%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT183^1 : 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 : n016.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 08:45:03 AM UTC 2026
% Result : Theorem 2.87s 1.90s
% Output : Refutation 2.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : DAT183^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n016.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 06:10:51 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : DAT183^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.38 % Domain : Data Structures
% 0.17/0.38 % Problem : Lazy lists II 951
% 0.17/0.38 % Version : [Bla16] axioms : Especial.
% 0.17/0.38 % English :
% 0.17/0.38
% 0.17/0.38 % Refs : [Fri04] Friedrich (2004), Lazy Lists II
% 0.17/0.38 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.17/0.38 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.17/0.38 % Source : [Bla16]
% 0.17/0.38 % Names : llist2__951.p [Bla16]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.17/0.38 % Syntax : Number of formulae : 340 ( 120 unt; 54 typ; 0 def)
% 0.17/0.38 % Number of atoms : 745 ( 236 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 7 ( 2 avg)
% 0.17/0.38 % Number of connectives : 3958 ( 103 ~; 29 |; 51 &;3421 @)
% 0.17/0.38 % ( 0 <=>; 354 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 19 ( 8 avg)
% 0.17/0.38 % Number of types : 3 ( 2 usr)
% 0.17/0.38 % Number of type conns : 153 ( 153 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 53 ( 52 usr; 1 con; 0-5 aty)
% 0.17/0.38 % Number of variables : 998 ( 12 ^; 885 !; 53 ?; 998 :)
% 0.17/0.38 % ( 48 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.38 % SPC : TH1_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.17/0.38 % 2016-07-13 14:50:30.967
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 %----Could-be-implicit typings (5)
% 0.17/0.38 thf(ty_t_Coinductive__List_Ollist,type,
% 0.17/0.38 coinductive_llist: $tType > $tType ).
% 0.17/0.38
% 0.17/0.38 thf(ty_t_Set_Oset,type,
% 0.17/0.38 set: $tType > $tType ).
% 0.17/0.38
% 0.17/0.38 thf(ty_t_Nat_Onat,type,
% 0.17/0.38 nat: $tType ).
% 0.17/0.38
% 0.17/0.38 thf(ty_t_itself,type,
% 0.17/0.38 itself: $tType > $tType ).
% 0.17/0.38
% 0.17/0.38 thf(ty_tf_a,type,
% 0.17/0.38 a: $tType ).
% 0.17/0.38
% 0.17/0.38 %----Explicit typings (49)
% 0.17/0.38 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.17/0.38 bounded_lattice:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_HOL_Otype,type,
% 0.17/0.38 type:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Oord,type,
% 0.17/0.38 ord:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Otop,type,
% 0.17/0.38 top:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Oorder,type,
% 0.17/0.38 order:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Ono__bot,type,
% 0.17/0.38 no_bot:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Ono__top,type,
% 0.17/0.38 no_top:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Olinorder,type,
% 0.17/0.38 linorder:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Opreorder,type,
% 0.17/0.38 preorder:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Oorder__top,type,
% 0.17/0.38 order_top:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Owellorder,type,
% 0.17/0.38 wellorder:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Orderings_Odense__order,type,
% 0.17/0.38 dense_order:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.17/0.38 linordered_idom:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Fields_Olinordered__field,type,
% 0.17/0.38 linordered_field:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.17/0.38 bounded_lattice_top:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.17/0.38 condit1656338222tinuum:
% 0.17/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.17/0.38 coindu328551480prefix:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Olappend,type,
% 0.17/0.38 coinductive_lappend:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.17/0.38 coinductive_lfinite:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Ollast,type,
% 0.17/0.38 coinductive_llast:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.17/0.38 coinductive_LCons:
% 0.17/0.38 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.17/0.38 coinductive_LNil:
% 0.17/0.38 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 0.17/0.38 coinductive_lnull:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Olmember,type,
% 0.17/0.38 coinductive_lmember:
% 0.17/0.38 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.17/0.38 coindu1478340336prefix:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.17/0.38 minus_minus:
% 0.17/0.38 !>[A: $tType] : ( A > A > A ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_HOL_Oundefined,type,
% 0.17/0.38 undefined:
% 0.17/0.38 !>[A: $tType] : A ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 0.17/0.38 lList2435255213lllsts:
% 0.17/0.38 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp,type,
% 0.17/0.38 lList21511617539llstsp:
% 0.17/0.38 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.17/0.38 lList2236698231inlsts:
% 0.17/0.38 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.17/0.38 lList21916056377ts_rec:
% 0.17/0.38 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp,type,
% 0.17/0.38 lList2860480441nlstsp:
% 0.17/0.38 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.17/0.38 lList22096119349pslsts:
% 0.17/0.38 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 0.17/0.38 lList21612149805nflsts:
% 0.17/0.38 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 0.17/0.38 lList2370560421utlast:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 0.17/0.38 lList2508575361_ldrop:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 0.17/0.38 lList2170638824_llast:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 0.17/0.38 lList21232602520length:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 0.17/0.38 lList2281150353e_lrev:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 0.17/0.38 lList22119844313_ltake:
% 0.17/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.17/0.38 lList21148268032oslsts:
% 0.17/0.38 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.17/0.38 sup_sup:
% 0.17/0.38 !>[A: $tType] : ( A > A > A ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Nat_OSuc,type,
% 0.17/0.38 suc: nat > nat ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.17/0.38 ord_less:
% 0.17/0.38 !>[A: $tType] : ( A > A > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.17/0.38 top_top:
% 0.17/0.38 !>[A: $tType] : A ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Pure_Otype,type,
% 0.17/0.38 type2:
% 0.17/0.38 !>[A: $tType] : ( itself @ A ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_Set_OCollect,type,
% 0.17/0.38 collect:
% 0.17/0.38 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_c_member,type,
% 0.17/0.38 member:
% 0.17/0.38 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.17/0.38
% 0.17/0.38 thf(sy_v_r,type,
% 0.17/0.38 r: coinductive_llist @ a ).
