45 = ( minus_minus @ A @ ( minus_minus @ A @ A4 @ B4 ) @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_right_commute
% 0.28/0.45 thf(fact_250_diff__eq__diff__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A,C2: A,D2: A] :
% 0.28/0.45 ( ( ( minus_minus @ A @ A4 @ B4 )
% 0.28/0.45 = ( minus_minus @ A @ C2 @ D2 ) )
% 0.28/0.45 => ( ( A4 = B4 )
% 0.28/0.45 = ( C2 = D2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_eq_diff_eq
% 0.28/0.45 thf(fact_251_lapp__take__less,axiom,
% 0.28/0.45 ! [A: $tType,I: nat,R: coinductive_llist @ A,S: coinductive_llist @ A] :
% 0.28/0.45 ( ( ord_less @ nat @ I @ ( lList21232602520length @ A @ R ) )
% 0.28/0.45 => ( ord_less @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S ) @ I ) @ R ) ) ).
% 0.28/0.45
% 0.28/0.45 % lapp_take_less
% 0.28/0.45 thf(fact_252_diff__strict__right__mono,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.28/0.45 => ! [A4: A,B4: A,C2: A] :
% 0.28/0.45 ( ( ord_less @ A @ A4 @ B4 )
% 0.28/0.46 => ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B4 @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_strict_right_mono
% 0.28/0.46 thf(fact_253_llast__lappend__LCons,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y2: A,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.28/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y2 @ Ys ) ) )
% 0.28/0.46 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y2 @ Ys ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % llast_lappend_LCons
% 0.28/0.46 thf(fact_254_pprefix__closed__def,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( lList21974196564closed @ A )
% 0.28/0.46 = ( ^ [A3: set @ ( coinductive_llist @ A )] :
% 0.28/0.46 ! [X2: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X2 @ A3 )
% 0.28/0.46 => ! [S3: coinductive_llist @ A] :
% 0.28/0.46 ( ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ X2 )
% 0.28/0.46 & ( S3
% 0.28/0.46 != ( coinductive_LNil @ A ) ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ S3 @ A3 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pprefix_closed_def
% 0.28/0.46 thf(fact_255_order__refl,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_refl
% 0.28/0.46
% 0.28/0.46 %----Type constructors (44)
% 0.28/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.28/0.46 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.28/0.46 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Orderings_Otop,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Groups_Ominus,axiom,
% 0.28/0.46 ! [A8: $tType,A9: $tType] :
% 0.28/0.46 ( ( minus @ A9 @ ( type2 @ A9 ) )
% 0.28/0.46 => ( minus @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.28/0.46 cancel146912293up_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 0.28/0.46 semilattice_sup @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.28/0.46 wellorder @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Opreorder_4,axiom,
% 0.28/0.46 preorder @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.28/0.46 linorder @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.28/0.46 no_top @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Lattices_Olattice_5,axiom,
% 0.28/0.46 lattice @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_6,axiom,
% 0.28/0.46 order @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Oord_7,axiom,
% 0.28/0.46 ord @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Groups_Ominus_8,axiom,
% 0.28/0.46 minus @ nat @ ( type2 @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_9,axiom,
% 0.28/0.46 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10,axiom,
% 0.28/0.46 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Orderings_Oorder__top_11,axiom,
% 0.28/0.46 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_12,axiom,
% 0.28/0.46 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Lattices_Olattice_13,axiom,
% 0.28/0.46 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Orderings_Oorder_14,axiom,
% 0.28/0.46 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Orderings_Otop_15,axiom,
% 0.28/0.46 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Orderings_Oord_16,axiom,
% 0.28/0.46 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Groups_Ominus_17,axiom,
% 0.28/0.46 ! [A8: $tType] : ( minus @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_18,axiom,
% 0.28/0.46 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_19,axiom,
% 0.28/0.46 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Oorder__top_20,axiom,
% 0.28/0.46 order_top @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_21,axiom,
% 0.28/0.46 preorder @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_22,axiom,
% 0.28/0.46 linorder @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Lattices_Olattice_23,axiom,
% 0.28/0.46 lattice @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_24,axiom,
% 0.28/0.46 order @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Otop_25,axiom,
% 0.28/0.46 top @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Oord_26,axiom,
% 0.28/0.46 ord @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Groups_Ominus_27,axiom,
% 0.28/0.46 minus @ $o @ ( type2 @ $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_28,axiom,
% 0.28/0.46 ! [A8: $tType] : ( preorder @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_29,axiom,
% 0.28/0.46 ! [A8: $tType] : ( order @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_30,axiom,
% 0.28/0.46 ! [A8: $tType] : ( ord @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %----Conjectures (4)
% 0.28/0.46 thf(conj_0,hypothesis,
% 0.28/0.46 lList21952340509veness @ a @ a2 @ p ).
% 0.28/0.46
% 0.28/0.46 thf(conj_1,hypothesis,
% 0.28/0.46 ! [T3: coinductive_llist @ a] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ a ) @ T3 @ ( lList2435255213lllsts @ a @ a2 ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ s @ T3 ) @ p )
% 0.28/0.46 => r ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(conj_2,hypothesis,
% 0.28/0.46 ( ~ ( member @ ( coinductive_llist @ a ) @ s @ ( lList22096119349pslsts @ a @ a2 ) )
% 0.28/0.46 => r ) ).
% 0.28/0.46
% 0.28/0.46 thf(conj_3,conjecture,
% 0.28/0.46 r ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 2.62/1.49 ---- Embedded in THF ---
% 2.62/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.62/1.49 %%% Generated on Tue Feb 24 06:10:34 EST 2026
% 2.62/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.62/1.49 %%% Logic specification used:
% 2.62/1.49 %%% thf(spec, logic, $$dhol).
% 2.62/1.49
% 2.62/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.iIZaSoWsFt/DTF2DTF418.p
% 2.62/1.49 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.62/1.49 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.62/1.49 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.62/1.49 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.62/1.49 thf(ty_tf_a, type, a: $tType).
% 2.62/1.49 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.62/1.49 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.62/1.49 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.62/1.49 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.62/1.49 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.62/1.49 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.62/1.49 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.62/1.49 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.62/1.49 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts, type, lList2435255213lllsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts, type, lList2236698231inlsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.62/1.49 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)))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinpref, type, lList21202317876inpref: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ (coinductive_llist @ A))))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts, type, lList22096119349pslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfliveness, type, lList21015763786veness: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts, type, lList21612149805nflsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsafety, type, lList21015939545safety: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsuff, type, lList2649413865nfsuff: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ (coinductive_llist @ A))))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast, type, lList2370560421utlast: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop, type, lList2508575361_ldrop: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oliveness, type, lList21805353693veness: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast, type, lList2170638824_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength, type, lList21232602520length: (!> [A:$tType]: (((coinductive_llist @ A) > nat)))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev, type, lList2281150353e_lrev: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake, type, lList22119844313_ltake: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opfinpref, type, lList2467029176inpref: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ (coinductive_llist @ A))))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposliveness, type, lList21952340509veness: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts, type, lList21148268032oslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opossafety, type, lList292406316safety: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opprefix__closed, type, lList21974196564closed: (!> [A:$tType]: (((set @ (coinductive_llist @ A)) > $o)))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oprefix__closed, type, lList21638733016closed: (!> [A:$tType]: (((set @ (coinductive_llist @ A)) > $o)))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osafety, type, lList21350011628safety: (!> [A:$tType]: (((set @ A) > ((set @ (coinductive_llist @ A)) > $o))))).
% 2.62/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuff, type, lList21475143548e_suff: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ (coinductive_llist @ A))))))).
% 2.62/1.49 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.62/1.49 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.62/1.49 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.62/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.62/1.49 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.62/1.49 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.62/1.49 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.62/1.49 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.62/1.49 thf(sy_v_A, type, a2: (set @ a)).
% 2.62/1.49 thf(sy_v_P, type, p: (set @ (coinductive_llist @ a))).
% 2.62/1.49 thf(sy_v_R, type, r: $o).
% 2.62/1.49 thf(sy_v_s, type, s: (coinductive_llist @ a)).
% 2.62/1.49 thf(fact_0_lappT, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_1_poslivenessI, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A))]: (((! [S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList22096119349pslsts @ A) @ A2)) => (? [X:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S2) @ X)) @ P))))))) => (((lList21952340509veness @ A) @ A2) @ P))))).
% 2.62/1.49 thf(fact_2_lapp__all__invT, axiom, (! [A:$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)))))).
% 2.62/1.49 thf(fact_3_posliveness__def, axiom, (! [A:$tType]: (((lList21952340509veness @ A) = (^ [A3:(set @ A),P2:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList22096119349pslsts @ A) @ A3)) => (? [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ ((lList2435255213lllsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X2) @ Y)) @ P2))))))))))))).
% 2.62/1.49 thf(fact_4_lappend__assoc, axiom, (! [A:$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)))))).
% 2.62/1.49 thf(fact_5_suff__all, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ (((lList21475143548e_suff @ A) @ A2) @ S)) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.62/1.49 thf(fact_6_safetyD, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A)),T:(coinductive_llist @ A)]: (((((lList21350011628safety @ A) @ A2) @ P) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => ((! [R2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R2) @ (((lList21202317876inpref @ A) @ A2) @ T)) => (? [X:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R2) @ X)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ T) @ P))))))).
% 2.62/1.49 thf(fact_7_safetyE, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A))]: (((((lList21350011628safety @ A) @ A2) @ P) => (! [X:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((! [Xa:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xa) @ (((lList21202317876inpref @ A) @ A2) @ X)) => (? [Xb:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xb) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Xa) @ Xb)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ X) @ P))))))))).
% 2.62/1.49 thf(fact_8_safetyI, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A))]: (((! [T2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T2) @ ((lList2435255213lllsts @ A) @ A2)) => ((! [X:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ (((lList21202317876inpref @ A) @ A2) @ T2)) => (? [Xa:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xa) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X) @ Xa)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ T2) @ P))))) => (((lList21350011628safety @ A) @ A2) @ P))))).
% 2.62/1.49 thf(fact_9_safety__def, axiom, (! [A:$tType]: (((lList21350011628safety @ A) = (^ [A3:(set @ A),P2:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList2435255213lllsts @ A) @ A3)) => ((! [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ (((lList21202317876inpref @ A) @ A3) @ X2)) => (? [Z:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Z) @ ((lList2435255213lllsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Y) @ Z)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ X2) @ P2))))))))))).
% 2.62/1.49 thf(fact_10_ldropT, axiom, (! [A:$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)))))).
% 2.62/1.49 thf(fact_11_alllsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ (top_top @ (set @ A))))))).
% 2.62/1.49 thf(fact_12_lapp__inf, axiom, (! [A:$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))))).
% 2.62/1.49 thf(fact_13_livenessE, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A)),S:(coinductive_llist @ A)]: (((((lList21805353693veness @ A) @ A2) @ P) => ((! [T2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T2) @ ((lList2435255213lllsts @ A) @ A2)) => (~ ((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T2)) @ P)))))) => (~ ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2))))))))).
% 2.62/1.49 thf(fact_14_livenessI, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A))]: (((! [S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList2236698231inlsts @ A) @ A2)) => (? [X:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S2) @ X)) @ P))))))) => (((lList21805353693veness @ A) @ A2) @ P))))).
% 2.62/1.49 thf(fact_15_liveness__def, axiom, (! [A:$tType]: (((lList21805353693veness @ A) = (^ [A3:(set @ A),P2:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList2236698231inlsts @ A) @ A3)) => (? [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ ((lList2435255213lllsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X2) @ Y)) @ P2))))))))))))).
% 2.62/1.49 thf(fact_16_lapp__fin__fin__iff, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_17_same__lappend__eq, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((((coinductive_lappend @ A) @ R) @ S) = (((coinductive_lappend @ A) @ R) @ T)) = (S = T)))))).
% 2.62/1.49 thf(fact_18_notfin__inf, axiom, (! [A:$tType,X3:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X3) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.62/1.49 thf(fact_19_notinf__fin, axiom, (! [A:$tType,X3:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X3) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.62/1.49 thf(fact_20_ldrop__fin__iffT, axiom, (! [A:$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)))))))).
% 2.62/1.49 thf(fact_21_ldrop__inf__iffT, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))) = (((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.62/1.49 thf(fact_22_inflstsI, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_23_inflstsE, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList21612149805nflsts @ A) @ A2)) => (~ (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))))))).
% 2.62/1.49 thf(fact_24_finT__simp, axiom, (! [A:$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)))))))).
% 2.62/1.49 thf(fact_25_infT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.62/1.49 thf(fact_26_fin__finite, axiom, (! [A:$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)))))))).
% 2.62/1.49 thf(fact_27_ldrop__finT, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.62/1.49 thf(fact_28_ldrop__infT, axiom, (! [A:$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)))))).
% 2.62/1.49 thf(fact_29_finpref__fin, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ (((lList21202317876inpref @ A) @ A2) @ S)) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.62/1.49 thf(fact_30_suff__finpref, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_31_fin__inf__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.62/1.49 thf(fact_32_suff__finpref__iff, axiom, (! [A:$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)))))))).
% 2.62/1.49 thf(fact_33_lapp__fin__infT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_34_lapp__inv2T, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_35_lapp__infT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A2)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_36_app__invT, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_37_alllstsE, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ A2)))) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_38_finpref__suff, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_39_lapp__allT__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A2)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_40_lapp__fin__fin__lemma, axiom, (! [A:$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)))))).
% 2.62/1.49 thf(fact_41_lappfin__finT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_42_finsubsetall, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.62/1.49 thf(fact_43_finite__lemma, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A),B2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2435255213lllsts @ A) @ B2)) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ B2))))))).
% 2.62/1.49 thf(fact_44_suff__appE, axiom, (! [A:$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)))))))))))).
% 2.62/1.49 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 2.62/1.49 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 2.62/1.49 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.62/1.49 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.62/1.49 thf(fact_49_infsubsetall, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.62/1.49 thf(fact_50_infsafety__def, axiom, (! [A:$tType]: (((lList21015939545safety @ A) = (^ [A3:(set @ A),P2:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ ((lList21612149805nflsts @ A) @ A3)) => ((! [Y:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Y) @ (((lList21202317876inpref @ A) @ A3) @ X2)) => (? [Z:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Z) @ ((lList21612149805nflsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Y) @ Z)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ X2) @ P2))))))))))).
% 2.62/1.49 thf(fact_51_infliveness__def, axiom, (! [A:$tType]: (((lList21015763786veness @ A) = (^ [A3:(set @ A),P2:(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)) @ P2))))))))))))).
% 2.62/1.49 thf(fact_52_safety__prefix__closed, axiom, (! [A:$tType,P:(set @ (coinductive_llist @ A))]: (((((lList21350011628safety @ A) @ (top_top @ (set @ A))) @ P) => ((lList21638733016closed @ A) @ P))))).
% 2.62/1.49 thf(fact_53_infsuff__finpref__iff, axiom, (! [A:$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)))))))).
% 2.62/1.49 thf(fact_54_UNIV__I, axiom, (! [A:$tType,X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))).
% 2.62/1.49 thf(fact_55_iso__tuple__UNIV__I, axiom, (! [A:$tType,X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))).
% 2.62/1.49 thf(fact_56_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X2:D]: ((top_top @ C)))))))).
% 2.62/1.49 thf(fact_57_lrev__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Ys) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ Ys)) @ ((lList2281150353e_lrev @ A) @ Xs)))))))).
% 2.62/1.49 thf(fact_58_infsuff__appE, axiom, (! [A:$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)))))))))))).
% 2.62/1.49 thf(fact_59_lapp__suff__llength, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((lList2508575361_ldrop @ A) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21232602520length @ A) @ R)) = S))))).
% 2.62/1.49 thf(fact_60_lrevT, axiom, (! [A:$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)))))).
% 2.62/1.49 thf(fact_61_lrev__is__lrev__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Ys) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = ((lList2281150353e_lrev @ A) @ Ys)) = (Xs = Ys))))))).
% 2.62/1.49 thf(fact_62_lrev__lrev__ident, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ ((lList2281150353e_lrev @ A) @ Xs)) = Xs))))).