% 0.17/0.38
% 0.17/0.38 %----Relevant facts (254)
% 0.17/0.38 thf(fact_0_lbutlast__LNil,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % lbutlast_LNil
% 0.17/0.38 thf(fact_1_LNil__less__LCons,axiom,
% 0.17/0.38 ! [A: $tType,A2: A,T: coinductive_llist @ A] : ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ A @ A2 @ T ) ) ).
% 0.17/0.38
% 0.17/0.38 % LNil_less_LCons
% 0.17/0.38 thf(fact_2_minf_I11_J,axiom,
% 0.17/0.38 ! [C: $tType,D: $tType] :
% 0.17/0.38 ( ( ord @ C @ ( type2 @ C ) )
% 0.17/0.38 => ! [F: D] :
% 0.17/0.38 ? [Z: C] :
% 0.17/0.38 ! [X: C] :
% 0.17/0.38 ( ( ord_less @ C @ X @ Z )
% 0.17/0.38 => ( F = F ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % minf(11)
% 0.17/0.38 thf(fact_3_minf_I7_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [T: A] :
% 0.17/0.38 ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ X @ Z )
% 0.17/0.38 => ~ ( ord_less @ A @ T @ X ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % minf(7)
% 0.17/0.38 thf(fact_4_minf_I5_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [T: A] :
% 0.17/0.38 ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ X @ Z )
% 0.17/0.38 => ( ord_less @ A @ X @ T ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % minf(5)
% 0.17/0.38 thf(fact_5_minf_I4_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [T: A] :
% 0.17/0.38 ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ X @ Z )
% 0.17/0.38 => ( X != T ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % minf(4)
% 0.17/0.38 thf(fact_6_minf_I3_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [T: A] :
% 0.17/0.38 ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ X @ Z )
% 0.17/0.38 => ( X != T ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % minf(3)
% 0.17/0.38 thf(fact_7_minf_I2_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.17/0.38 ( ? [Z2: A] :
% 0.17/0.38 ! [X2: A] :
% 0.17/0.38 ( ( ord_less @ A @ X2 @ Z2 )
% 0.17/0.38 => ( ( P @ X2 )
% 0.17/0.38 = ( P2 @ X2 ) ) )
% 0.17/0.38 => ( ? [Z2: A] :
% 0.17/0.38 ! [X2: A] :
% 0.17/0.38 ( ( ord_less @ A @ X2 @ Z2 )
% 0.17/0.38 => ( ( Q @ X2 )
% 0.17/0.38 = ( Q2 @ X2 ) ) )
% 0.17/0.38 => ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ X @ Z )
% 0.17/0.38 => ( ( ( P @ X )
% 0.17/0.38 | ( Q @ X ) )
% 0.17/0.38 = ( ( P2 @ X )
% 0.17/0.38 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % minf(2)
% 0.17/0.38 thf(fact_8_minf_I1_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.17/0.38 ( ? [Z2: A] :
% 0.17/0.38 ! [X2: A] :
% 0.17/0.38 ( ( ord_less @ A @ X2 @ Z2 )
% 0.17/0.38 => ( ( P @ X2 )
% 0.17/0.38 = ( P2 @ X2 ) ) )
% 0.17/0.38 => ( ? [Z2: A] :
% 0.17/0.38 ! [X2: A] :
% 0.17/0.38 ( ( ord_less @ A @ X2 @ Z2 )
% 0.17/0.38 => ( ( Q @ X2 )
% 0.17/0.38 = ( Q2 @ X2 ) ) )
% 0.17/0.38 => ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ X @ Z )
% 0.17/0.38 => ( ( ( P @ X )
% 0.17/0.38 & ( Q @ X ) )
% 0.17/0.38 = ( ( P2 @ X )
% 0.17/0.38 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % minf(1)
% 0.17/0.38 thf(fact_9_pinf_I11_J,axiom,
% 0.17/0.38 ! [C: $tType,D: $tType] :
% 0.17/0.38 ( ( ord @ C @ ( type2 @ C ) )
% 0.17/0.38 => ! [F: D] :
% 0.17/0.38 ? [Z: C] :
% 0.17/0.38 ! [X: C] :
% 0.17/0.38 ( ( ord_less @ C @ Z @ X )
% 0.17/0.38 => ( F = F ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % pinf(11)
% 0.17/0.38 thf(fact_10_pinf_I7_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [T: A] :
% 0.17/0.38 ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z @ X )
% 0.17/0.38 => ( ord_less @ A @ T @ X ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % pinf(7)
% 0.17/0.38 thf(fact_11_pinf_I5_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [T: A] :
% 0.17/0.38 ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z @ X )
% 0.17/0.38 => ~ ( ord_less @ A @ X @ T ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % pinf(5)
% 0.17/0.38 thf(fact_12_llistE,axiom,
% 0.17/0.38 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.17/0.38 ( ( Y
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ~ ! [X21: A,X22: coinductive_llist @ A] :
% 0.17/0.38 ( Y
% 0.17/0.38 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % llistE
% 0.17/0.38 thf(fact_13_pinf_I1_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.17/0.38 ( ? [Z2: A] :
% 0.17/0.38 ! [X2: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z2 @ X2 )
% 0.17/0.38 => ( ( P @ X2 )
% 0.17/0.38 = ( P2 @ X2 ) ) )
% 0.17/0.38 => ( ? [Z2: A] :
% 0.17/0.38 ! [X2: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z2 @ X2 )
% 0.17/0.38 => ( ( Q @ X2 )
% 0.17/0.38 = ( Q2 @ X2 ) ) )
% 0.17/0.38 => ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z @ X )
% 0.17/0.38 => ( ( ( P @ X )
% 0.17/0.38 & ( Q @ X ) )
% 0.17/0.38 = ( ( P2 @ X )
% 0.17/0.38 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % pinf(1)
% 0.17/0.38 thf(fact_14_pinf_I2_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.17/0.38 ( ? [Z2: A] :
% 0.17/0.38 ! [X2: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z2 @ X2 )
% 0.17/0.38 => ( ( P @ X2 )
% 0.17/0.38 = ( P2 @ X2 ) ) )
% 0.17/0.38 => ( ? [Z2: A] :
% 0.17/0.38 ! [X2: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z2 @ X2 )
% 0.17/0.38 => ( ( Q @ X2 )
% 0.17/0.38 = ( Q2 @ X2 ) ) )
% 0.17/0.38 => ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z @ X )
% 0.17/0.38 => ( ( ( P @ X )
% 0.17/0.38 | ( Q @ X ) )
% 0.17/0.38 = ( ( P2 @ X )
% 0.17/0.38 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % pinf(2)
% 0.17/0.38 thf(fact_15_pinf_I3_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [T: A] :
% 0.17/0.38 ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z @ X )
% 0.17/0.38 => ( X != T ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % pinf(3)
% 0.17/0.38 thf(fact_16_pinf_I4_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [T: A] :
% 0.17/0.38 ? [Z: A] :
% 0.17/0.38 ! [X: A] :
% 0.17/0.38 ( ( ord_less @ A @ Z @ X )
% 0.17/0.38 => ( X != T ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % pinf(4)
% 0.17/0.38 thf(fact_17_llist_Oinject,axiom,
% 0.17/0.38 ! [A: $tType,X212: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.17/0.38 ( ( ( coinductive_LCons @ A @ X212 @ X222 )
% 0.17/0.38 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.17/0.38 = ( ( X212 = Y21 )
% 0.17/0.38 & ( X222 = Y22 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist.inject
% 0.17/0.38 thf(fact_18_neq__LNil__conv,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( Xs
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( ? [X3: A,Xs2: coinductive_llist @ A] :
% 0.17/0.38 ( Xs
% 0.17/0.38 = ( coinductive_LCons @ A @ X3 @ Xs2 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % neq_LNil_conv
% 0.17/0.38 thf(fact_19_llist_Odistinct_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_LNil @ A )
% 0.17/0.38 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist.distinct(1)
% 0.17/0.38 thf(fact_20_fps__induct,axiom,
% 0.17/0.38 ! [A: $tType,L: coinductive_llist @ A,A3: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A3 ) )
% 0.17/0.38 => ( ! [A4: A] :
% 0.17/0.38 ( ( member @ A @ A4 @ A3 )
% 0.17/0.38 => ( P @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) )
% 0.17/0.38 => ( ! [A4: A,L2: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList22096119349pslsts @ A @ A3 ) )
% 0.17/0.38 => ( ( P @ L2 )
% 0.17/0.38 => ( ( member @ A @ A4 @ A3 )
% 0.17/0.38 => ( P @ ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) )
% 0.17/0.38 => ( P @ L ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % fps_induct
% 0.17/0.38 thf(fact_21_lbutlast__LCons,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,A2: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( ( R
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A2 @ R ) )
% 0.17/0.38 = ( coinductive_LNil @ A ) ) )
% 0.17/0.38 & ( ( R
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A2 @ R ) )
% 0.17/0.38 = ( coinductive_LCons @ A @ A2 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lbutlast_LCons
% 0.17/0.38 thf(fact_22_alllstsp_Ocoinduct,axiom,
% 0.17/0.38 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X5: coinductive_llist @ A,A3: A > $o] :
% 0.17/0.38 ( ( X4 @ X5 )
% 0.17/0.38 => ( ! [X2: coinductive_llist @ A] :
% 0.17/0.38 ( ( X4 @ X2 )
% 0.17/0.38 => ( ( X2
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 | ? [L3: coinductive_llist @ A,A5: A] :
% 0.17/0.38 ( ( X2
% 0.17/0.38 = ( coinductive_LCons @ A @ A5 @ L3 ) )
% 0.17/0.38 & ( ( X4 @ L3 )
% 0.17/0.38 | ( lList21511617539llstsp @ A @ A3 @ L3 ) )
% 0.17/0.38 & ( A3 @ A5 ) ) ) )
% 0.17/0.38 => ( lList21511617539llstsp @ A @ A3 @ X5 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllstsp.coinduct
% 0.17/0.38 thf(fact_23_finlstsp_Oinducts,axiom,
% 0.17/0.38 ! [A: $tType,A3: A > $o,X5: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.38 ( ( lList2860480441nlstsp @ A @ A3 @ X5 )
% 0.17/0.38 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ! [L2: coinductive_llist @ A,A4: A] :
% 0.17/0.38 ( ( lList2860480441nlstsp @ A @ A3 @ L2 )
% 0.17/0.38 => ( ( P @ L2 )
% 0.17/0.38 => ( ( A3 @ A4 )
% 0.17/0.38 => ( P @ ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) )
% 0.17/0.38 => ( P @ X5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlstsp.inducts
% 0.17/0.38 thf(fact_24_finlstsp_Osimps,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( lList2860480441nlstsp @ A )
% 0.17/0.38 = ( ^ [A6: A > $o,A7: coinductive_llist @ A] :
% 0.17/0.38 ( ( A7
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 | ? [L4: coinductive_llist @ A,B2: A] :
% 0.17/0.38 ( ( A7
% 0.17/0.38 = ( coinductive_LCons @ A @ B2 @ L4 ) )
% 0.17/0.38 & ( lList2860480441nlstsp @ A @ A6 @ L4 )
% 0.17/0.38 & ( A6 @ B2 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlstsp.simps