% 2.62/1.49 thf(fact_63_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.62/1.49 thf(fact_64_infsuff__inf, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ (((lList2649413865nfsuff @ A) @ A2) @ S)) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList21612149805nflsts @ A) @ A2)))))).
% 2.62/1.49 thf(fact_65_UNIV__witness, axiom, (! [A:$tType]: ((? [X4:A]: ((((member @ A) @ X4) @ (top_top @ (set @ A)))))))).
% 2.62/1.49 thf(fact_66_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X4:A]: ((((member @ A) @ X4) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.62/1.49 thf(fact_67_infsuff__finpref, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),R:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T) @ (((lList2649413865nfsuff @ A) @ A2) @ R)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ (((lList21202317876inpref @ A) @ A2) @ T))))))).
% 2.62/1.49 thf(fact_68_finpref__infsuff, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_69_ltake__lappend__llength, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((lList22119844313_ltake @ A) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21232602520length @ A) @ R)) = R))))).
% 2.62/1.49 thf(fact_70_llength__take, axiom, (! [A:$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))))).
% 2.62/1.49 thf(fact_71_take__fin, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ T) @ I)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.62/1.49 thf(fact_72_ltake__fin, axiom, (! [A:$tType,R:(coinductive_llist @ A),I:nat]: ((((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ R) @ I)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))).
% 2.62/1.49 thf(fact_73_inflsts__def, axiom, (! [A:$tType]: (((lList21612149805nflsts @ A) = (^ [A3:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A3)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))))).
% 2.62/1.49 thf(fact_74_lrev__is__LNil__conv, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_75_LNil__is__lrev__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((coinductive_LNil @ A) = ((lList2281150353e_lrev @ A) @ Xs)) = (Xs = (coinductive_LNil @ A))))))).
% 2.62/1.49 thf(fact_76_Diff__idemp, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ B2) = (((minus_minus @ (set @ A)) @ A2) @ B2))))).
% 2.62/1.49 thf(fact_77_Diff__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C2) @ A2) & (~ ((((member @ A) @ C2) @ B2)))))))).
% 2.62/1.49 thf(fact_78_DiffI, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A2) => ((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2))))))).
% 2.62/1.49 thf(fact_79_top1I, axiom, (! [A:$tType,X3:A]: (((top_top @ (A > $o)) @ X3)))).
% 2.62/1.49 thf(fact_80_lappend__eq__LNil__iff, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_81_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.62/1.49 thf(fact_82_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 2.62/1.49 thf(fact_83_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.62/1.49 thf(fact_84_lappend__is__LNil__conv, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_85_LNil__is__lappend__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ S) @ T)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.62/1.49 thf(fact_86_LList2__Mirabelle__hamjzmohle_Oldrop__LNil, axiom, (! [A:$tType,I:nat]: (((((lList2508575361_ldrop @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 2.62/1.49 thf(fact_87_LList2__Mirabelle__hamjzmohle_Oltake__LNil, axiom, (! [A:$tType,I:nat]: (((((lList22119844313_ltake @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 2.62/1.49 thf(fact_88_lrev__LNil, axiom, (! [A:$tType]: ((((lList2281150353e_lrev @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.62/1.49 thf(fact_89_LNil__suff, axiom, (! [A:$tType,A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (((lList21475143548e_suff @ A) @ A2) @ S)) = (S = (coinductive_LNil @ A)))))).
% 2.62/1.49 thf(fact_90_fpslsts__iff, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_91_suff__LNil, axiom, (! [A:$tType,A2:(set @ A)]: (((((lList21475143548e_suff @ A) @ A2) @ (coinductive_LNil @ A)) = ((lList2435255213lllsts @ A) @ A2))))).
% 2.62/1.49 thf(fact_92_infsuff__LNil, axiom, (! [A:$tType,A2:(set @ A)]: (((((lList2649413865nfsuff @ A) @ A2) @ (coinductive_LNil @ A)) = ((lList21612149805nflsts @ A) @ A2))))).
% 2.62/1.49 thf(fact_93_DiffD2, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ ((((member @ A) @ C2) @ B2))))))).
% 2.62/1.49 thf(fact_94_DiffD1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C2) @ A2))))).
% 2.62/1.49 thf(fact_95_DiffE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B2)))))))).
% 2.62/1.49 thf(fact_96_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.62/1.49 thf(fact_97_finlsts_OLNil__fin, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2236698231inlsts @ A) @ A2))))).
% 2.62/1.49 thf(fact_98_alllsts_OLNil__all, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2435255213lllsts @ A) @ A2))))).
% 2.62/1.49 thf(fact_99_drop__nonLNil, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: ((((((lList2508575361_ldrop @ A) @ T) @ I) != (coinductive_LNil @ A)) => (T != (coinductive_LNil @ A)))))).
% 2.62/1.49 thf(fact_100_llength__drop__take, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: ((((((lList2508575361_ldrop @ A) @ T) @ I) != (coinductive_LNil @ A)) => (((lList21232602520length @ A) @ (((lList22119844313_ltake @ A) @ T) @ I)) = I))))).
% 2.62/1.49 thf(fact_101_ltake__ldrop__id, axiom, (! [A:$tType,X3:(coinductive_llist @ A),I:nat]: (((((coinductive_lappend @ A) @ (((lList22119844313_ltake @ A) @ X3) @ I)) @ (((lList2508575361_ldrop @ A) @ X3) @ I)) = X3)))).
% 2.62/1.49 thf(fact_102_pfinpref__iff, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X3) @ (((lList2467029176inpref @ A) @ A2) @ S)) = ((((member @ (coinductive_llist @ A)) @ X3) @ (((lList21202317876inpref @ A) @ A2) @ S)) & (X3 != (coinductive_LNil @ A))))))).
% 2.62/1.49 thf(fact_103_minus__apply, axiom, (! [B:$tType,A:$tType]: ((((minus @ B) @ (type2 @ B)) => ((minus_minus @ (A > B)) = (^ [A3:(A > B),B3:(A > B),X2:A]: ((((minus_minus @ B) @ (A3 @ X2)) @ (B3 @ X2))))))))).
% 2.62/1.49 thf(fact_104_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A))))))))).
% 2.62/1.49 thf(fact_105_poslsts__iff, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_106_poslsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ (top_top @ (set @ A)))) = (S != (coinductive_LNil @ A)))))).
% 2.62/1.49 thf(fact_107_lrev__LCons, axiom, (! [A:$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)))))))).
% 2.62/1.49 thf(fact_108_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X22) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.62/1.49 thf(fact_109_lappend__code_I2_J, axiom, (! [A:$tType,Xa2:A,X3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_LCons @ A) @ Xa2) @ X3)) @ Ys) = (((coinductive_LCons @ A) @ Xa2) @ (((coinductive_lappend @ A) @ X3) @ Ys)))))).
% 2.62/1.49 thf(fact_110_LConsE, axiom, (! [A:$tType,X3:A,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X3) @ Xs)) @ ((lList2435255213lllsts @ A) @ A2)) = ((((member @ A) @ X3) @ A2) & (((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_111_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X21) @ X22))))).
% 2.62/1.49 thf(fact_112_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X2:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs2)))))))).
% 2.62/1.49 thf(fact_113_llistE, axiom, (! [A:$tType,Y2:(coinductive_llist @ A)]: (((Y2 != (coinductive_LNil @ A)) => (~ ((! [X212:A,X222:(coinductive_llist @ A)]: ((Y2 != (((coinductive_LCons @ A) @ X212) @ X222)))))))))).
% 2.62/1.49 thf(fact_114_finlsts_OLCons__fin, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A4) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ L)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_115_alllsts_OLCons__all, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_116_inflsts__cases, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => (~ ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ A) @ A5) @ A2) => (S != (((coinductive_LCons @ A) @ A5) @ L2)))))))))))).
% 2.62/1.49 thf(fact_117_inflstsI2, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_118_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y2:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y2) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y2) @ Ys)))))).
% 2.62/1.49 thf(fact_119_finlsts_Ocases, axiom, (! [A:$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)))))))))))))).
% 2.62/1.49 thf(fact_120_finlsts_Osimps, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2236698231inlsts @ A) @ A2)) = ((A4 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A6:A]: (((A4 = (((coinductive_LCons @ A) @ A6) @ L3)) & ((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ A) @ A6) @ A2)))))))))).
% 2.62/1.49 thf(fact_121_finlsts__induct, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ A2)) => ((! [L2:(coinductive_llist @ A)]: (((L2 = (coinductive_LNil @ A)) => (P @ L2)))) => ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A5) @ A2) => (P @ (((coinductive_LCons @ A) @ A5) @ L2))))))) => (P @ X3))))))).
% 2.62/1.49 thf(fact_122_finlsts_Oinducts, axiom, (! [A:$tType,X3:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [L2:(coinductive_llist @ A),A5:A]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A5) @ A2) => (P @ (((coinductive_LCons @ A) @ A5) @ L2))))))) => (P @ X3))))))).
% 2.62/1.49 thf(fact_123_alllsts_Ocoinduct, axiom, (! [A:$tType,X5:((coinductive_llist @ A) > $o),X3:(coinductive_llist @ A),A2:(set @ A)]: (((X5 @ X3) => ((! [X4:(coinductive_llist @ A)]: (((X5 @ X4) => ((X4 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A7:A]: (((X4 = (((coinductive_LCons @ A) @ A7) @ L4)) & (((X5 @ L4) | (((member @ (coinductive_llist @ A)) @ L4) @ ((lList2435255213lllsts @ A) @ A2))) & (((member @ A) @ A7) @ A2))))))))) => (((member @ (coinductive_llist @ A)) @ X3) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.62/1.49 thf(fact_124_alllsts_Osimps, axiom, (! [A:$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)))))))))).
% 2.62/1.49 thf(fact_125_alllsts_Ocases, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2435255213lllsts @ A) @ A2)) => ((A4 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A5:A]: (((A4 = (((coinductive_LCons @ A) @ A5) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2435255213lllsts @ A) @ A2)) => (~ ((((member @ A) @ A5) @ A2)))))))))))))).
% 2.62/1.49 thf(fact_126_fps__induct, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList22096119349pslsts @ A) @ A2)) => ((! [A5:A]: (((((member @ A) @ A5) @ A2) => (P @ (((coinductive_LCons @ A) @ A5) @ (coinductive_LNil @ A)))))) => ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList22096119349pslsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A5) @ A2) => (P @ (((coinductive_LCons @ A) @ A5) @ L2))))))) => (P @ L))))))).
% 2.62/1.49 thf(fact_127_fpslsts__cases, axiom, (! [A:$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)))))))))))))).
% 2.62/1.49 thf(fact_128_finlsts__rev__cases, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => ((T != (coinductive_LNil @ A)) => (~ ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A5) @ A2) => (T != (((coinductive_lappend @ A) @ L2) @ (((coinductive_LCons @ A) @ A5) @ (coinductive_LNil @ A))))))))))))))).
% 2.62/1.49 thf(fact_129_lrev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [X4:A,Xs3:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs3) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ Xs3) => ((((member @ A) @ X4) @ A2) => (P @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ X4) @ (coinductive_LNil @ A))))))))) => (P @ Xs))))))).
% 2.62/1.49 thf(fact_130_fun__diff__def, axiom, (! [B:$tType,A:$tType]: ((((minus @ B) @ (type2 @ B)) => ((minus_minus @ (A > B)) = (^ [A3:(A > B),B3:(A > B),X2:A]: ((((minus_minus @ B) @ (A3 @ X2)) @ (B3 @ X2))))))))).
% 2.62/1.49 thf(fact_131_lbutlast__snoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),X3:A]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2370560421utlast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A)))) = Xs))))).
% 2.62/1.49 thf(fact_132_possafetyD, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A)),T:(coinductive_llist @ A)]: (((((lList292406316safety @ A) @ A2) @ P) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21148268032oslsts @ A) @ A2)) => ((! [R2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R2) @ (((lList2467029176inpref @ A) @ A2) @ T)) => (? [X:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R2) @ X)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ T) @ P))))))).
% 2.62/1.49 thf(fact_133_possafetyE, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A))]: (((((lList292406316safety @ A) @ A2) @ P) => (! [X:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21148268032oslsts @ A) @ A2)) => ((! [Xa:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xa) @ (((lList2467029176inpref @ A) @ A2) @ X)) => (? [Xb:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xb) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Xa) @ Xb)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ X) @ P))))))))).
% 2.62/1.49 thf(fact_134_possafetyI, axiom, (! [A:$tType,A2:(set @ A),P:(set @ (coinductive_llist @ A))]: (((! [T2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ T2) @ ((lList21148268032oslsts @ A) @ A2)) => ((! [X:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ (((lList2467029176inpref @ A) @ A2) @ T2)) => (? [Xa:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xa) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ X) @ Xa)) @ P))))))) => (((member @ (coinductive_llist @ A)) @ T2) @ P))))) => (((lList292406316safety @ A) @ A2) @ P))))).
% 2.62/1.49 thf(fact_135_possafety__def, axiom, (! [A:$tType]: (((lList292406316safety @ A) = (^ [A3:(set @ A),P2:(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)) @ P2))))))) => (((member @ (coinductive_llist @ A)) @ X2) @ P2))))))))))).
% 2.62/1.49 thf(fact_136_lbutlast__LNil, axiom, (! [A:$tType]: ((((lList2370560421utlast @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.62/1.49 thf(fact_137_lbutlast__LCons, axiom, (! [A:$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))))))))).
% 2.62/1.49 thf(fact_138_llast__snoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),X3:A]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2170638824_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A)))) = X3))))).
% 2.62/1.49 thf(fact_139_LList2__Mirabelle__hamjzmohle_Ollast__lappend, axiom, (! [A:$tType,X3:(coinductive_llist @ A),Y2:(coinductive_llist @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ X3) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Y2) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2170638824_llast @ A) @ (((coinductive_lappend @ A) @ X3) @ (((coinductive_LCons @ A) @ A4) @ Y2))) = ((lList2170638824_llast @ A) @ (((coinductive_LCons @ A) @ A4) @ Y2)))))))).
% 2.62/1.49 thf(fact_140_lbutlast__lapp__llast, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList22096119349pslsts @ A) @ A2)) => (L = (((coinductive_lappend @ A) @ ((lList2370560421utlast @ A) @ L)) @ (((coinductive_LCons @ A) @ ((lList2170638824_llast @ A) @ L)) @ (coinductive_LNil @ A)))))))).
% 2.62/1.49 thf(fact_141_possafety__pprefix__closed, axiom, (! [A:$tType,P:(set @ (coinductive_llist @ A))]: (((((lList292406316safety @ A) @ (top_top @ (set @ A))) @ P) => ((lList21974196564closed @ A) @ P))))).
% 2.62/1.49 thf(fact_142_LList2__Mirabelle__hamjzmohle_Ollast__LCons, axiom, (! [B:$tType,R:(coinductive_llist @ B),A2:(set @ B),A4:B]: (((((member @ (coinductive_llist @ B)) @ R) @ ((lList2236698231inlsts @ B) @ A2)) => (((R = (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A4) @ R)) = A4)) & ((R != (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A4) @ R)) = ((lList2170638824_llast @ B) @ R)))))))).
% 2.62/1.49 thf(fact_143_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y2:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y2) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y2) @ Xs2)) & (((coindu328551480prefix @ A) @ Xs2) @ Ys))))))))).
% 2.62/1.49 thf(fact_144_top__conj_I1_J, axiom, (! [A:$tType,X3:A,P:$o]: (((((top_top @ (A > $o)) @ X3) & P) = P)))).
% 2.62/1.49 thf(fact_145_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X3:A]: (((P & ((top_top @ (A > $o)) @ X3)) = P)))).
% 2.62/1.49 thf(fact_146_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y2:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y2) @ Ys))))).
% 2.62/1.49 thf(fact_147_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X3:B,Xs:(coinductive_llist @ B),Y2:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X3) @ Xs)) @ (((coinductive_LCons @ B) @ Y2) @ Ys)) = ((X3 = Y2) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 2.62/1.49 thf(fact_148_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.62/1.49 thf(fact_149_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X3:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X3) @ Xs)) @ (coinductive_LNil @ B))))))).
% 2.62/1.49 thf(fact_150_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs3:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs3) => (P @ Ys2)))) => (P @ Xs3)))) => (P @ Xs))))).
% 2.62/1.49 thf(fact_151_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 2.62/1.49 thf(fact_152_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.62/1.49 thf(fact_153_finlsts__rec__LCons__def, axiom, (! [B:$tType,A:$tType,F:((coinductive_llist @ A) > B),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B))),R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((F @ (((coinductive_LCons @ A) @ A4) @ R)) = (((D2 @ A4) @ R) @ (F @ R)))))))).
% 2.62/1.49 thf(fact_154_finlsts__rec__LCons, axiom, (! [B:$tType,A:$tType,R:(coinductive_llist @ A),A2:(set @ A),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B))),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2) @ (((coinductive_LCons @ A) @ A4) @ R)) = (((D2 @ A4) @ R) @ (((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2) @ R))))))).
% 2.62/1.49 thf(fact_155_LList2__Mirabelle__hamjzmohle_Ollength__LCons, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_156_finlsts__rec__LNil__def, axiom, (! [A:$tType,B:$tType,F:((coinductive_llist @ A) > B),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B)))]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2)) => ((F @ (coinductive_LNil @ A)) = C2))))).
% 2.62/1.49 thf(fact_157_finlsts__rec__LNil, axiom, (! [B:$tType,A:$tType,C2:A,D2:(B > ((coinductive_llist @ B) > (A > A)))]: (((((((lList21916056377ts_rec @ A) @ B) @ C2) @ D2) @ (coinductive_LNil @ B)) = C2)))).
% 2.62/1.49 thf(fact_158_ltake__LCons__Suc, axiom, (! [A:$tType,A4:A,L:(coinductive_llist @ A),I:nat]: (((((lList22119844313_ltake @ A) @ (((coinductive_LCons @ A) @ A4) @ L)) @ (suc @ I)) = (((coinductive_LCons @ A) @ A4) @ (((lList22119844313_ltake @ A) @ L) @ I)))))).
% 2.62/1.49 thf(fact_159_llast__singleton, axiom, (! [A:$tType,X3:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A))) = X3)))).
% 2.62/1.49 thf(fact_160_take__inf__less, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))) => (((ord_less @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ T) @ I)) @ T))))).
% 2.62/1.49 thf(fact_161_fin__Un__inf, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A2)) @ ((lList21612149805nflsts @ A) @ A2)) = ((lList2435255213lllsts @ A) @ A2))))).
% 2.62/1.49 thf(fact_162_sup_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A4) @ B4)) @ B4) = (((sup_sup @ A) @ A4) @ B4)))))))).
% 2.62/1.49 thf(fact_163_sup__left__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ X3) @ Y2)) = (((sup_sup @ A) @ X3) @ Y2)))))))).
% 2.62/1.49 thf(fact_164_sup_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ A4) @ B4)) = (((sup_sup @ A) @ A4) @ B4)))))))).
% 2.62/1.49 thf(fact_165_sup__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X3:A]: (((((sup_sup @ A) @ X3) @ X3) = X3))))))).
% 2.62/1.49 thf(fact_166_sup_Oidem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A]: (((((sup_sup @ A) @ A4) @ A4) = A4))))))).
% 2.62/1.49 thf(fact_167_sup__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.62/1.49 thf(fact_168_Un__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C2) @ A2) | (((member @ A) @ C2) @ B2)))))).
% 2.62/1.49 thf(fact_169_UnCI, axiom, (! [A:$tType,C2:A,B2:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ A2)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.62/1.49 thf(fact_170_sup__top__right, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X3:A]: (((((sup_sup @ A) @ X3) @ (top_top @ A)) = (top_top @ A)))))))).
% 2.62/1.49 thf(fact_171_sup__top__left, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X3:A]: (((((sup_sup @ A) @ (top_top @ A)) @ X3) = (top_top @ A)))))))).
% 2.62/1.49 thf(fact_172_Un__Diff__cancel, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.62/1.49 thf(fact_173_Un__Diff__cancel2, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) @ A2) = (((sup_sup @ (set @ A)) @ B2) @ A2))))).
% 2.62/1.49 thf(fact_174_llast__LCons2, axiom, (! [A:$tType,X3:A,Y2:A,Xs:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X3) @ (((coinductive_LCons @ A) @ Y2) @ Xs))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y2) @ Xs)))))).
% 2.62/1.49 thf(fact_175_less__LCons, axiom, (! [A:$tType,A4:A,R:(coinductive_llist @ A),B4:A,T:(coinductive_llist @ A)]: (((((ord_less @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ R)) @ (((coinductive_LCons @ A) @ B4) @ T)) = ((A4 = B4) & (((ord_less @ (coinductive_llist @ A)) @ R) @ T)))))).
% 2.62/1.49 thf(fact_176_llist__less__finT, axiom, (! [A:$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))))))).
% 2.62/1.49 thf(fact_177_LNil__less__LCons, axiom, (! [A:$tType,A4:A,T:(coinductive_llist @ A)]: ((((ord_less @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (((coinductive_LCons @ A) @ A4) @ T))))).
% 2.62/1.49 thf(fact_178_sup_Ostrict__coboundedI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,B4:A,A4:A]: (((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ (((sup_sup @ A) @ A4) @ B4))))))))).
% 2.62/1.49 thf(fact_179_sup_Ostrict__coboundedI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,A4:A,B4:A]: (((((ord_less @ A) @ C2) @ A4) => (((ord_less @ A) @ C2) @ (((sup_sup @ A) @ A4) @ B4))))))))).
% 2.62/1.49 thf(fact_180_sup_Ostrict__order__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [B5:A,A6:A]: (((A6 = (((sup_sup @ A) @ A6) @ B5)) & (A6 != B5))))))))).
% 2.62/1.49 thf(fact_181_sup_Ostrict__boundedE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B4:A,C2:A,A4:A]: (((((ord_less @ A) @ (((sup_sup @ A) @ B4) @ C2)) @ A4) => (~ (((((ord_less @ A) @ B4) @ A4) => (~ ((((ord_less @ A) @ C2) @ A4))))))))))))).
% 2.62/1.49 thf(fact_182_sup__left__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X3:A,Y2:A,Z2:A]: (((((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ Y2) @ Z2)) = (((sup_sup @ A) @ Y2) @ (((sup_sup @ A) @ X3) @ Z2))))))))).
% 2.62/1.49 thf(fact_183_sup_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B4:A,A4:A,C2:A]: (((((sup_sup @ A) @ B4) @ (((sup_sup @ A) @ A4) @ C2)) = (((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ B4) @ C2))))))))).
% 2.62/1.49 thf(fact_184_sup__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y:A]: ((((sup_sup @ A) @ Y) @ X2)))))))).
% 2.62/1.49 thf(fact_185_sup_Ocommute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [A6:A,B5:A]: ((((sup_sup @ A) @ B5) @ A6)))))))).
% 2.62/1.49 thf(fact_186_less__supI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X3:A,B4:A,A4:A]: (((((ord_less @ A) @ X3) @ B4) => (((ord_less @ A) @ X3) @ (((sup_sup @ A) @ A4) @ B4))))))))).
% 2.62/1.49 thf(fact_187_less__supI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X3:A,A4:A,B4:A]: (((((ord_less @ A) @ X3) @ A4) => (((ord_less @ A) @ X3) @ (((sup_sup @ A) @ A4) @ B4))))))))).
% 2.62/1.49 thf(fact_188_sup__assoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X3:A,Y2:A,Z2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X3) @ Y2)) @ Z2) = (((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ Y2) @ Z2))))))))).
% 2.62/1.49 thf(fact_189_sup_Oassoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A4) @ B4)) @ C2) = (((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ B4) @ C2))))))))).
% 2.62/1.49 thf(fact_190_sup__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.62/1.49 thf(fact_191_inf__sup__aci_I5_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y:A]: ((((sup_sup @ A) @ Y) @ X2)))))))).
% 2.62/1.49 thf(fact_192_inf__sup__aci_I6_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X3:A,Y2:A,Z2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X3) @ Y2)) @ Z2) = (((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ Y2) @ Z2))))))))).
% 2.62/1.49 thf(fact_193_inf__sup__aci_I7_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X3:A,Y2:A,Z2:A]: (((((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ Y2) @ Z2)) = (((sup_sup @ A) @ Y2) @ (((sup_sup @ A) @ X3) @ Z2))))))))).
% 2.62/1.49 thf(fact_194_inf__sup__aci_I8_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ X3) @ Y2)) = (((sup_sup @ A) @ X3) @ Y2)))))))).
% 2.62/1.49 thf(fact_195_Un__UNIV__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.62/1.49 thf(fact_196_Un__UNIV__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (top_top @ (set @ A))) @ B2) = (top_top @ (set @ A)))))).
% 2.62/1.49 thf(fact_197_top_Onot__eq__extremum, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: (((A4 != (top_top @ A)) = (((ord_less @ A) @ A4) @ (top_top @ A))))))))).
% 2.62/1.49 thf(fact_198_top_Oextremum__strict, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: ((~ ((((ord_less @ A) @ (top_top @ A)) @ A4))))))))).
% 2.62/1.49 thf(fact_199_Un__Diff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C3) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ C3)) @ (((minus_minus @ (set @ A)) @ B2) @ C3)))))).
% 2.62/1.49 thf(fact_200_not__less__LNil, axiom, (! [A:$tType,R:(coinductive_llist @ A)]: ((~ ((((ord_less @ (coinductive_llist @ A)) @ R) @ (coinductive_LNil @ A))))))).
% 2.62/1.49 thf(fact_201_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B4:A,A4:A]: (((((ord_less @ A) @ B4) @ A4) => (A4 != B4)))))))).
% 2.62/1.49 thf(fact_202_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => (A4 != B4)))))))).
% 2.62/1.49 thf(fact_203_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) = ((((ord_less @ A) @ Y2) @ X3) | (X3 = Y2))))))))).
% 2.62/1.49 thf(fact_204_dual__order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B4:A,A4:A,C2:A]: (((((ord_less @ A) @ B4) @ A4) => ((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ A4))))))))).
% 2.62/1.49 thf(fact_205_less__imp__not__less, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 2.62/1.49 thf(fact_206_order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A]: (((((ord_less @ A) @ A4) @ B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.62/1.49 thf(fact_207_dual__order_Oirrefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ A4))))))))).
% 2.62/1.49 thf(fact_208_linorder__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => ((X3 != Y2) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 2.62/1.49 thf(fact_209_less__imp__triv, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A,P:$o]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ X3) => P)))))))).
% 2.62/1.49 thf(fact_210_less__imp__not__eq2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (Y2 != X3)))))))).
% 2.62/1.49 thf(fact_211_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y2:A,X3:A]: (((~ ((((ord_less @ A) @ Y2) @ X3))) => ((~ ((((ord_less @ A) @ X3) @ Y2))) = (X3 = Y2))))))))).
% 2.62/1.49 thf(fact_212_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A4:A]: (((! [X4:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X4) => (P @ Y3)))) => (P @ X4)))) => (P @ A4)))))))).
% 2.62/1.49 thf(fact_213_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 2.62/1.49 thf(fact_214_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (X3 != Y2)))))))).
% 2.62/1.49 thf(fact_215_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B4:A,A4:A]: (((((ord_less @ A) @ B4) @ A4) => (~ ((((ord_less @ A) @ A4) @ B4)))))))))).
% 2.62/1.49 thf(fact_216_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A]: (((((ord_less @ A) @ A4) @ B4) => ((B4 = C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.62/1.49 thf(fact_217_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A]: (((A4 = B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.62/1.49 thf(fact_218_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A]: ((~ ((((ord_less @ A) @ X3) @ X3))))))))).
% 2.62/1.49 thf(fact_219_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) | ((X3 = Y2) | (((ord_less @ A) @ Y2) @ X3))))))))).
% 2.62/1.49 thf(fact_220_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ Z2) => (((ord_less @ A) @ X3) @ Z2))))))))).
% 2.62/1.49 thf(fact_221_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => (~ ((((ord_less @ A) @ B4) @ A4)))))))))).
% 2.62/1.49 thf(fact_222_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 2.62/1.49 thf(fact_223_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (X3 != Y2)))))))).
% 2.62/1.49 thf(fact_224_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (? [Z3:A]: (((((ord_less @ A) @ X3) @ Z3) & (((ord_less @ A) @ Z3) @ Y2))))))))))).
% 2.62/1.49 thf(fact_225_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => (~ ((((ord_less @ A) @ B4) @ A4)))))))))).
% 2.62/1.49 thf(fact_226_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((X3 != Y2) = ((((ord_less @ A) @ X3) @ Y2) | (((ord_less @ A) @ Y2) @ X3))))))))).
% 2.62/1.49 thf(fact_227_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y2:A]: (((X3 != Y2) => ((~ ((((ord_less @ A) @ X3) @ Y2))) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 2.62/1.49 thf(fact_228_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X3:A]: ((? [X1:A]: ((((ord_less @ A) @ X3) @ X1))))))))).
% 2.62/1.49 thf(fact_229_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X3:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X3))))))))).
% 2.62/1.49 thf(fact_230_order__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,B4:A,F:(A > C),C2:C]: (((((ord_less @ A) @ A4) @ B4) => ((((ord_less @ C) @ (F @ B4)) @ C2) => ((! [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) => (((ord_less @ C) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less @ C) @ (F @ A4)) @ C2)))))))))).
% 2.62/1.49 thf(fact_231_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((((ord_less @ A) @ A4) @ (F @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X4:B,Y4:B]: (((((ord_less @ B) @ X4) @ Y4) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 2.62/1.49 thf(fact_232_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,B4:A,F:(A > B),C2:B]: (((((ord_less @ A) @ A4) @ B4) => (((F @ B4) = C2) => ((! [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) => (((ord_less @ B) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less @ B) @ (F @ A4)) @ C2)))))))))).
% 2.62/1.49 thf(fact_233_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((A4 = (F @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X4:B,Y4:B]: (((((ord_less @ B) @ X4) @ Y4) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 2.62/1.49 thf(fact_234_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C3)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A2) @ C3)))))).
% 2.62/1.49 thf(fact_235_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.62/1.49 thf(fact_236_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((((sup_sup @ (set @ A)) @ B3) @ A3))))))).
% 2.62/1.49 thf(fact_237_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 2.62/1.49 thf(fact_238_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C3) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C3)))))).
% 2.62/1.49 thf(fact_239_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A2) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B2) => (P @ X2))))))))).
% 2.62/1.49 thf(fact_240_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B2) & (P @ X2))))))))).
% 2.62/1.49 thf(fact_241_UnI2, axiom, (! [A:$tType,C2:A,B2:(set @ A),A2:(set @ A)]: (((((member @ A) @ C2) @ B2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.62/1.49 thf(fact_242_UnI1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.62/1.49 thf(fact_243_UnE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => ((~ ((((member @ A) @ C2) @ A2))) => (((member @ A) @ C2) @ B2)))))).
% 2.62/1.49 thf(fact_244_diff__strict__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A,D2:A,C2:A]: (((((ord_less @ A) @ A4) @ B4) => ((((ord_less @ A) @ D2) @ C2) => (((ord_less @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ (((minus_minus @ A) @ B4) @ D2)))))))))).
% 2.62/1.49 thf(fact_245_diff__eq__diff__less, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A,D2:A]: ((((((minus_minus @ A) @ A4) @ B4) = (((minus_minus @ A) @ C2) @ D2)) => ((((ord_less @ A) @ A4) @ B4) = (((ord_less @ A) @ C2) @ D2))))))))).
% 2.62/1.49 thf(fact_246_diff__strict__left__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B4:A,A4:A,C2:A]: (((((ord_less @ A) @ B4) @ A4) => (((ord_less @ A) @ (((minus_minus @ A) @ C2) @ A4)) @ (((minus_minus @ A) @ C2) @ B4))))))))).
% 2.62/1.49 thf(fact_247_LList2__Mirabelle__hamjzmohle_Ollength__mono, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((ord_less @ (coinductive_llist @ A)) @ S) @ R) => (((ord_less @ nat) @ ((lList21232602520length @ A) @ S)) @ ((lList21232602520length @ A) @ R))))))).