% 0.17/0.38 thf(fact_25_finlstsp_Ocases,axiom,
% 0.17/0.38 ! [A: $tType,A3: A > $o,A2: coinductive_llist @ A] :
% 0.17/0.38 ( ( lList2860480441nlstsp @ A @ A3 @ A2 )
% 0.17/0.38 => ( ( A2
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ~ ! [L2: coinductive_llist @ A,A4: A] :
% 0.17/0.38 ( ( A2
% 0.17/0.38 = ( coinductive_LCons @ A @ A4 @ L2 ) )
% 0.17/0.38 => ( ( lList2860480441nlstsp @ A @ A3 @ L2 )
% 0.17/0.38 => ~ ( A3 @ A4 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlstsp.cases
% 0.17/0.38 thf(fact_26_alllstsp_Osimps,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( lList21511617539llstsp @ A )
% 0.17/0.38 = ( ^ [A6: A > $o,A7: coinductive_llist @ A] :
% 0.17/0.38 ( ( A7
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 | ? [L4: coinductive_llist @ A,B2: A] :
% 0.17/0.38 ( ( A7
% 0.17/0.38 = ( coinductive_LCons @ A @ B2 @ L4 ) )
% 0.17/0.38 & ( lList21511617539llstsp @ A @ A6 @ L4 )
% 0.17/0.38 & ( A6 @ B2 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllstsp.simps
% 0.17/0.38 thf(fact_27_alllstsp_Ocases,axiom,
% 0.17/0.38 ! [A: $tType,A3: A > $o,A2: coinductive_llist @ A] :
% 0.17/0.38 ( ( lList21511617539llstsp @ A @ A3 @ A2 )
% 0.17/0.38 => ( ( A2
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ~ ! [L2: coinductive_llist @ A,A4: A] :
% 0.17/0.38 ( ( A2
% 0.17/0.38 = ( coinductive_LCons @ A @ A4 @ L2 ) )
% 0.17/0.38 => ( ( lList21511617539llstsp @ A @ A3 @ L2 )
% 0.17/0.38 => ~ ( A3 @ A4 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllstsp.cases
% 0.17/0.38 thf(fact_28_llist__less__finT,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( ord_less @ ( coinductive_llist @ A ) @ R @ S )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist_less_finT
% 0.17/0.38 thf(fact_29_fpslsts__iff,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A3 ) )
% 0.17/0.38 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 & ( S
% 0.17/0.38 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % fpslsts_iff
% 0.17/0.38 thf(fact_30_fpslsts__cases,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A3 ) )
% 0.17/0.38 => ~ ! [A4: A,Rs: coinductive_llist @ A] :
% 0.17/0.38 ( ( R
% 0.17/0.38 = ( coinductive_LCons @ A @ A4 @ Rs ) )
% 0.17/0.38 => ( ( member @ A @ A4 @ A3 )
% 0.17/0.38 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % fpslsts_cases
% 0.17/0.38 thf(fact_31_finlsts_OLCons__fin,axiom,
% 0.17/0.38 ! [A: $tType,L: coinductive_llist @ A,A3: set @ A,A2: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ A @ A2 @ A3 )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A2 @ L ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts.LCons_fin
% 0.17/0.38 thf(fact_32_finlsts_OLNil__fin,axiom,
% 0.17/0.38 ! [A: $tType,A3: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A3 ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts.LNil_fin
% 0.17/0.38 thf(fact_33_finlstsp_OLCons__fin,axiom,
% 0.17/0.38 ! [A: $tType,A3: A > $o,L: coinductive_llist @ A,A2: A] :
% 0.17/0.38 ( ( lList2860480441nlstsp @ A @ A3 @ L )
% 0.17/0.38 => ( ( A3 @ A2 )
% 0.17/0.38 => ( lList2860480441nlstsp @ A @ A3 @ ( coinductive_LCons @ A @ A2 @ L ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlstsp.LCons_fin
% 0.17/0.38 thf(fact_34_alllstsp_OLCons__all,axiom,
% 0.17/0.38 ! [A: $tType,A3: A > $o,L: coinductive_llist @ A,A2: A] :
% 0.17/0.38 ( ( lList21511617539llstsp @ A @ A3 @ L )
% 0.17/0.38 => ( ( A3 @ A2 )
% 0.17/0.38 => ( lList21511617539llstsp @ A @ A3 @ ( coinductive_LCons @ A @ A2 @ L ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllstsp.LCons_all
% 0.17/0.38 thf(fact_35_alllstsp_OLNil__all,axiom,
% 0.17/0.38 ! [A: $tType,A3: A > $o] : ( lList21511617539llstsp @ A @ A3 @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllstsp.LNil_all
% 0.17/0.38 thf(fact_36_finlstsp_OLNil__fin,axiom,
% 0.17/0.38 ! [A: $tType,A3: A > $o] : ( lList2860480441nlstsp @ A @ A3 @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlstsp.LNil_fin
% 0.17/0.38 thf(fact_37_finlsts_Ocases,axiom,
% 0.17/0.38 ! [A: $tType,A2: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ A2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( A2
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ~ ! [L2: coinductive_llist @ A,A4: A] :
% 0.17/0.38 ( ( A2
% 0.17/0.38 = ( coinductive_LCons @ A @ A4 @ L2 ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ~ ( member @ A @ A4 @ A3 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts.cases
% 0.17/0.38 thf(fact_38_finlsts_Osimps,axiom,
% 0.17/0.38 ! [A: $tType,A2: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ A2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 = ( ( A2
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 | ? [L4: coinductive_llist @ A,A7: A] :
% 0.17/0.38 ( ( A2
% 0.17/0.38 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 0.17/0.38 & ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 & ( member @ A @ A7 @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts.simps
% 0.17/0.38 thf(fact_39_finlsts__induct,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ! [L2: coinductive_llist @ A] :
% 0.17/0.38 ( ( L2
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( P @ L2 ) )
% 0.17/0.38 => ( ! [A4: A,L2: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( P @ L2 )
% 0.17/0.38 => ( ( member @ A @ A4 @ A3 )
% 0.17/0.38 => ( P @ ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) )
% 0.17/0.38 => ( P @ X5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts_induct
% 0.17/0.38 thf(fact_40_finlsts_Oinducts,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ! [L2: coinductive_llist @ A,A4: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( P @ L2 )
% 0.17/0.38 => ( ( member @ A @ A4 @ A3 )
% 0.17/0.38 => ( P @ ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) )
% 0.17/0.38 => ( P @ X5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts.inducts
% 0.17/0.38 thf(fact_41_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 0.17/0.38 ! [B: $tType,R: coinductive_llist @ B,A3: set @ B,A2: B] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A3 ) )
% 0.17/0.38 => ( ( ( R
% 0.17/0.38 = ( coinductive_LNil @ B ) )
% 0.17/0.38 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A2 @ R ) )
% 0.17/0.38 = A2 ) )
% 0.17/0.38 & ( ( R
% 0.17/0.38 != ( coinductive_LNil @ B ) )
% 0.17/0.38 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A2 @ R ) )
% 0.17/0.38 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % LList2_Mirabelle_hamjzmohle.llast_LCons
% 0.17/0.38 thf(fact_42_lbutlast__snoc,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,A3: set @ A,X5: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( lList2370560421utlast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X5 @ ( coinductive_LNil @ A ) ) ) )
% 0.17/0.38 = Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % lbutlast_snoc
% 0.17/0.38 thf(fact_43_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.17/0.38 = ( ( Xs
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 | ? [Xs2: coinductive_llist @ A] :
% 0.17/0.38 ( ( Xs
% 0.17/0.38 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 0.17/0.38 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.17/0.38 thf(fact_44_lstrict__prefix__code_I3_J,axiom,
% 0.17/0.38 ! [B: $tType,X5: B,Xs: coinductive_llist @ B] :
% 0.17/0.38 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X5 @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.17/0.38
% 0.17/0.38 % lstrict_prefix_code(3)
% 0.17/0.38 thf(fact_45_mem__Collect__eq,axiom,
% 0.17/0.38 ! [A: $tType,A2: A,P: A > $o] :
% 0.17/0.38 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.17/0.38 = ( P @ A2 ) ) ).
% 0.17/0.38
% 0.17/0.38 % mem_Collect_eq
% 0.17/0.38 thf(fact_46_Collect__mem__eq,axiom,
% 0.17/0.38 ! [A: $tType,A3: set @ A] :
% 0.17/0.38 ( ( collect @ A
% 0.17/0.38 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.17/0.38 = A3 ) ).
% 0.17/0.38
% 0.17/0.38 % Collect_mem_eq
% 0.17/0.38 thf(fact_47_Collect__cong,axiom,
% 0.17/0.38 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.17/0.38 ( ! [X2: A] :
% 0.17/0.38 ( ( P @ X2 )
% 0.17/0.38 = ( Q @ X2 ) )
% 0.17/0.38 => ( ( collect @ A @ P )
% 0.17/0.38 = ( collect @ A @ Q ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % Collect_cong
% 0.17/0.38 thf(fact_48_ext,axiom,
% 0.17/0.38 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 0.17/0.38 ( ! [X2: A] :
% 0.17/0.38 ( ( F2 @ X2 )
% 0.17/0.38 = ( G @ X2 ) )
% 0.17/0.38 => ( F2 = G ) ) ).
% 0.17/0.38
% 0.17/0.38 % ext
% 0.17/0.38 thf(fact_49_lstrict__prefix__code_I2_J,axiom,
% 0.17/0.38 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.17/0.38
% 0.17/0.38 % lstrict_prefix_code(2)
% 0.17/0.38 thf(fact_50_finlsts__rec__LCons__def,axiom,
% 0.17/0.38 ! [B: $tType,A: $tType,F2: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A3: set @ A,A2: A] :
% 0.17/0.38 ( ( F2
% 0.17/0.38 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( F2 @ ( coinductive_LCons @ A @ A2 @ R ) )
% 0.17/0.38 = ( D2 @ A2 @ R @ ( F2 @ R ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts_rec_LCons_def
% 0.17/0.38 thf(fact_51_finlsts__rec__LCons,axiom,
% 0.17/0.38 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A3: set @ A,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,A2: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ ( coinductive_LCons @ A @ A2 @ R ) )
% 0.17/0.38 = ( D2 @ A2 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ R ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts_rec_LCons
% 0.17/0.38 thf(fact_52_llast__singleton,axiom,
% 0.17/0.38 ! [A: $tType,X5: A] :
% 0.17/0.38 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X5 @ ( coinductive_LNil @ A ) ) )
% 0.17/0.38 = X5 ) ).