% 2.62/1.49 thf(fact_248_psubset__imp__ex__mem, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B2) => (? [B6:A]: ((((member @ A) @ B6) @ (((minus_minus @ (set @ A)) @ B2) @ A2)))))))).
% 2.62/1.49 thf(fact_249_diff__right__commute, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A4:A,C2:A,B4:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ B4) = (((minus_minus @ A) @ (((minus_minus @ A) @ A4) @ B4)) @ C2)))))))).
% 2.62/1.49 thf(fact_250_diff__eq__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A,D2:A]: ((((((minus_minus @ A) @ A4) @ B4) = (((minus_minus @ A) @ C2) @ D2)) => ((A4 = B4) = (C2 = D2))))))))).
% 2.62/1.49 thf(fact_251_lapp__take__less, axiom, (! [A:$tType,I:nat,R:(coinductive_llist @ A),S:(coinductive_llist @ A)]: (((((ord_less @ nat) @ I) @ ((lList21232602520length @ A) @ R)) => (((ord_less @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ (((coinductive_lappend @ A) @ R) @ S)) @ I)) @ R))))).
% 2.62/1.49 thf(fact_252_diff__strict__right__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A]: (((((ord_less @ A) @ A4) @ B4) => (((ord_less @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ (((minus_minus @ A) @ B4) @ C2))))))))).
% 2.62/1.49 thf(fact_253_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y2:A,Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y2) @ Ys))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y2) @ Ys))))))).
% 2.62/1.49 thf(fact_254_pprefix__closed__def, axiom, (! [A:$tType]: (((lList21974196564closed @ A) = (^ [A3:(set @ (coinductive_llist @ A))]: ((! [X2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X2) @ A3) => (! [S3:(coinductive_llist @ A)]: ((((((ord_less_eq @ (coinductive_llist @ A)) @ S3) @ X2) & (S3 != (coinductive_LNil @ A))) => (((member @ (coinductive_llist @ A)) @ S3) @ A3))))))))))))).
% 2.62/1.49 thf(fact_255_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.62/1.49 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: (((bounded_lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Lattices_Obounded__lattice__top, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: ((((semilattice_sup @ A9) @ (type2 @ A9)) => ((semilattice_sup @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A8:$tType,A9:$tType]: ((((order_top @ A9) @ (type2 @ A9)) => ((order_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: ((((lattice @ A9) @ (type2 @ A9)) => ((lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A9) @ (type2 @ A9)) => ((order @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_fun___Groups_Ominus, axiom, (! [A8:$tType,A9:$tType]: ((((minus @ A9) @ (type2 @ A9)) => ((minus @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.62/1.49 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, ((cancel146912293up_add @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3, axiom, ((semilattice_sup @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, ((wellorder @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Orderings_Opreorder_4, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, ((no_top @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Lattices_Olattice_5, axiom, ((lattice @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Orderings_Oorder_6, axiom, ((order @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Orderings_Oord_7, axiom, ((ord @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Nat_Onat___Groups_Ominus_8, axiom, ((minus @ nat) @ (type2 @ nat))).
% 2.62/1.49 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_9, axiom, (! [A8:$tType]: (((bounded_lattice_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10, axiom, (! [A8:$tType]: (((semilattice_sup @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_Set_Oset___Orderings_Oorder__top_11, axiom, (! [A8:$tType]: (((order_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_Set_Oset___Orderings_Opreorder_12, axiom, (! [A8:$tType]: (((preorder @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_Set_Oset___Lattices_Olattice_13, axiom, (! [A8:$tType]: (((lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_Set_Oset___Orderings_Oorder_14, axiom, (! [A8:$tType]: (((order @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_Set_Oset___Orderings_Otop_15, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_Set_Oset___Orderings_Oord_16, axiom, (! [A8:$tType]: (((ord @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_Set_Oset___Groups_Ominus_17, axiom, (! [A8:$tType]: (((minus @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.62/1.49 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_18, axiom, ((bounded_lattice_top @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_19, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Orderings_Oorder__top_20, axiom, ((order_top @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Orderings_Opreorder_21, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Orderings_Olinorder_22, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Lattices_Olattice_23, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Orderings_Oorder_24, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Orderings_Otop_25, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Orderings_Oord_26, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_HOL_Obool___Groups_Ominus_27, axiom, ((minus @ $o) @ (type2 @ $o))).
% 2.62/1.49 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_28, axiom, (! [A8:$tType]: (((preorder @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.62/1.49 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_29, axiom, (! [A8:$tType]: (((order @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.62/1.49 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_30, axiom, (! [A8:$tType]: (((ord @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.62/1.49 thf(conj_0, hypothesis, (((lList21952340509veness @ a) @ a2) @ p)).
% 2.62/1.49 thf(conj_1, hypothesis, (! [T3:(coinductive_llist @ a)]: (((((member @ (coinductive_llist @ a)) @ T3) @ ((lList2435255213lllsts @ a) @ a2)) => ((((member @ (coinductive_llist @ a)) @ (((coinductive_lappend @ a) @ s) @ T3)) @ p) => r))))).
% 2.62/1.49 thf(conj_2, hypothesis, ((~ ((((member @ (coinductive_llist @ a)) @ s) @ ((lList22096119349pslsts @ a) @ a2)))) => r)).
% 2.62/1.49 thf(conj_3, conjecture, r).
% 2.62/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.iIZaSoWsFt/DTF2DTF418.p
% 2.62/1.49 ------------------------
% 2.83/1.54 ---- Cleaned THF ---
% 2.83/1.55 thf(ty_t_Coinductive__List_Ollist,type,
% 2.83/1.55 coinductive_llist: $tType > $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Set_Oset,type,
% 2.83/1.55 set: $tType > $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Nat_Onat,type,
% 2.83/1.55 nat: $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_itself,type,
% 2.83/1.55 itself: $tType > $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_tf_a,type,
% 2.83/1.55 a: $tType ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.83/1.55 bounded_lattice:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_HOL_Otype,type,
% 2.83/1.55 type:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Groups_Ominus,type,
% 2.83/1.55 minus:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Oord,type,
% 2.83/1.55 ord:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Otop,type,
% 2.83/1.55 top:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Oorder,type,
% 2.83/1.55 order:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Groups_Ogroup__add,type,
% 2.83/1.55 group_add:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Lattices_Olattice,type,
% 2.83/1.55 lattice:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Ono__bot,type,
% 2.83/1.55 no_bot:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Ono__top,type,
% 2.83/1.55 no_top:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 2.83/1.55 linorder:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Opreorder,type,
% 2.83/1.55 preorder:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Oorder__top,type,
% 2.83/1.55 order_top:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Owellorder,type,
% 2.83/1.55 wellorder:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Odense__order,type,
% 2.83/1.55 dense_order:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.83/1.55 semilattice_sup:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.83/1.55 ordered_ab_group_add:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 2.83/1.55 bounded_lattice_top:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 2.83/1.55 cancel146912293up_add:
% 2.83/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.83/1.55 coindu328551480prefix:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Coinductive__List_Olappend,type,
% 2.83/1.55 coinductive_lappend:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Coinductive__List_Olfinite,type,
% 2.83/1.55 coinductive_lfinite:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Coinductive__List_Ollast,type,
% 2.83/1.55 coinductive_llast:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.83/1.55 coinductive_LCons:
% 2.83/1.55 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.83/1.55 coinductive_LNil:
% 2.83/1.55 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.83/1.55 coindu1478340336prefix:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.83/1.55 minus_minus:
% 2.83/1.55 !>[A: $tType] : ( A > A > A ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 2.83/1.55 lList2435255213lllsts:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 2.83/1.55 lList2236698231inlsts:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 2.83/1.55 lList21916056377ts_rec:
% 2.83/1.55 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinpref,type,
% 2.83/1.55 lList21202317876inpref:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 2.83/1.55 lList22096119349pslsts:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfliveness,type,
% 2.83/1.55 lList21015763786veness:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 2.83/1.55 lList21612149805nflsts:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsafety,type,
% 2.83/1.55 lList21015939545safety:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinfsuff,type,
% 2.83/1.55 lList2649413865nfsuff:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 2.83/1.55 lList2370560421utlast:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 2.83/1.55 lList2508575361_ldrop:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oliveness,type,
% 2.83/1.55 lList21805353693veness:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 2.83/1.55 lList2170638824_llast:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 2.83/1.55 lList21232602520length:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 2.83/1.55 lList2281150353e_lrev:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 2.83/1.55 lList22119844313_ltake:
% 2.83/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opfinpref,type,
% 2.83/1.55 lList2467029176inpref:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposliveness,type,
% 2.83/1.55 lList21952340509veness:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 2.83/1.55 lList21148268032oslsts:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opossafety,type,
% 2.83/1.55 lList292406316safety:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Opprefix__closed,type,
% 2.83/1.55 lList21974196564closed:
% 2.83/1.55 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oprefix__closed,type,
% 2.83/1.55 lList21638733016closed:
% 2.83/1.55 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osafety,type,
% 2.83/1.55 lList21350011628safety:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_LList2__Mirabelle__hamjzmohle_Osuff,type,
% 2.83/1.55 lList21475143548e_suff:
% 2.83/1.55 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.83/1.55 sup_sup:
% 2.83/1.55 !>[A: $tType] : ( A > A > A ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Nat_OSuc,type,
% 2.83/1.55 suc: nat > nat ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.83/1.55 ord_less:
% 2.83/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.83/1.55 ord_less_eq:
% 2.83/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.83/1.55 top_top:
% 2.83/1.55 !>[A: $tType] : A ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Pure_Otype,type,
% 2.83/1.55 type2:
% 2.83/1.55 !>[A: $tType] : ( itself @ A ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Set_OCollect,type,
% 2.83/1.55 collect:
% 2.83/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_member,type,
% 2.83/1.55 member:
% 2.83/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_A,type,
% 2.83/1.55 a2: set @ a ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_P,type,
% 2.83/1.55 p: set @ ( coinductive_llist @ a ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_R,type,
% 2.83/1.55 r: $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_s,type,
% 2.83/1.55 s: coinductive_llist @ a ).
% 2.83/1.55
% 2.83/1.55 thf(fact_0_lappT,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_1_poslivenessI,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ( ! [S2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.83/1.55 => ? [X: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S2 @ X ) @ P ) ) )
% 2.83/1.55 => ( lList21952340509veness @ A @ A2 @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_2_lapp__all__invT,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_3_posliveness__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList21952340509veness @ A )
% 2.83/1.55 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ! [X2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList22096119349pslsts @ A @ A3 ) )
% 2.83/1.55 => ? [Y: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_4_lappend__assoc,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.83/1.55 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 2.83/1.55 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_5_suff__all,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21475143548e_suff @ A @ A2 @ S ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_6_safetyD,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A ),T: coinductive_llist @ A] :
% 2.83/1.55 ( ( lList21350011628safety @ A @ A2 @ P )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ! [R2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R2 @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 2.83/1.55 => ? [X: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R2 @ X ) @ P ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ T @ P ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_7_safetyE,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ( ( lList21350011628safety @ A @ A2 @ P )
% 2.83/1.55 => ! [X: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ! [Xa: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList21202317876inpref @ A @ A2 @ X ) )
% 2.83/1.55 => ? [Xb: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xb @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xa @ Xb ) @ P ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X @ P ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_8_safetyI,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ( ! [T2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ! [X: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21202317876inpref @ A @ A2 @ T2 ) )
% 2.83/1.55 => ? [Xa: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X @ Xa ) @ P ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ T2 @ P ) ) )
% 2.83/1.55 => ( lList21350011628safety @ A @ A2 @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_9_safety__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList21350011628safety @ A )
% 2.83/1.55 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ! [X2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.83/1.55 => ( ! [Y: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21202317876inpref @ A @ A3 @ X2 ) )
% 2.83/1.55 => ? [Z: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P2 ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X2 @ P2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_10_ldropT,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_11_alllsts__UNIV,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_12_lapp__inf,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( ( coinductive_lappend @ A @ S @ T )
% 2.83/1.55 = S ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_13_livenessE,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A ),S: coinductive_llist @ A] :
% 2.83/1.55 ( ( lList21805353693veness @ A @ A2 @ P )
% 2.83/1.55 => ( ! [T2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ~ ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T2 ) @ P ) )
% 2.83/1.55 => ~ ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_14_livenessI,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ( ! [S2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ? [X: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S2 @ X ) @ P ) ) )
% 2.83/1.55 => ( lList21805353693veness @ A @ A2 @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_15_liveness__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList21805353693veness @ A )
% 2.83/1.55 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ! [X2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.83/1.55 => ? [Y: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_16_lapp__fin__fin__iff,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_17_same__lappend__eq,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( ( coinductive_lappend @ A @ R @ S )
% 2.83/1.55 = ( coinductive_lappend @ A @ R @ T ) )
% 2.83/1.55 = ( S = T ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_18_notfin__inf,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A] :
% 2.83/1.55 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.83/1.55 = ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_19_notinf__fin,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A] :
% 2.83/1.55 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.83/1.55 = ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_20_ldrop__fin__iffT,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_21_ldrop__inf__iffT,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_22_inflstsI,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ~ ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_23_inflstsE,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ~ ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_24_finT__simp,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_25_infT__simp,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_26_fin__finite,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_27_ldrop__finT,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_28_ldrop__infT,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_29_finpref__fin,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21202317876inpref @ A @ A2 @ S ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_30_suff__finpref,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,R: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_31_fin__inf__cases,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A] :
% 2.83/1.55 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_32_suff__finpref__iff,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 2.83/1.55 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_33_lapp__fin__infT,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_34_lapp__inv2T,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 2.83/1.55 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_35_lapp__infT,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 2.83/1.55 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_36_app__invT,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_37_alllstsE,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ~ ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_38_finpref__suff,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_39_lapp__allT__iff,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.83/1.55 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_40_lapp__fin__fin__lemma,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_41_lappfin__finT,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_42_finsubsetall,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_43_finite__lemma,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ B2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_44_suff__appE,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21475143548e_suff @ A @ A2 @ R ) )
% 2.83/1.55 => ~ ! [S2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( T
% 2.83/1.55 != ( coinductive_lappend @ A @ R @ S2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_45_mem__Collect__eq,axiom,
% 2.83/1.55 ! [A: $tType,A4: A,P: A > $o] :
% 2.83/1.55 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 2.83/1.55 = ( P @ A4 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_46_Collect__mem__eq,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] :
% 2.83/1.55 ( ( collect @ A
% 2.83/1.55 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 2.83/1.55 = A2 ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_47_Collect__cong,axiom,
% 2.83/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.55 ( ! [X4: A] :
% 2.83/1.55 ( ( P @ X4 )