% 0.17/0.38
% 0.17/0.38 % llast_singleton
% 0.17/0.38 thf(fact_53_lmember__code_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,X5: A] :
% 0.17/0.38 ~ ( coinductive_lmember @ A @ X5 @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % lmember_code(1)
% 0.17/0.38 thf(fact_54_lappend__code_I2_J,axiom,
% 0.17/0.38 ! [A: $tType,Xa: A,X5: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X5 ) @ Ys )
% 0.17/0.38 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X5 @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_code(2)
% 0.17/0.38 thf(fact_55_lappend__is__LNil__conv,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.17/0.38 ( ( ( coinductive_lappend @ A @ S @ T )
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( ( S
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 & ( T
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_is_LNil_conv
% 0.17/0.38 thf(fact_56_LNil__is__lappend__conv,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.17/0.38 ( ( ( coinductive_LNil @ A )
% 0.17/0.38 = ( coinductive_lappend @ A @ S @ T ) )
% 0.17/0.38 = ( ( S
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 & ( T
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % LNil_is_lappend_conv
% 0.17/0.38 thf(fact_57_lappend__eq__LNil__iff,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( ( Xs
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 & ( Ys
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_eq_LNil_iff
% 0.17/0.38 thf(fact_58_LNil__eq__lappend__iff,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( ( coinductive_LNil @ A )
% 0.17/0.38 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.38 = ( ( Xs
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 & ( Ys
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % LNil_eq_lappend_iff
% 0.17/0.38 thf(fact_59_lappend__LNil2,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.17/0.38 = Xs ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_LNil2
% 0.17/0.38 thf(fact_60_lappend__code_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.17/0.38 = Ys ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_code(1)
% 0.17/0.38 thf(fact_61_same__lappend__eq,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( ( coinductive_lappend @ A @ R @ S )
% 0.17/0.38 = ( coinductive_lappend @ A @ R @ T ) )
% 0.17/0.38 = ( S = T ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % same_lappend_eq
% 0.17/0.38 thf(fact_62_lapp__fin__fin__iff,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_fin_fin_iff
% 0.17/0.38 thf(fact_63_llast__LCons2,axiom,
% 0.17/0.38 ! [A: $tType,X5: A,Y: A,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X5 @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 0.17/0.38 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % llast_LCons2
% 0.17/0.38 thf(fact_64_lstrict__prefix__code_I4_J,axiom,
% 0.17/0.38 ! [B: $tType,X5: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.17/0.38 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X5 @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.17/0.38 = ( ( X5 = Y )
% 0.17/0.38 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lstrict_prefix_code(4)
% 0.17/0.38 thf(fact_65_lstrict__prefix__code_I1_J,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % lstrict_prefix_code(1)
% 0.17/0.38 thf(fact_66_llast__snoc,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,A3: set @ A,X5: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X5 @ ( coinductive_LNil @ A ) ) ) )
% 0.17/0.38 = X5 ) ) ).
% 0.17/0.38
% 0.17/0.38 % llast_snoc
% 0.17/0.38 thf(fact_67_llist__less__induct,axiom,
% 0.17/0.38 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ! [Xs3: coinductive_llist @ A] :
% 0.17/0.38 ( ! [Ys2: coinductive_llist @ A] :
% 0.17/0.38 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.17/0.38 => ( P @ Ys2 ) )
% 0.17/0.38 => ( P @ Xs3 ) )
% 0.17/0.38 => ( P @ Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist_less_induct
% 0.17/0.38 thf(fact_68_lappend__assoc,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.17/0.38 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_assoc
% 0.17/0.38 thf(fact_69_lappend__LNil__LNil,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_LNil_LNil
% 0.17/0.38 thf(fact_70_lappfin__finT,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A,T: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappfin_finT
% 0.17/0.38 thf(fact_71_lapp__fin__fin__lemma,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_fin_fin_lemma
% 0.17/0.38 thf(fact_72_lappend__snocL1__conv__LCons2,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.17/0.38 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_snocL1_conv_LCons2
% 0.17/0.38 thf(fact_73_finlsts__rec__LNil__def,axiom,
% 0.17/0.38 ! [A: $tType,B: $tType,F2: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 0.17/0.38 ( ( F2
% 0.17/0.38 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.17/0.38 => ( ( F2 @ ( coinductive_LNil @ A ) )
% 0.17/0.38 = C2 ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts_rec_LNil_def
% 0.17/0.38 thf(fact_74_finlsts__rec__LNil,axiom,
% 0.17/0.38 ! [B: $tType,A: $tType,C2: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 0.17/0.38 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D2 @ ( coinductive_LNil @ B ) )
% 0.17/0.38 = C2 ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts_rec_LNil
% 0.17/0.38 thf(fact_75_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( Xs
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.17/0.38 thf(fact_76_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.17/0.38
% 0.17/0.38 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.17/0.38 thf(fact_77_lrev__induct,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,A3: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ! [X2: A,Xs3: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( P @ Xs3 )
% 0.17/0.38 => ( ( member @ A @ X2 @ A3 )
% 0.17/0.38 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 0.17/0.38 => ( P @ Xs ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lrev_induct
% 0.17/0.38 thf(fact_78_finlsts__rev__cases,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( T
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ~ ! [A4: A,L2: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ A @ A4 @ A3 )
% 0.17/0.38 => ( T
% 0.17/0.38 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finlsts_rev_cases
% 0.17/0.38 thf(fact_79_lbutlast__lapp__llast,axiom,
% 0.17/0.38 ! [A: $tType,L: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A3 ) )
% 0.17/0.38 => ( L
% 0.17/0.38 = ( coinductive_lappend @ A @ ( lList2370560421utlast @ A @ L ) @ ( coinductive_LCons @ A @ ( lList2170638824_llast @ A @ L ) @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lbutlast_lapp_llast
% 0.17/0.38 thf(fact_80_lmember__code_I2_J,axiom,
% 0.17/0.38 ! [A: $tType,X5: A,Y: A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lmember @ A @ X5 @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.17/0.38 = ( ( X5 = Y )
% 0.17/0.38 | ( coinductive_lmember @ A @ X5 @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lmember_code(2)
% 0.17/0.38 thf(fact_81_lrev__LCons,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,A2: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A2 @ R ) )
% 0.17/0.38 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A2 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lrev_LCons
% 0.17/0.38 thf(fact_82_LList2__Mirabelle__hamjzmohle_Ollast__lappend,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,Y: coinductive_llist @ A,A2: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ X5 @ ( coinductive_LCons @ A @ A2 @ Y ) ) )
% 0.17/0.38 = ( lList2170638824_llast @ A @ ( coinductive_LCons @ A @ A2 @ Y ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % LList2_Mirabelle_hamjzmohle.llast_lappend
% 0.17/0.38 thf(fact_83_llast__lappend__LCons,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 0.17/0.38 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % llast_lappend_LCons
% 0.17/0.38 thf(fact_84_llimit__induct,axiom,
% 0.17/0.38 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ! [X2: A,Xs3: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.17/0.38 => ( ( P @ Xs3 )
% 0.17/0.38 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs3 ) ) ) )
% 0.17/0.38 => ( ( ! [Ys2: coinductive_llist @ A] :
% 0.17/0.38 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs )
% 0.17/0.38 => ( P @ Ys2 ) )
% 0.17/0.38 => ( P @ Xs ) )
% 0.17/0.38 => ( P @ Xs ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % llimit_induct
% 0.17/0.38 thf(fact_85_ex__gt__or__lt,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A] :
% 0.17/0.38 ? [B3: A] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ B3 )
% 0.17/0.38 | ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ex_gt_or_lt
% 0.17/0.38 thf(fact_86_linorder__neqE__linordered__idom,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( X5 != Y )
% 0.17/0.38 => ( ~ ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ( ord_less @ A @ Y @ X5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % linorder_neqE_linordered_idom
% 0.17/0.38 thf(fact_87_dual__order_Ostrict__implies__not__eq,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [B4: A,A2: A] :
% 0.17/0.38 ( ( ord_less @ A @ B4 @ A2 )
% 0.17/0.38 => ( A2 != B4 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % dual_order.strict_implies_not_eq
% 0.17/0.38 thf(fact_88_linordered__field__no__ub,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X: A] :
% 0.17/0.38 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 0.17/0.38
% 0.17/0.38 % linordered_field_no_ub
% 0.17/0.38 thf(fact_89_top__apply,axiom,
% 0.17/0.38 ! [C: $tType,D: $tType] :
% 0.17/0.38 ( ( top @ C @ ( type2 @ C ) )
% 0.17/0.38 => ( ( top_top @ ( D > C ) )
% 0.17/0.38 = ( ^ [X3: D] : ( top_top @ C ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % top_apply
% 0.17/0.38 thf(fact_90_lfinite__LCons,axiom,
% 0.17/0.38 ! [A: $tType,X5: A,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X5 @ Xs ) )
% 0.17/0.38 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite_LCons
% 0.17/0.38 thf(fact_91_lfinite__code_I2_J,axiom,
% 0.17/0.38 ! [B: $tType,X5: B,Xs: coinductive_llist @ B] :
% 0.17/0.38 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X5 @ Xs ) )
% 0.17/0.38 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite_code(2)
% 0.17/0.38 thf(fact_92_lfinite__code_I1_J,axiom,
% 0.17/0.38 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite_code(1)
% 0.17/0.38 thf(fact_93_lfinite__lappend,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.38 = ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite_lappend
% 0.17/0.38 thf(fact_94_lrev__LNil,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % lrev_LNil
% 0.17/0.38 thf(fact_95_lrevT,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lrevT
% 0.17/0.38 thf(fact_96_lrev__is__lrev__conv,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.17/0.38 = ( lList2281150353e_lrev @ A @ Ys ) )
% 0.17/0.38 = ( Xs = Ys ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lrev_is_lrev_conv
% 0.17/0.38 thf(fact_97_lrev__lrev__ident,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 0.17/0.38 = Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % lrev_lrev_ident
% 0.17/0.38 thf(fact_98_LNil__is__lrev__conv,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( ( coinductive_LNil @ A )
% 0.17/0.38 = ( lList2281150353e_lrev @ A @ Xs ) )
% 0.17/0.38 = ( Xs
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % LNil_is_lrev_conv
% 0.17/0.38 thf(fact_99_lrev__is__LNil__conv,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( Xs
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lrev_is_LNil_conv
% 0.17/0.38 thf(fact_100_lrev__lappend,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.38 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lrev_lappend
% 0.17/0.38 thf(fact_101_top_Onot__eq__extremum,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order_top @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A] :
% 0.17/0.38 ( ( A2
% 0.17/0.38 != ( top_top @ A ) )
% 0.17/0.38 = ( ord_less @ A @ A2 @ ( top_top @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % top.not_eq_extremum
% 0.17/0.38 thf(fact_102_top_Oextremum__strict,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order_top @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A] :
% 0.17/0.38 ~ ( ord_less @ A @ ( top_top @ A ) @ A2 ) ) ).