% 2.83/1.55 = ( Q @ X4 ) )
% 2.83/1.55 => ( ( collect @ A @ P )
% 2.83/1.55 = ( collect @ A @ Q ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_48_ext,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.83/1.55 ( ! [X4: A] :
% 2.83/1.55 ( ( F @ X4 )
% 2.83/1.55 = ( G @ X4 ) )
% 2.83/1.55 => ( F = G ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_49_infsubsetall,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_50_infsafety__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList21015939545safety @ A )
% 2.83/1.55 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ! [X2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.83/1.55 => ( ! [Y: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21202317876inpref @ A @ A3 @ X2 ) )
% 2.83/1.55 => ? [Z: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P2 ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X2 @ P2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_51_infliveness__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList21015763786veness @ A )
% 2.83/1.55 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ! [X2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.83/1.55 => ? [Y: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X2 @ Y ) @ P2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_52_safety__prefix__closed,axiom,
% 2.83/1.55 ! [A: $tType,P: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ( ( lList21350011628safety @ A @ ( top_top @ ( set @ A ) ) @ P )
% 2.83/1.55 => ( lList21638733016closed @ A @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_53_infsuff__finpref__iff,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21202317876inpref @ A @ A2 @ R ) )
% 2.83/1.55 = ( member @ ( coinductive_llist @ A ) @ R @ ( lList2649413865nfsuff @ A @ A2 @ T ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_54_UNIV__I,axiom,
% 2.83/1.55 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_55_iso__tuple__UNIV__I,axiom,
% 2.83/1.55 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_56_top__apply,axiom,
% 2.83/1.55 ! [C: $tType,D: $tType] :
% 2.83/1.55 ( ( top @ C @ ( type2 @ C ) )
% 2.83/1.55 => ( ( top_top @ ( D > C ) )
% 2.83/1.55 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_57_lrev__lappend,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.83/1.55 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_58_infsuff__appE,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) )
% 2.83/1.55 => ~ ! [S2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( T
% 2.83/1.55 != ( coinductive_lappend @ A @ R @ S2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_59_lapp__suff__llength,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( lList2508575361_ldrop @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 2.83/1.55 = S ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_60_lrevT,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_61_lrev__is__lrev__conv,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.83/1.55 = ( lList2281150353e_lrev @ A @ Ys ) )
% 2.83/1.55 = ( Xs = Ys ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_62_lrev__lrev__ident,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 2.83/1.55 = Xs ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_63_top__set__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( top_top @ ( set @ A ) )
% 2.83/1.55 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_64_infsuff__inf,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2649413865nfsuff @ A @ A2 @ S ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21612149805nflsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_65_UNIV__witness,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ? [X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_66_UNIV__eq__I,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] :
% 2.83/1.55 ( ! [X4: A] : ( member @ A @ X4 @ A2 )
% 2.83/1.55 => ( ( top_top @ ( set @ A ) )
% 2.83/1.55 = A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_67_infsuff__finpref,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,R: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_68_finpref__infsuff,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21202317876inpref @ A @ A2 @ T ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ T @ ( lList2649413865nfsuff @ A @ A2 @ R ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_69_ltake__lappend__llength,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 2.83/1.55 = R ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_70_llength__take,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 2.83/1.55 = I ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_71_take__fin,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_72_ltake__fin,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_73_inflsts__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList21612149805nflsts @ A )
% 2.83/1.55 = ( ^ [A3: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A3 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_74_lrev__is__LNil__conv,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( Xs
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_75_LNil__is__lrev__conv,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( ( coinductive_LNil @ A )
% 2.83/1.55 = ( lList2281150353e_lrev @ A @ Xs ) )
% 2.83/1.55 = ( Xs
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_76_Diff__idemp,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 2.83/1.55 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_77_Diff__iff,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 = ( ( member @ A @ C2 @ A2 )
% 2.83/1.55 & ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_78_DiffI,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ A2 )
% 2.83/1.55 => ( ~ ( member @ A @ C2 @ B2 )
% 2.83/1.55 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_79_top1I,axiom,
% 2.83/1.55 ! [A: $tType,X3: A] : ( top_top @ ( A > $o ) @ X3 ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_80_lappend__eq__LNil__iff,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( ( Xs
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 & ( Ys
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_81_LNil__eq__lappend__iff,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( ( coinductive_LNil @ A )
% 2.83/1.55 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.83/1.55 = ( ( Xs
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 & ( Ys
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_82_lappend__LNil2,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.83/1.55 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.83/1.55 = Xs ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_83_lappend__code_I1_J,axiom,
% 2.83/1.55 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.83/1.55 = Ys ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_84_lappend__is__LNil__conv,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( ( coinductive_lappend @ A @ S @ T )
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( ( S
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 & ( T
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_85_LNil__is__lappend__conv,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( ( coinductive_LNil @ A )
% 2.83/1.55 = ( coinductive_lappend @ A @ S @ T ) )
% 2.83/1.55 = ( ( S
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 & ( T
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_86_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 2.83/1.55 ! [A: $tType,I: nat] :
% 2.83/1.55 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_87_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 2.83/1.55 ! [A: $tType,I: nat] :
% 2.83/1.55 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_88_lrev__LNil,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_89_LNil__suff,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList21475143548e_suff @ A @ A2 @ S ) )
% 2.83/1.55 = ( S
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_90_fpslsts__iff,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.83/1.55 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 & ( S
% 2.83/1.55 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_91_suff__LNil,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] :
% 2.83/1.55 ( ( lList21475143548e_suff @ A @ A2 @ ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_92_infsuff__LNil,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] :
% 2.83/1.55 ( ( lList2649413865nfsuff @ A @ A2 @ ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( lList21612149805nflsts @ A @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_93_DiffD2,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 => ~ ( member @ A @ C2 @ B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_94_DiffD1,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 => ( member @ A @ C2 @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_95_DiffE,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 => ~ ( ( member @ A @ C2 @ A2 )
% 2.83/1.55 => ( member @ A @ C2 @ B2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_96_lappend__LNil__LNil,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_97_finlsts_OLNil__fin,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_98_alllsts_OLNil__all,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_99_drop__nonLNil,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.83/1.55 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 2.83/1.55 != ( coinductive_LNil @ A ) )
% 2.83/1.55 => ( T
% 2.83/1.55 != ( coinductive_LNil @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_100_llength__drop__take,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.83/1.55 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 2.83/1.55 != ( coinductive_LNil @ A ) )
% 2.83/1.55 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 2.83/1.55 = I ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_101_ltake__ldrop__id,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,I: nat] :
% 2.83/1.55 ( ( coinductive_lappend @ A @ ( lList22119844313_ltake @ A @ X3 @ I ) @ ( lList2508575361_ldrop @ A @ X3 @ I ) )
% 2.83/1.55 = X3 ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_102_pfinpref__iff,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2467029176inpref @ A @ A2 @ S ) )
% 2.83/1.55 = ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList21202317876inpref @ A @ A2 @ S ) )
% 2.83/1.55 & ( X3
% 2.83/1.55 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_103_minus__apply,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType] :
% 2.83/1.55 ( ( minus @ B @ ( type2 @ B ) )
% 2.83/1.55 => ( ( minus_minus @ ( A > B ) )
% 2.83/1.55 = ( ^ [A3: A > B,B3: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B3 @ X2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_104_top__empty__eq,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( top_top @ ( A > $o ) )
% 2.83/1.55 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_105_poslsts__iff,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.83/1.55 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( S
% 2.83/1.55 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_106_poslsts__UNIV,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 = ( S
% 2.83/1.55 != ( coinductive_LNil @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_107_lrev__LCons,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.83/1.55 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_108_llist_Oinject,axiom,
% 2.83/1.55 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.83/1.55 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 2.83/1.55 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.83/1.55 = ( ( X21 = Y21 )
% 2.83/1.55 & ( X22 = Y22 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_109_lappend__code_I2_J,axiom,
% 2.83/1.55 ! [A: $tType,Xa2: A,X3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa2 @ X3 ) @ Ys )
% 2.83/1.55 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_lappend @ A @ X3 @ Ys ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_110_LConsE,axiom,
% 2.83/1.55 ! [A: $tType,X3: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X3 @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 = ( ( member @ A @ X3 @ A2 )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_111_llist_Odistinct_I1_J,axiom,
% 2.83/1.55 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 2.83/1.55 ( ( coinductive_LNil @ A )
% 2.83/1.55 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_112_neq__LNil__conv,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.83/1.55 ( ( Xs
% 2.83/1.55 != ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 2.83/1.55 ( Xs
% 2.83/1.55 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_113_llistE,axiom,
% 2.83/1.55 ! [A: $tType,Y2: coinductive_llist @ A] :
% 2.83/1.55 ( ( Y2
% 2.83/1.55 != ( coinductive_LNil @ A ) )
% 2.83/1.55 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 2.83/1.55 ( Y2
% 2.83/1.55 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_114_finlsts_OLCons__fin,axiom,
% 2.83/1.55 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ A @ A4 @ A2 )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_115_alllsts_OLCons__all,axiom,
% 2.83/1.55 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ A @ A4 @ A2 )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_116_inflsts__cases,axiom,
% 2.83/1.55 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ A @ A5 @ A2 )
% 2.83/1.55 => ( S
% 2.83/1.55 != ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_117_inflstsI2,axiom,
% 2.83/1.55 ! [A: $tType,A4: A,A2: set @ A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ A @ A4 @ A2 )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_118_lappend__snocL1__conv__LCons2,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Y2: A,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y2 @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.83/1.55 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y2 @ Ys ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_119_finlsts_Ocases,axiom,
% 2.83/1.55 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( A4
% 2.83/1.55 != ( coinductive_LNil @ A ) )
% 2.83/1.55 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 2.83/1.55 ( ( A4
% 2.83/1.55 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_120_finlsts_Osimps,axiom,
% 2.83/1.55 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 = ( ( A4
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 | ? [L3: coinductive_llist @ A,A6: A] :
% 2.83/1.55 ( ( A4
% 2.83/1.55 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_121_finlsts__induct,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ! [L2: coinductive_llist @ A] :
% 2.83/1.55 ( ( L2
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 => ( P @ L2 ) )
% 2.83/1.55 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( P @ L2 )
% 2.83/1.55 => ( ( member @ A @ A5 @ A2 )
% 2.83/1.55 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 2.83/1.55 => ( P @ X3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_122_finlsts_Oinducts,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.83/1.55 => ( ! [L2: coinductive_llist @ A,A5: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( P @ L2 )
% 2.83/1.55 => ( ( member @ A @ A5 @ A2 )
% 2.83/1.55 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 2.83/1.55 => ( P @ X3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_123_alllsts_Ocoinduct,axiom,
% 2.83/1.55 ! [A: $tType,X5: ( coinductive_llist @ A ) > $o,X3: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( X5 @ X3 )
% 2.83/1.55 => ( ! [X4: coinductive_llist @ A] :
% 2.83/1.55 ( ( X5 @ X4 )
% 2.83/1.55 => ( ( X4
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 | ? [L4: coinductive_llist @ A,A7: A] :
% 2.83/1.55 ( ( X4
% 2.83/1.55 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 2.83/1.55 & ( ( X5 @ L4 )
% 2.83/1.55 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.83/1.55 & ( member @ A @ A7 @ A2 ) ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_124_alllsts_Osimps,axiom,
% 2.83/1.55 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 = ( ( A4
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 | ? [L3: coinductive_llist @ A,A6: A] :
% 2.83/1.55 ( ( A4
% 2.83/1.55 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_125_alllsts_Ocases,axiom,
% 2.83/1.55 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ( ( A4
% 2.83/1.55 != ( coinductive_LNil @ A ) )
% 2.83/1.55 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 2.83/1.55 ( ( A4
% 2.83/1.55 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_126_fps__induct,axiom,
% 2.83/1.55 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.83/1.55 => ( ! [A5: A] :
% 2.83/1.55 ( ( member @ A @ A5 @ A2 )
% 2.83/1.55 => ( P @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) )
% 2.83/1.55 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.83/1.55 => ( ( P @ L2 )
% 2.83/1.55 => ( ( member @ A @ A5 @ A2 )
% 2.83/1.55 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 2.83/1.55 => ( P @ L ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_127_fpslsts__cases,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.83/1.55 => ~ ! [A5: A,Rs: coinductive_llist @ A] :
% 2.83/1.55 ( ( R
% 2.83/1.55 = ( coinductive_LCons @ A @ A5 @ Rs ) )
% 2.83/1.55 => ( ( member @ A @ A5 @ A2 )
% 2.83/1.55 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_128_finlsts__rev__cases,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( T
% 2.83/1.55 != ( coinductive_LNil @ A ) )
% 2.83/1.55 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( member @ A @ A5 @ A2 )
% 2.83/1.55 => ( T
% 2.83/1.55 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_129_lrev__induct,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.83/1.55 => ( ! [X4: A,Xs3: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( P @ Xs3 )
% 2.83/1.55 => ( ( member @ A @ X4 @ A2 )
% 2.83/1.55 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X4 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 2.83/1.55 => ( P @ Xs ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_130_fun__diff__def,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType] :
% 2.83/1.55 ( ( minus @ B @ ( type2 @ B ) )
% 2.83/1.55 => ( ( minus_minus @ ( A > B ) )
% 2.83/1.55 = ( ^ [A3: A > B,B3: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B3 @ X2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_131_lbutlast__snoc,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X3: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( lList2370560421utlast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) )
% 2.83/1.55 = Xs ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_132_possafetyD,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A ),T: coinductive_llist @ A] :
% 2.83/1.55 ( ( lList292406316safety @ A @ A2 @ P )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.83/1.55 => ( ! [R2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R2 @ ( lList2467029176inpref @ A @ A2 @ T ) )
% 2.83/1.55 => ? [X: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R2 @ X ) @ P ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ T @ P ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_133_possafetyE,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ( ( lList292406316safety @ A @ A2 @ P )
% 2.83/1.55 => ! [X: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.83/1.55 => ( ! [Xa: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2467029176inpref @ A @ A2 @ X ) )
% 2.83/1.55 => ? [Xb: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xb @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xa @ Xb ) @ P ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X @ P ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_134_possafetyI,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,P: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ( ! [T2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.83/1.55 => ( ! [X: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2467029176inpref @ A @ A2 @ T2 ) )
% 2.83/1.55 => ? [Xa: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xa @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ X @ Xa ) @ P ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ T2 @ P ) ) )
% 2.83/1.55 => ( lList292406316safety @ A @ A2 @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_135_possafety__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList292406316safety @ A )
% 2.83/1.55 = ( ^ [A3: set @ A,P2: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ! [X2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X2 @ ( lList21148268032oslsts @ A @ A3 ) )
% 2.83/1.55 => ( ! [Y: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2467029176inpref @ A @ A3 @ X2 ) )
% 2.83/1.55 => ? [Z: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Z @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.83/1.55 & ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Y @ Z ) @ P2 ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ X2 @ P2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_136_lbutlast__LNil,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_137_lbutlast__LCons,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( ( R
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.83/1.55 = ( coinductive_LNil @ A ) ) )
% 2.83/1.55 & ( ( R
% 2.83/1.55 != ( coinductive_LNil @ A ) )
% 2.83/1.55 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.83/1.55 = ( coinductive_LCons @ A @ A4 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_138_llast__snoc,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X3: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) )
% 2.83/1.55 = X3 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_139_LList2__Mirabelle__hamjzmohle_Ollast__lappend,axiom,
% 2.83/1.55 ! [A: $tType,X3: coinductive_llist @ A,Y2: coinductive_llist @ A,A4: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X3 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ Y2 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ X3 @ ( coinductive_LCons @ A @ A4 @ Y2 ) ) )
% 2.83/1.55 = ( lList2170638824_llast @ A @ ( coinductive_LCons @ A @ A4 @ Y2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_140_lbutlast__lapp__llast,axiom,
% 2.83/1.55 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.83/1.55 => ( L
% 2.83/1.55 = ( coinductive_lappend @ A @ ( lList2370560421utlast @ A @ L ) @ ( coinductive_LCons @ A @ ( lList2170638824_llast @ A @ L ) @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_141_possafety__pprefix__closed,axiom,
% 2.83/1.55 ! [A: $tType,P: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ( ( lList292406316safety @ A @ ( top_top @ ( set @ A ) ) @ P )
% 2.83/1.55 => ( lList21974196564closed @ A @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_142_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 2.83/1.55 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A4: B] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 2.83/1.55 => ( ( ( R
% 2.83/1.55 = ( coinductive_LNil @ B ) )
% 2.83/1.55 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 2.83/1.55 = A4 ) )
% 2.83/1.55 & ( ( R
% 2.83/1.55 != ( coinductive_LNil @ B ) )
% 2.83/1.55 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 2.83/1.55 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_143_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Y2: A,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y2 @ Ys ) )
% 2.83/1.55 = ( ( Xs
% 2.83/1.55 = ( coinductive_LNil @ A ) )
% 2.83/1.55 | ? [Xs2: coinductive_llist @ A] :
% 2.83/1.55 ( ( Xs
% 2.83/1.55 = ( coinductive_LCons @ A @ Y2 @ Xs2 ) )
% 2.83/1.55 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_144_top__conj_I1_J,axiom,
% 2.83/1.55 ! [A: $tType,X3: A,P: $o] :
% 2.83/1.55 ( ( ( top_top @ ( A > $o ) @ X3 )
% 2.83/1.55 & P )
% 2.83/1.55 = P ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_145_top__conj_I2_J,axiom,
% 2.83/1.55 ! [A: $tType,P: $o,X3: A] :
% 2.83/1.55 ( ( P
% 2.83/1.55 & ( top_top @ ( A > $o ) @ X3 ) )
% 2.83/1.55 = P ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_146_lstrict__prefix__code_I2_J,axiom,
% 2.83/1.55 ! [B: $tType,Y2: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y2 @ Ys ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_147_lstrict__prefix__code_I4_J,axiom,
% 2.83/1.55 ! [B: $tType,X3: B,Xs: coinductive_llist @ B,Y2: B,Ys: coinductive_llist @ B] :
% 2.83/1.55 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X3 @ Xs ) @ ( coinductive_LCons @ B @ Y2 @ Ys ) )
% 2.83/1.55 = ( ( X3 = Y2 )
% 2.83/1.55 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_148_lstrict__prefix__code_I1_J,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_149_lstrict__prefix__code_I3_J,axiom,
% 2.83/1.55 ! [B: $tType,X3: B,Xs: coinductive_llist @ B] :
% 2.83/1.55 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X3 @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_150_llist__less__induct,axiom,
% 2.83/1.55 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.83/1.55 ( ! [Xs3: coinductive_llist @ A] :
% 2.83/1.55 ( ! [Ys2: coinductive_llist @ A] :
% 2.83/1.55 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 2.83/1.55 => ( P @ Ys2 ) )
% 2.83/1.55 => ( P @ Xs3 ) )
% 2.83/1.55 => ( P @ Xs ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_151_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.83/1.55 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.83/1.55 = ( Xs
% 2.83/1.55 = ( coinductive_LNil @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_152_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_153_finlsts__rec__LCons__def,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.83/1.55 ( ( F
% 2.83/1.55 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( F @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.83/1.55 = ( D2 @ A4 @ R @ ( F @ R ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_154_finlsts__rec__LCons,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,A4: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.83/1.55 = ( D2 @ A4 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ R ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_155_LList2__Mirabelle__hamjzmohle_Ollength__LCons,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( lList21232602520length @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 2.83/1.55 = ( suc @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_156_finlsts__rec__LNil__def,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 2.83/1.55 ( ( F
% 2.83/1.55 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 2.83/1.55 => ( ( F @ ( coinductive_LNil @ A ) )
% 2.83/1.55 = C2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_157_finlsts__rec__LNil,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,C2: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 2.83/1.55 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D2 @ ( coinductive_LNil @ B ) )
% 2.83/1.55 = C2 ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_158_ltake__LCons__Suc,axiom,
% 2.83/1.55 ! [A: $tType,A4: A,L: coinductive_llist @ A,I: nat] :
% 2.83/1.55 ( ( lList22119844313_ltake @ A @ ( coinductive_LCons @ A @ A4 @ L ) @ ( suc @ I ) )
% 2.83/1.55 = ( coinductive_LCons @ A @ A4 @ ( lList22119844313_ltake @ A @ L @ I ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_159_llast__singleton,axiom,
% 2.83/1.55 ! [A: $tType,X3: A] :
% 2.83/1.55 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) )
% 2.83/1.55 = X3 ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_160_take__inf__less,axiom,
% 2.83/1.55 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.83/1.55 => ( ord_less @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ T ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_161_fin__Un__inf,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.83/1.55 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_162_sup_Oright__idem,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A] :
% 2.83/1.55 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B4 ) @ B4 )
% 2.83/1.55 = ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_163_sup__left__idem,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ X3 @ Y2 ) )
% 2.83/1.55 = ( sup_sup @ A @ X3 @ Y2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_164_sup_Oleft__idem,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A] :
% 2.83/1.55 ( ( sup_sup @ A @ A4 @ ( sup_sup @ A @ A4 @ B4 ) )
% 2.83/1.55 = ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_165_sup__idem,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A] :
% 2.83/1.55 ( ( sup_sup @ A @ X3 @ X3 )
% 2.83/1.55 = X3 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_166_sup_Oidem,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A] :
% 2.83/1.55 ( ( sup_sup @ A @ A4 @ A4 )
% 2.83/1.55 = A4 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_167_sup__apply,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.83/1.55 => ( ( sup_sup @ ( A > B ) )
% 2.83/1.55 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_168_Un__iff,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 = ( ( member @ A @ C2 @ A2 )
% 2.83/1.55 | ( member @ A @ C2 @ B2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_169_UnCI,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 2.83/1.55 ( ( ~ ( member @ A @ C2 @ B2 )
% 2.83/1.55 => ( member @ A @ C2 @ A2 ) )
% 2.83/1.55 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_170_sup__top__right,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A] :
% 2.83/1.55 ( ( sup_sup @ A @ X3 @ ( top_top @ A ) )
% 2.83/1.55 = ( top_top @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_171_sup__top__left,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A] :
% 2.83/1.55 ( ( sup_sup @ A @ ( top_top @ A ) @ X3 )
% 2.83/1.55 = ( top_top @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_172_Un__Diff__cancel,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 2.83/1.55 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_173_Un__Diff__cancel2,axiom,
% 2.83/1.55 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) @ A2 )
% 2.83/1.55 = ( sup_sup @ ( set @ A ) @ B2 @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_174_llast__LCons2,axiom,
% 2.83/1.55 ! [A: $tType,X3: A,Y2: A,Xs: coinductive_llist @ A] :
% 2.83/1.55 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LCons @ A @ Y2 @ Xs ) ) )
% 2.83/1.55 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y2 @ Xs ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_175_less__LCons,axiom,
% 2.83/1.55 ! [A: $tType,A4: A,R: coinductive_llist @ A,B4: A,T: coinductive_llist @ A] :
% 2.83/1.55 ( ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ R ) @ ( coinductive_LCons @ A @ B4 @ T ) )
% 2.83/1.55 = ( ( A4 = B4 )
% 2.83/1.55 & ( ord_less @ ( coinductive_llist @ A ) @ R @ T ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_176_llist__less__finT,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.83/1.55 ( ( ord_less @ ( coinductive_llist @ A ) @ R @ S )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_177_LNil__less__LCons,axiom,
% 2.83/1.55 ! [A: $tType,A4: A,T: coinductive_llist @ A] : ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_178_sup_Ostrict__coboundedI2,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [C2: A,B4: A,A4: A] :
% 2.83/1.55 ( ( ord_less @ A @ C2 @ B4 )
% 2.83/1.55 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_179_sup_Ostrict__coboundedI1,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [C2: A,A4: A,B4: A] :
% 2.83/1.55 ( ( ord_less @ A @ C2 @ A4 )
% 2.83/1.55 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_180_sup_Ostrict__order__iff,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ( ( ord_less @ A )
% 2.83/1.55 = ( ^ [B5: A,A6: A] :
% 2.83/1.55 ( ( A6
% 2.83/1.55 = ( sup_sup @ A @ A6 @ B5 ) )
% 2.83/1.55 & ( A6 != B5 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_181_sup_Ostrict__boundedE,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [B4: A,C2: A,A4: A] :
% 2.83/1.55 ( ( ord_less @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A4 )
% 2.83/1.55 => ~ ( ( ord_less @ A @ B4 @ A4 )
% 2.83/1.55 => ~ ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_182_sup__left__commute,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A,Z2: A] :
% 2.83/1.55 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) )
% 2.83/1.55 = ( sup_sup @ A @ Y2 @ ( sup_sup @ A @ X3 @ Z2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_183_sup_Oleft__commute,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [B4: A,A4: A,C2: A] :
% 2.83/1.55 ( ( sup_sup @ A @ B4 @ ( sup_sup @ A @ A4 @ C2 ) )
% 2.83/1.55 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_184_sup__commute,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ( ( sup_sup @ A )
% 2.83/1.55 = ( ^ [X2: A,Y: A] : ( sup_sup @ A @ Y @ X2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_185_sup_Ocommute,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ( ( sup_sup @ A )
% 2.83/1.55 = ( ^ [A6: A,B5: A] : ( sup_sup @ A @ B5 @ A6 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_186_less__supI2,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,B4: A,A4: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ B4 )
% 2.83/1.55 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_187_less__supI1,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,A4: A,B4: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ A4 )
% 2.83/1.55 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_188_sup__assoc,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A,Z2: A] :
% 2.83/1.55 ( ( sup_sup @ A @ ( sup_sup @ A @ X3 @ Y2 ) @ Z2 )
% 2.83/1.55 = ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_189_sup_Oassoc,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A,C2: A] :
% 2.83/1.55 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B4 ) @ C2 )
% 2.83/1.55 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_190_sup__fun__def,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.83/1.55 => ( ( sup_sup @ ( A > B ) )
% 2.83/1.55 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_191_inf__sup__aci_I5_J,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.55 => ( ( sup_sup @ A )
% 2.83/1.55 = ( ^ [X2: A,Y: A] : ( sup_sup @ A @ Y @ X2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_192_inf__sup__aci_I6_J,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A,Z2: A] :
% 2.83/1.55 ( ( sup_sup @ A @ ( sup_sup @ A @ X3 @ Y2 ) @ Z2 )
% 2.83/1.55 = ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_193_inf__sup__aci_I7_J,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A,Z2: A] :
% 2.83/1.55 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) )
% 2.83/1.55 = ( sup_sup @ A @ Y2 @ ( sup_sup @ A @ X3 @ Z2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_194_inf__sup__aci_I8_J,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ X3 @ Y2 ) )
% 2.83/1.55 = ( sup_sup @ A @ X3 @ Y2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_195_Un__UNIV__right,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 2.83/1.55 = ( top_top @ ( set @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_196_Un__UNIV__left,axiom,
% 2.83/1.55 ! [A: $tType,B2: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 2.83/1.55 = ( top_top @ ( set @ A ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_197_top_Onot__eq__extremum,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order_top @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A] :
% 2.83/1.55 ( ( A4
% 2.83/1.55 != ( top_top @ A ) )
% 2.83/1.55 = ( ord_less @ A @ A4 @ ( top_top @ A ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_198_top_Oextremum__strict,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order_top @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A] :
% 2.83/1.55 ~ ( ord_less @ A @ ( top_top @ A ) @ A4 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_199_Un__Diff,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 2.83/1.55 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 2.83/1.55 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_200_not__less__LNil,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A] :
% 2.83/1.55 ~ ( ord_less @ ( coinductive_llist @ A ) @ R @ ( coinductive_LNil @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_201_dual__order_Ostrict__implies__not__eq,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [B4: A,A4: A] :
% 2.83/1.55 ( ( ord_less @ A @ B4 @ A4 )
% 2.83/1.55 => ( A4 != B4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_202_order_Ostrict__implies__not__eq,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ( A4 != B4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_203_not__less__iff__gr__or__eq,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 2.83/1.55 = ( ( ord_less @ A @ Y2 @ X3 )
% 2.83/1.55 | ( X3 = Y2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_204_dual__order_Ostrict__trans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [B4: A,A4: A,C2: A] :
% 2.83/1.55 ( ( ord_less @ A @ B4 @ A4 )
% 2.83/1.55 => ( ( ord_less @ A @ C2 @ B4 )
% 2.83/1.55 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_205_less__imp__not__less,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_206_order_Ostrict__trans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A,C2: A] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ( ( ord_less @ A @ B4 @ C2 )
% 2.83/1.55 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_207_dual__order_Oirrefl,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A] :
% 2.83/1.55 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_208_linorder__cases,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ( ( X3 != Y2 )
% 2.83/1.55 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_209_less__imp__triv,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A,P: $o] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ( ( ord_less @ A @ Y2 @ X3 )
% 2.83/1.55 => P ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_210_less__imp__not__eq2,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ( Y2 != X3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_211_antisym__conv3,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [Y2: A,X3: A] :
% 2.83/1.55 ( ~ ( ord_less @ A @ Y2 @ X3 )
% 2.83/1.55 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 2.83/1.55 = ( X3 = Y2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_212_less__induct,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [P: A > $o,A4: A] :
% 2.83/1.55 ( ! [X4: A] :
% 2.83/1.55 ( ! [Y3: A] :
% 2.83/1.55 ( ( ord_less @ A @ Y3 @ X4 )
% 2.83/1.55 => ( P @ Y3 ) )
% 2.83/1.55 => ( P @ X4 ) )
% 2.83/1.55 => ( P @ A4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_213_less__not__sym,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_214_less__imp__not__eq,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ( X3 != Y2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_215_dual__order_Oasym,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [B4: A,A4: A] :
% 2.83/1.55 ( ( ord_less @ A @ B4 @ A4 )
% 2.83/1.55 => ~ ( ord_less @ A @ A4 @ B4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_216_ord__less__eq__trans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ord @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A,C2: A] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ( ( B4 = C2 )
% 2.83/1.55 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_217_ord__eq__less__trans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ord @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A,C2: A] :
% 2.83/1.55 ( ( A4 = B4 )
% 2.83/1.55 => ( ( ord_less @ A @ B4 @ C2 )
% 2.83/1.55 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_218_less__irrefl,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A] :
% 2.83/1.55 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_219_less__linear,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 | ( X3 = Y2 )
% 2.83/1.55 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_220_less__trans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A,Z2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ( ( ord_less @ A @ Y2 @ Z2 )
% 2.83/1.55 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_221_less__asym_H,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ~ ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_222_less__asym,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_223_less__imp__neq,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ( X3 != Y2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_224_dense,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( dense_order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ? [Z3: A] :
% 2.83/1.55 ( ( ord_less @ A @ X3 @ Z3 )
% 2.83/1.55 & ( ord_less @ A @ Z3 @ Y2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_225_order_Oasym,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ~ ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_226_neq__iff,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( X3 != Y2 )
% 2.83/1.55 = ( ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 | ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_227_neqE,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A,Y2: A] :
% 2.83/1.55 ( ( X3 != Y2 )
% 2.83/1.55 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 2.83/1.55 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_228_gt__ex,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( no_top @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A] :
% 2.83/1.55 ? [X1: A] : ( ord_less @ A @ X3 @ X1 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_229_lt__ex,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( no_bot @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A] :
% 2.83/1.55 ? [Y4: A] : ( ord_less @ A @ Y4 @ X3 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_230_order__less__subst2,axiom,
% 2.83/1.55 ! [A: $tType,C: $tType] :
% 2.83/1.55 ( ( ( order @ C @ ( type2 @ C ) )
% 2.83/1.55 & ( order @ A @ ( type2 @ A ) ) )
% 2.83/1.55 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ( ( ord_less @ C @ ( F @ B4 ) @ C2 )
% 2.83/1.55 => ( ! [X4: A,Y4: A] :
% 2.83/1.55 ( ( ord_less @ A @ X4 @ Y4 )
% 2.83/1.55 => ( ord_less @ C @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.83/1.55 => ( ord_less @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_231_order__less__subst1,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType] :
% 2.83/1.55 ( ( ( order @ B @ ( type2 @ B ) )
% 2.83/1.55 & ( order @ A @ ( type2 @ A ) ) )
% 2.83/1.55 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ ( F @ B4 ) )
% 2.83/1.55 => ( ( ord_less @ B @ B4 @ C2 )
% 2.83/1.55 => ( ! [X4: B,Y4: B] :
% 2.83/1.55 ( ( ord_less @ B @ X4 @ Y4 )
% 2.83/1.55 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.83/1.55 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_232_ord__less__eq__subst,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType] :
% 2.83/1.55 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.83/1.55 & ( ord @ A @ ( type2 @ A ) ) )
% 2.83/1.55 => ! [A4: A,B4: A,F: A > B,C2: B] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ( ( ( F @ B4 )
% 2.83/1.55 = C2 )
% 2.83/1.55 => ( ! [X4: A,Y4: A] :
% 2.83/1.55 ( ( ord_less @ A @ X4 @ Y4 )
% 2.83/1.55 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.83/1.55 => ( ord_less @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_233_ord__eq__less__subst,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType] :
% 2.83/1.55 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.83/1.55 & ( ord @ A @ ( type2 @ A ) ) )
% 2.83/1.55 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 2.83/1.55 ( ( A4
% 2.83/1.55 = ( F @ B4 ) )
% 2.83/1.55 => ( ( ord_less @ B @ B4 @ C2 )
% 2.83/1.55 => ( ! [X4: B,Y4: B] :
% 2.83/1.55 ( ( ord_less @ B @ X4 @ Y4 )
% 2.83/1.55 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.83/1.55 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_234_Un__left__commute,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 2.83/1.55 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_235_Un__left__absorb,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_236_Un__commute,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) )
% 2.83/1.55 = ( ^ [A3: set @ A,B3: set @ A] : ( sup_sup @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_237_Un__absorb,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 2.83/1.55 = A2 ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_238_Un__assoc,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 2.83/1.55 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 2.83/1.55 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_239_ball__Un,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 2.83/1.55 ( ( ! [X2: A] :
% 2.83/1.55 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 => ( P @ X2 ) ) )
% 2.83/1.55 = ( ! [X2: A] :
% 2.83/1.55 ( ( member @ A @ X2 @ A2 )
% 2.83/1.55 => ( P @ X2 ) )
% 2.83/1.55 & ! [X2: A] :
% 2.83/1.55 ( ( member @ A @ X2 @ B2 )
% 2.83/1.55 => ( P @ X2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_240_bex__Un,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 2.83/1.55 ( ( ? [X2: A] :
% 2.83/1.55 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 & ( P @ X2 ) ) )
% 2.83/1.55 = ( ? [X2: A] :
% 2.83/1.55 ( ( member @ A @ X2 @ A2 )
% 2.83/1.55 & ( P @ X2 ) )
% 2.83/1.55 | ? [X2: A] :
% 2.83/1.55 ( ( member @ A @ X2 @ B2 )
% 2.83/1.55 & ( P @ X2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_241_UnI2,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ B2 )
% 2.83/1.55 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_242_UnI1,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ A2 )
% 2.83/1.55 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_243_UnE,axiom,
% 2.83/1.55 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.83/1.55 => ( ~ ( member @ A @ C2 @ A2 )
% 2.83/1.55 => ( member @ A @ C2 @ B2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_244_diff__strict__mono,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A,D2: A,C2: A] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ( ( ord_less @ A @ D2 @ C2 )
% 2.83/1.55 => ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B4 @ D2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_245_diff__eq__diff__less,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A,C2: A,D2: A] :
% 2.83/1.55 ( ( ( minus_minus @ A @ A4 @ B4 )
% 2.83/1.55 = ( minus_minus @ A @ C2 @ D2 ) )
% 2.83/1.55 => ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 = ( ord_less @ A @ C2 @ D2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_246_diff__strict__left__mono,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [B4: A,A4: A,C2: A] :
% 2.83/1.55 ( ( ord_less @ A @ B4 @ A4 )
% 2.83/1.55 => ( ord_less @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_247_LList2__Mirabelle__hamjzmohle_Ollength__mono,axiom,
% 2.83/1.55 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.83/1.55 => ( ( ord_less @ ( coinductive_llist @ A ) @ S @ R )
% 2.83/1.55 => ( ord_less @ nat @ ( lList21232602520length @ A @ S ) @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_248_psubset__imp__ex__mem,axiom,
% 2.83/1.55 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.83/1.55 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 2.83/1.55 => ? [B6: A] : ( member @ A @ B6 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_249_diff__right__commute,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,C2: A,B4: A] :
% 2.83/1.55 ( ( minus_minus @ A @ ( minus_minus @ A @ A4 @ C2 ) @ B4 )
% 2.83/1.55 = ( minus_minus @ A @ ( minus_minus @ A @ A4 @ B4 ) @ C2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_250_diff__eq__diff__eq,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( group_add @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A,C2: A,D2: A] :
% 2.83/1.55 ( ( ( minus_minus @ A @ A4 @ B4 )
% 2.83/1.55 = ( minus_minus @ A @ C2 @ D2 ) )
% 2.83/1.55 => ( ( A4 = B4 )
% 2.83/1.55 = ( C2 = D2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_251_lapp__take__less,axiom,
% 2.83/1.55 ! [A: $tType,I: nat,R: coinductive_llist @ A,S: coinductive_llist @ A] :
% 2.83/1.55 ( ( ord_less @ nat @ I @ ( lList21232602520length @ A @ R ) )
% 2.83/1.55 => ( ord_less @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S ) @ I ) @ R ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_252_diff__strict__right__mono,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [A4: A,B4: A,C2: A] :
% 2.83/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 2.83/1.55 => ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B4 @ C2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_253_llast__lappend__LCons,axiom,
% 2.83/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Y2: A,Ys: coinductive_llist @ A] :
% 2.83/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.83/1.55 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y2 @ Ys ) ) )
% 2.83/1.55 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y2 @ Ys ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_254_pprefix__closed__def,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( lList21974196564closed @ A )
% 2.83/1.55 = ( ^ [A3: set @ ( coinductive_llist @ A )] :
% 2.83/1.55 ! [X2: coinductive_llist @ A] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ A ) @ X2 @ A3 )
% 2.83/1.55 => ! [S3: coinductive_llist @ A] :
% 2.83/1.55 ( ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S3 @ X2 )
% 2.83/1.55 & ( S3
% 2.83/1.55 != ( coinductive_LNil @ A ) ) )
% 2.83/1.55 => ( member @ ( coinductive_llist @ A ) @ S3 @ A3 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_255_order__refl,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A @ ( type2 @ A ) )
% 2.83/1.55 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.83/1.55 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.83/1.55 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( order @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Orderings_Otop,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( top @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Orderings_Oord,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Groups_Ominus,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( minus @ A9 @ ( type2 @ A9 ) )
% 2.83/1.55 => ( minus @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 2.83/1.55 cancel146912293up_add @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 2.83/1.55 semilattice_sup @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.83/1.55 wellorder @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Orderings_Opreorder_4,axiom,
% 2.83/1.55 preorder @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.83/1.55 linorder @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 2.83/1.55 no_top @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Lattices_Olattice_5,axiom,
% 2.83/1.55 lattice @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Orderings_Oorder_6,axiom,
% 2.83/1.55 order @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Orderings_Oord_7,axiom,
% 2.83/1.55 ord @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Nat_Onat___Groups_Ominus_8,axiom,
% 2.83/1.55 minus @ nat @ ( type2 @ nat ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_9,axiom,
% 2.83/1.55 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10,axiom,
% 2.83/1.55 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Orderings_Oorder__top_11,axiom,
% 2.83/1.55 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Orderings_Opreorder_12,axiom,
% 2.83/1.55 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Lattices_Olattice_13,axiom,
% 2.83/1.55 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Orderings_Oorder_14,axiom,
% 2.83/1.55 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Orderings_Otop_15,axiom,
% 2.83/1.55 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Orderings_Oord_16,axiom,
% 2.83/1.55 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Groups_Ominus_17,axiom,
% 2.83/1.55 ! [A8: $tType] : ( minus @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_18,axiom,
% 2.83/1.55 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_19,axiom,
% 2.83/1.55 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Oorder__top_20,axiom,
% 2.83/1.55 order_top @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Opreorder_21,axiom,
% 2.83/1.55 preorder @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Olinorder_22,axiom,
% 2.83/1.55 linorder @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Lattices_Olattice_23,axiom,
% 2.83/1.55 lattice @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_24,axiom,
% 2.83/1.55 order @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Otop_25,axiom,
% 2.83/1.55 top @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Oord_26,axiom,
% 2.83/1.55 ord @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Groups_Ominus_27,axiom,
% 2.83/1.55 minus @ $o @ ( type2 @ $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_28,axiom,
% 2.83/1.55 ! [A8: $tType] : ( preorder @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_29,axiom,
% 2.83/1.55 ! [A8: $tType] : ( order @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_30,axiom,
% 2.83/1.55 ! [A8: $tType] : ( ord @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(conj_0,hypothesis,
% 2.83/1.55 lList21952340509veness @ a @ a2 @ p ).
% 2.83/1.55
% 2.83/1.55 thf(conj_1,hypothesis,
% 2.83/1.55 ! [T3: coinductive_llist @ a] :
% 2.83/1.55 ( ( member @ ( coinductive_llist @ a ) @ T3 @ ( lList2435255213lllsts @ a @ a2 ) )
% 2.83/1.55 => ( ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ s @ T3 ) @ p )
% 2.83/1.55 => r ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(conj_2,hypothesis,
% 2.83/1.55 ( ~ ( member @ ( coinductive_llist @ a ) @ s @ ( lList22096119349pslsts @ a @ a2 ) )
% 2.83/1.55 => r ) ).
% 2.83/1.55
% 2.83/1.55 thf(conj_3,conjecture,
% 2.83/1.55 r ).
% 2.83/1.55 ------------------------
% 2.83/1.58 % (760)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_418 for (2999ds/2Mi)
% 2.83/1.58 % (759)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_418 for (2999ds/27Mi)
% 2.83/1.59 % (762)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_418 for (2999ds/275Mi)
% 2.83/1.59 % (760)Instruction limit reached!
% 2.83/1.59 % (760)------------------------------
% 2.83/1.59 % (760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (760)Termination reason: Unknown
% 2.83/1.59 % (760)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (760)Memory used [KB]: 1407
% 2.83/1.59 % (760)Time elapsed: 0.002 s
% 2.83/1.59 % (760)Instructions burned: 3 (million)
% 2.83/1.59 % (760)------------------------------
% 2.83/1.59 % (760)------------------------------
% 2.83/1.59 % (757)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_418 for (2999ds/183Mi)
% 2.83/1.59 % (758)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_418 for (2999ds/4Mi)
% 2.83/1.59 % (761)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_418 for (2999ds/2Mi)
% 2.83/1.59 % (763)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_418 for (2999ds/18Mi)
% 2.83/1.59 % (761)Instruction limit reached!
% 2.83/1.59 % (761)------------------------------
% 2.83/1.59 % (761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (761)Termination reason: Unknown
% 2.83/1.59 % (761)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (761)Memory used [KB]: 1407
% 2.83/1.59 % (761)Time elapsed: 0.003 s
% 2.83/1.59 % (761)Instructions burned: 3 (million)
% 2.83/1.59 % (761)------------------------------
% 2.83/1.59 % (761)------------------------------
% 2.83/1.59 % (758)Instruction limit reached!
% 2.83/1.59 % (758)------------------------------
% 2.83/1.59 % (758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (758)Termination reason: Unknown
% 2.83/1.59 % (758)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (758)Memory used [KB]: 1407
% 2.83/1.59 % (758)Time elapsed: 0.004 s
% 2.83/1.59 % (758)Instructions burned: 4 (million)
% 2.83/1.59 % (758)------------------------------
% 2.83/1.59 % (758)------------------------------
% 2.83/1.59 % (759)Instruction limit reached!
% 2.83/1.59 % (759)------------------------------
% 2.83/1.59 % (759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (759)Termination reason: Unknown
% 2.83/1.59 % (759)Termination phase: Property scanning
% 2.83/1.59
% 2.83/1.59 % (759)Memory used [KB]: 1918
% 2.83/1.59 % (759)Time elapsed: 0.011 s
% 2.83/1.59 % (759)Instructions burned: 29 (million)
% 2.83/1.59 % (759)------------------------------
% 2.83/1.59 % (759)------------------------------
% 2.83/1.60 % (764)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_418 for (2999ds/3Mi)
% 2.89/1.60 % (764)Instruction limit reached!
% 2.89/1.60 % (764)------------------------------
% 2.89/1.60 % (764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.60 % (764)Termination reason: Unknown
% 2.89/1.60 % (764)Termination phase: shuffling
% 2.89/1.60
% 2.89/1.60 % (764)Memory used [KB]: 1407
% 2.89/1.60 % (764)Time elapsed: 0.003 s
% 2.89/1.60 % (764)Instructions burned: 5 (million)
% 2.89/1.60 % (764)------------------------------
% 2.89/1.60 % (764)------------------------------
% 2.89/1.60 % (767)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_418 for (2999ds/3Mi)
% 2.89/1.61 % (763)Instruction limit reached!
% 2.89/1.61 % (763)------------------------------
% 2.89/1.61 % (763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.61 % (763)Termination reason: Unknown
% 2.89/1.61 % (763)Termination phase: shuffling
% 2.89/1.61
% 2.89/1.61 % (763)Memory used [KB]: 1663
% 2.89/1.61 % (763)Time elapsed: 0.015 s
% 2.89/1.61 % (763)Instructions burned: 19 (million)
% 2.89/1.61 % (763)------------------------------
% 2.89/1.61 % (763)------------------------------
% 2.89/1.61 % (767)Instruction limit reached!
% 2.89/1.61 % (767)------------------------------
% 2.89/1.61 % (767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.61 % (767)Termination reason: Unknown
% 2.89/1.61 % (767)Termination phase: shuffling
% 2.89/1.61
% 2.89/1.61 % (767)Memory used [KB]: 1407
% 2.89/1.61 % (767)Time elapsed: 0.003 s
% 2.89/1.61 % (767)Instructions burned: 5 (million)
% 2.89/1.61 % (767)------------------------------
% 2.89/1.61 % (767)------------------------------
% 2.89/1.61 % (769)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_418 for (2999ds/1041Mi)
% 2.89/1.61 % (765)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_418 for (2999ds/37Mi)
% 2.89/1.61 % (766)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_418 for (2999ds/15Mi)
% 2.89/1.61 % (762)First to succeed.
% 2.89/1.62 % (771)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_418 for (2999ds/16Mi)
% 2.89/1.62 % (762)Refutation found. Thanks to Tanya!
% 2.89/1.62 % SZS status Theorem for DTF2THF_418
% 2.89/1.62 % SZS output start Proof for DTF2THF_418
% 2.89/1.62 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.89/1.62 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 2.89/1.62 thf(type_def_8, type, set: ($tType) > $tType).
% 2.89/1.62 thf(type_def_9, type, nat: $tType).
% 2.89/1.62 thf(type_def_10, type, a: $tType).
% 2.89/1.62 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 2.89/1.62 thf(func_def_1, type, set: ($tType) > $tType).
% 2.89/1.62 thf(func_def_2, type, nat: $tType).
% 2.89/1.62 thf(func_def_3, type, itself: ($tType) > $tType).
% 2.89/1.62 thf(func_def_4, type, a: $tType).
% 2.89/1.62 thf(func_def_5, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_7, type, minus: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_8, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_9, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_10, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_11, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_12, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_13, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_14, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_15, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_16, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_17, type, order_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_18, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_19, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_20, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_21, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_22, type, bounded_lattice_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_23, type, cancel146912293up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.62 thf(func_def_24, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_25, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_26, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_27, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_28, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_29, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_30, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_31, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.89/1.62 thf(func_def_32, type, lList2435255213lllsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_33, type, lList2236698231inlsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_34, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0)).
% 2.89/1.62 thf(func_def_35, type, lList21202317876inpref: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_36, type, lList22096119349pslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_37, type, lList21015763786veness: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_38, type, lList21612149805nflsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_39, type, lList21015939545safety: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_40, type, lList2649413865nfsuff: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_41, type, lList2370560421utlast: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_42, type, lList2508575361_ldrop: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_43, type, lList21805353693veness: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_44, type, lList2170638824_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_45, type, lList21232602520length: !>[X0: $tType]:(coinductive_llist @ X0 > nat)).
% 2.89/1.62 thf(func_def_46, type, lList2281150353e_lrev: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_47, type, lList22119844313_ltake: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_48, type, lList2467029176inpref: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_49, type, lList21952340509veness: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_50, type, lList21148268032oslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_51, type, lList292406316safety: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_52, type, lList21974196564closed: !>[X0: $tType]:(set @ coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_53, type, lList21638733016closed: !>[X0: $tType]:(set @ coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_54, type, lList21350011628safety: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0 > $o)).
% 2.89/1.62 thf(func_def_55, type, lList21475143548e_suff: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_56, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.89/1.62 thf(func_def_57, type, suc: nat > nat).
% 2.89/1.62 thf(func_def_58, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.89/1.62 thf(func_def_59, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.89/1.62 thf(func_def_60, type, top_top: !>[X0: $tType]:(X0)).
% 2.89/1.62 thf(func_def_61, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.89/1.62 thf(func_def_62, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.89/1.62 thf(func_def_63, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.89/1.62 thf(func_def_64, type, a2: set @ a).
% 2.89/1.62 thf(func_def_65, type, p: set @ coinductive_llist @ a).
% 2.89/1.62 thf(func_def_67, type, s: coinductive_llist @ a).
% 2.89/1.62 thf(func_def_83, type, sK0: !>[X0: $tType]:(set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_84, type, sK1: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.89/1.62 thf(func_def_85, type, sK2: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_86, type, sK3: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.89/1.62 thf(func_def_87, type, sK4: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_88, type, sK5: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_89, type, sK6: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_90, type, sK7: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_91, type, sK8: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_92, type, sK9: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_93, type, sK10: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.89/1.62 thf(func_def_94, type, sK11: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_95, type, sK12: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.89/1.62 thf(func_def_96, type, sK13: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_97, type, sK14: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_98, type, sK15: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_99, type, sK16: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_100, type, sK17: !>[X0: $tType]:(set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_101, type, sK18: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_102, type, sK19: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_103, type, sK20: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_104, type, sK21: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.89/1.62 thf(func_def_105, type, sK22: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_106, type, sK23: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_107, type, sK24: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_108, type, sK25: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_109, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.89/1.62 thf(func_def_110, type, sK27: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.89/1.62 thf(func_def_111, type, sK28: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.89/1.62 thf(func_def_113, type, ph30: !>[X0: $tType]:(X0)).
% 2.89/1.62 thf(func_def_114, type, sK31: coinductive_llist @ a > coinductive_llist @ a).
% 2.89/1.62 thf(f1124,plain,(
% 2.89/1.62 $false),
% 2.89/1.62 inference(trivial_inequality_removal,[status(thm)],[f1121])).
% 2.89/1.62 thf(f1121,plain,(
% 2.89/1.62 ($false = $true)),
% 2.89/1.62 inference(superposition,[status(thm)],[f1100,f1118])).
% 2.89/1.62 thf(f1118,plain,(
% 2.89/1.62 ((member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) = $false)),
% 2.89/1.62 inference(subsumption_resolution,[status(thm)],[f1108,f1098])).
% 2.89/1.62 thf(f1098,plain,(
% 2.89/1.62 ( ! [X1 : coinductive_llist @ a] : (($true = (member @ coinductive_llist @ a @ (sK31 @ X1) @ (lList2435255213lllsts @ a @ a2))) | ($false = (member @ coinductive_llist @ a @ X1 @ (lList22096119349pslsts @ a @ a2)))) )),
% 2.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f1096])).
% 2.89/1.62 thf(f1096,plain,(
% 2.89/1.62 ( ! [X1 : coinductive_llist @ a] : ((((member @ coinductive_llist @ a @ (sK31 @ X1) @ (lList2435255213lllsts @ a @ a2)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ X1 @ (sK31 @ X1)) @ p)) = $true) | ($false = (member @ coinductive_llist @ a @ X1 @ (lList22096119349pslsts @ a @ a2)))) )),
% 2.89/1.62 inference(beta_eta_normalization,[status(thm)],[f1095])).
% 2.89/1.62 thf(f1095,plain,(
% 2.89/1.62 ( ! [X1 : coinductive_llist @ a] : (($true = ((^[Y0 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y0 @ (lList2435255213lllsts @ a @ a2)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ X1 @ Y0) @ p))) @ (sK31 @ X1))) | ($false = (member @ coinductive_llist @ a @ X1 @ (lList22096119349pslsts @ a @ a2)))) )),
% 2.89/1.62 inference(sigma_clausification,[status(thm)],[f1094])).
% 2.89/1.62 thf(f1094,plain,(
% 2.89/1.62 ( ! [X1 : coinductive_llist @ a] : (($true = (?? @ coinductive_llist @ a @ (^[Y0 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y0 @ (lList2435255213lllsts @ a @ a2)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ X1 @ Y0) @ p))))) | ($false = (member @ coinductive_llist @ a @ X1 @ (lList22096119349pslsts @ a @ a2)))) )),
% 2.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f1093])).
% 2.89/1.62 thf(f1093,plain,(
% 2.89/1.62 ( ! [X1 : coinductive_llist @ a] : (($true = ((member @ coinductive_llist @ a @ X1 @ (lList22096119349pslsts @ a @ a2)) => (?? @ coinductive_llist @ a @ (^[Y0 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y0 @ (lList2435255213lllsts @ a @ a2)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ X1 @ Y0) @ p))))))) )),
% 2.89/1.62 inference(beta_eta_normalization,[status(thm)],[f1092])).
% 2.89/1.62 thf(f1092,plain,(
% 2.89/1.62 ( ! [X1 : coinductive_llist @ a] : ((((^[Y0 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y0 @ (lList22096119349pslsts @ a @ a2)) => (?? @ coinductive_llist @ a @ (^[Y1 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y1 @ (lList2435255213lllsts @ a @ a2)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ Y0 @ Y1) @ p)))))) @ X1) = $true)) )),
% 2.89/1.62 inference(pi_clausification,[status(thm)],[f1091])).
% 2.89/1.62 thf(f1091,plain,(
% 2.89/1.62 ($true = (!! @ coinductive_llist @ a @ (^[Y0 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y0 @ (lList22096119349pslsts @ a @ a2)) => (?? @ coinductive_llist @ a @ (^[Y1 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y1 @ (lList2435255213lllsts @ a @ a2)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ Y0 @ Y1) @ p))))))))),
% 2.89/1.62 inference(beta_eta_normalization,[status(thm)],[f1070])).
% 2.89/1.62 thf(f1070,plain,(
% 2.89/1.62 ($true = ((^[Y0 : set @ a]: ((^[Y1 : set @ coinductive_llist @ a]: (!! @ coinductive_llist @ a @ (^[Y2 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y2 @ (lList22096119349pslsts @ a @ Y0)) => (?? @ coinductive_llist @ a @ (^[Y3 : coinductive_llist @ a]: ((member @ coinductive_llist @ a @ Y3 @ (lList2435255213lllsts @ a @ Y0)) & (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ Y2 @ Y3) @ Y1)))))))))) @ a2 @ p))),
% 2.89/1.62 inference(definition_unfolding,[status(thm)],[f967,f968])).
% 2.89/1.62 thf(f968,plain,(
% 2.89/1.62 ( ! [X0 : $tType] : ((lList21952340509veness @ X0 = (^[Y0 : set @ X0]: ((^[Y1 : set @ coinductive_llist @ X0]: (!! @ coinductive_llist @ X0 @ (^[Y2 : coinductive_llist @ X0]: ((member @ coinductive_llist @ X0 @ Y2 @ (lList22096119349pslsts @ X0 @ Y0)) => (?? @ coinductive_llist @ X0 @ (^[Y3 : coinductive_llist @ X0]: ((member @ coinductive_llist @ X0 @ Y3 @ (lList2435255213lllsts @ X0 @ Y0)) & (member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ Y2 @ Y3) @ Y1)))))))))))) )),
% 2.89/1.62 inference(cnf_transformation,[status(thm)],[f524])).
% 2.89/1.62 thf(f524,plain,(
% 2.89/1.62 ! [X0 : $tType] : (lList21952340509veness @ X0 = (^[Y0 : set @ X0]: ((^[Y1 : set @ coinductive_llist @ X0]: (!! @ coinductive_llist @ X0 @ (^[Y2 : coinductive_llist @ X0]: ((member @ coinductive_llist @ X0 @ Y2 @ (lList22096119349pslsts @ X0 @ Y0)) => (?? @ coinductive_llist @ X0 @ (^[Y3 : coinductive_llist @ X0]: ((member @ coinductive_llist @ X0 @ Y3 @ (lList2435255213lllsts @ X0 @ Y0)) & (member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ Y2 @ Y3) @ Y1)))))))))))),
% 2.89/1.62 inference(fool_elimination,[status(thm)],[f523])).
% 2.89/1.62 thf(f523,plain,(
% 2.89/1.62 ! [X0 : $tType] : (lList21952340509veness @ X0 = (^[X1 : set @ X0, X2 : set @ coinductive_llist @ X0] : (! [X3 : coinductive_llist @ X0] : ((member @ coinductive_llist @ X0 @ X3 @ (lList22096119349pslsts @ X0 @ X1)) => ? [X4 : coinductive_llist @ X0] : ((member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X3 @ X4) @ X2) & (member @ coinductive_llist @ X0 @ X4 @ (lList2435255213lllsts @ X0 @ X1)))))))),
% 2.89/1.62 inference(rectify,[status(thm)],[f4])).
% 2.89/1.62 thf(f4,axiom,(
% 2.89/1.62 ! [X0 : $tType] : (lList21952340509veness @ X0 = (^[X9 : set @ X0, X10 : set @ coinductive_llist @ X0] : (! [X11 : coinductive_llist @ X0] : ((member @ coinductive_llist @ X0 @ X11 @ (lList22096119349pslsts @ X0 @ X9)) => ? [X12 : coinductive_llist @ X0] : ((member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X11 @ X12) @ X10) & (member @ coinductive_llist @ X0 @ X12 @ (lList2435255213lllsts @ X0 @ X9)))))))),
% 2.89/1.62 file('/export/starexec/sandbox/tmp/tmp.iIZaSoWsFt/DTF2THF_418.p',fact_3_posliveness__def)).
% 2.89/1.62 thf(f967,plain,(
% 2.89/1.62 ((lList21952340509veness @ a @ a2 @ p) = $true)),
% 2.89/1.62 inference(cnf_transformation,[status(thm)],[f656])).
% 2.89/1.62 thf(f656,plain,(
% 2.89/1.62 ((lList21952340509veness @ a @ a2 @ p) = $true)),
% 2.89/1.62 inference(fool_elimination,[status(thm)],[f655])).
% 2.89/1.62 thf(f655,plain,(
% 2.89/1.62 (lList21952340509veness @ a @ a2 @ p)),
% 2.89/1.62 inference(rectify,[status(thm)],[f301])).
% 2.89/1.62 thf(f301,axiom,(
% 2.89/1.62 (lList21952340509veness @ a @ a2 @ p)),
% 2.89/1.62 file('/export/starexec/sandbox/tmp/tmp.iIZaSoWsFt/DTF2THF_418.p',conj_0)).
% 2.89/1.62 thf(f1108,plain,(
% 2.89/1.62 ($true != (member @ coinductive_llist @ a @ (sK31 @ s) @ (lList2435255213lllsts @ a @ a2))) | ((member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) = $false)),
% 2.89/1.62 inference(trivial_inequality_removal,[status(thm)],[f1107])).
% 2.89/1.62 thf(f1107,plain,(
% 2.89/1.62 ($true != $true) | ($true != (member @ coinductive_llist @ a @ (sK31 @ s) @ (lList2435255213lllsts @ a @ a2))) | ((member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) = $false)),
% 2.89/1.62 inference(superposition,[status(thm)],[f1099,f1097])).
% 2.89/1.62 thf(f1097,plain,(
% 2.89/1.62 ( ! [X1 : coinductive_llist @ a] : (($true = (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ X1 @ (sK31 @ X1)) @ p)) | ($false = (member @ coinductive_llist @ a @ X1 @ (lList22096119349pslsts @ a @ a2)))) )),
% 2.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f1096])).
% 2.89/1.62 thf(f1099,plain,(
% 2.89/1.62 ( ! [X0 : coinductive_llist @ a] : (($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ s @ X0) @ p)) | ($true != (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ a2)))) )),
% 2.89/1.62 inference(subsumption_resolution,[status(thm)],[f1042,f991])).
% 2.89/1.62 thf(f991,plain,(
% 2.89/1.62 (r != $true)),
% 2.89/1.62 inference(cnf_transformation,[status(thm)],[f837])).
% 2.89/1.62 thf(f837,plain,(
% 2.89/1.62 (r != $true)),
% 2.89/1.62 inference(flattening,[status(thm)],[f422])).
% 2.89/1.62 thf(f422,plain,(
% 2.89/1.62 ~(r = $true)),
% 2.89/1.62 inference(fool_elimination,[status(thm)],[f421])).
% 2.89/1.62 thf(f421,plain,(
% 2.89/1.62 ~r),
% 2.89/1.62 inference(rectify,[status(thm)],[f305])).
% 2.89/1.62 thf(f305,negated_conjecture,(
% 2.89/1.62 ~r),
% 2.89/1.62 inference(negated_conjecture,[status(cth)],[f304])).
% 2.89/1.62 thf(f304,conjecture,(
% 2.89/1.62 r),
% 2.89/1.62 file('/export/starexec/sandbox/tmp/tmp.iIZaSoWsFt/DTF2THF_418.p',conj_3)).
% 2.89/1.62 thf(f1042,plain,(
% 2.89/1.62 ( ! [X0 : coinductive_llist @ a] : ((r = $true) | ($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ s @ X0) @ p)) | ($true != (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ a2)))) )),
% 2.89/1.62 inference(cnf_transformation,[status(thm)],[f859])).
% 2.89/1.62 thf(f859,plain,(
% 2.89/1.62 ! [X0 : coinductive_llist @ a] : (($true != (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ a2))) | (r = $true) | ($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ s @ X0) @ p)))),
% 2.89/1.62 inference(flattening,[status(thm)],[f858])).
% 2.89/1.62 thf(f858,plain,(
% 2.89/1.62 ! [X0 : coinductive_llist @ a] : (((r = $true) | ($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ s @ X0) @ p))) | ($true != (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ a2))))),
% 2.89/1.62 inference(ennf_transformation,[status(thm)],[f610])).
% 2.89/1.62 thf(f610,plain,(
% 2.89/1.62 ! [X0 : coinductive_llist @ a] : (($true = (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ a2))) => (($true = (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ s @ X0) @ p)) => (r = $true)))),
% 2.89/1.62 inference(fool_elimination,[status(thm)],[f609])).
% 2.89/1.62 thf(f609,plain,(
% 2.89/1.62 ! [X0 : coinductive_llist @ a] : ((member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ a2)) => ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ s @ X0) @ p) => r))),
% 2.89/1.62 inference(rectify,[status(thm)],[f302])).
% 2.89/1.62 thf(f302,axiom,(
% 2.89/1.62 ! [X68 : coinductive_llist @ a] : ((member @ coinductive_llist @ a @ X68 @ (lList2435255213lllsts @ a @ a2)) => ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ s @ X68) @ p) => r))),
% 2.89/1.62 file('/export/starexec/sandbox/tmp/tmp.iIZaSoWsFt/DTF2THF_418.p',conj_1)).
% 2.89/1.62 thf(f1100,plain,(
% 2.89/1.62 ((member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) = $true)),
% 2.89/1.62 inference(subsumption_resolution,[status(thm)],[f1045,f991])).
% 2.89/1.62 thf(f1045,plain,(
% 2.89/1.62 ((member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) = $true) | (r = $true)),
% 2.89/1.62 inference(cnf_transformation,[status(thm)],[f879])).
% 2.89/1.62 thf(f879,plain,(
% 2.89/1.62 (r = $true) | ((member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) = $true)),
% 2.89/1.62 inference(ennf_transformation,[status(thm)],[f838])).
% 2.89/1.62 thf(f838,plain,(
% 2.89/1.62 ((member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) != $true) => (r = $true)),
% 2.89/1.62 inference(flattening,[status(thm)],[f742])).
% 2.89/1.62 thf(f742,plain,(
% 2.89/1.62 ~((member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) = $true) => (r = $true)),
% 2.89/1.62 inference(fool_elimination,[status(thm)],[f741])).
% 2.89/1.62 thf(f741,plain,(
% 2.89/1.62 ~(member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) => r),
% 2.89/1.62 inference(rectify,[status(thm)],[f303])).
% 2.89/1.62 thf(f303,axiom,(
% 2.89/1.62 ~(member @ coinductive_llist @ a @ s @ (lList22096119349pslsts @ a @ a2)) => r),
% 2.89/1.62 file('/export/starexec/sandbox/tmp/tmp.iIZaSoWsFt/DTF2THF_418.p',conj_2)).
% 2.89/1.62 % SZS output end Proof for DTF2THF_418
% 2.89/1.62 % (762)------------------------------
% 2.89/1.62 % (762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.62 % (762)Termination reason: Refutation
% 2.89/1.62
% 2.89/1.62 % (762)Memory used [KB]: 6780
% 2.89/1.62 % (762)Time elapsed: 0.031 s
% 2.89/1.62 % (762)Instructions burned: 85 (million)
% 2.89/1.62 % (762)------------------------------
% 2.89/1.62 % (762)------------------------------
% 2.89/1.62 % (756)Success in time 0.06 s
%------------------------------------------------------------------------------