% 0.17/0.38
% 0.17/0.38 % top.extremum_strict
% 0.17/0.38 thf(fact_103_lfinite__LConsI,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,X5: A] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X5 @ Xs ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite_LConsI
% 0.17/0.38 thf(fact_104_lfinite__LNil,axiom,
% 0.17/0.38 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite_LNil
% 0.17/0.38 thf(fact_105_lappend__inf,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.17/0.38 = Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_inf
% 0.17/0.38 thf(fact_106_fin__finite,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % fin_finite
% 0.17/0.38 thf(fact_107_finT__simp,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finT_simp
% 0.17/0.38 thf(fact_108_lstrict__prefix__lfinite1,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 0.17/0.38 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % lstrict_prefix_lfinite1
% 0.17/0.38 thf(fact_109_lfinite_Oinducts,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ X5 )
% 0.17/0.38 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ! [Xs3: coinductive_llist @ A,X2: A] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.17/0.38 => ( ( P @ Xs3 )
% 0.17/0.38 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs3 ) ) ) )
% 0.17/0.38 => ( P @ X5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite.inducts
% 0.17/0.38 thf(fact_110_lfinite_Osimps,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( coinductive_lfinite @ A )
% 0.17/0.38 = ( ^ [A7: coinductive_llist @ A] :
% 0.17/0.38 ( ( A7
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 | ? [Xs4: coinductive_llist @ A,X3: A] :
% 0.17/0.38 ( ( A7
% 0.17/0.38 = ( coinductive_LCons @ A @ X3 @ Xs4 ) )
% 0.17/0.38 & ( coinductive_lfinite @ A @ Xs4 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite.simps
% 0.17/0.38 thf(fact_111_lfinite_Ocases,axiom,
% 0.17/0.38 ! [A: $tType,A2: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ A2 )
% 0.17/0.38 => ( ( A2
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ~ ! [Xs3: coinductive_llist @ A] :
% 0.17/0.38 ( ? [X2: A] :
% 0.17/0.38 ( A2
% 0.17/0.38 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 0.17/0.38 => ~ ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite.cases
% 0.17/0.38 thf(fact_112_lfinite__rev__induct,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ! [X2: A,Xs3: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.17/0.38 => ( ( P @ Xs3 )
% 0.17/0.38 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 0.17/0.38 => ( P @ Xs ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lfinite_rev_induct
% 0.17/0.38 thf(fact_113_ord__eq__less__subst,axiom,
% 0.17/0.38 ! [A: $tType,B: $tType] :
% 0.17/0.38 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.17/0.38 & ( ord @ A @ ( type2 @ A ) ) )
% 0.17/0.38 => ! [A2: A,F2: B > A,B4: B,C2: B] :
% 0.17/0.38 ( ( A2
% 0.17/0.38 = ( F2 @ B4 ) )
% 0.17/0.38 => ( ( ord_less @ B @ B4 @ C2 )
% 0.17/0.38 => ( ! [X2: B,Y2: B] :
% 0.17/0.38 ( ( ord_less @ B @ X2 @ Y2 )
% 0.17/0.38 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.17/0.38 => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ord_eq_less_subst
% 0.17/0.38 thf(fact_114_ord__less__eq__subst,axiom,
% 0.17/0.38 ! [A: $tType,B: $tType] :
% 0.17/0.38 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.17/0.38 & ( ord @ A @ ( type2 @ A ) ) )
% 0.17/0.38 => ! [A2: A,B4: A,F2: A > B,C2: B] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ B4 )
% 0.17/0.38 => ( ( ( F2 @ B4 )
% 0.17/0.38 = C2 )
% 0.17/0.38 => ( ! [X2: A,Y2: A] :
% 0.17/0.38 ( ( ord_less @ A @ X2 @ Y2 )
% 0.17/0.38 => ( ord_less @ B @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.17/0.38 => ( ord_less @ B @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ord_less_eq_subst
% 0.17/0.38 thf(fact_115_order__less__subst1,axiom,
% 0.17/0.38 ! [A: $tType,B: $tType] :
% 0.17/0.38 ( ( ( order @ B @ ( type2 @ B ) )
% 0.17/0.38 & ( order @ A @ ( type2 @ A ) ) )
% 0.17/0.38 => ! [A2: A,F2: B > A,B4: B,C2: B] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ ( F2 @ B4 ) )
% 0.17/0.38 => ( ( ord_less @ B @ B4 @ C2 )
% 0.17/0.38 => ( ! [X2: B,Y2: B] :
% 0.17/0.38 ( ( ord_less @ B @ X2 @ Y2 )
% 0.17/0.38 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.17/0.38 => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % order_less_subst1
% 0.17/0.38 thf(fact_116_order__less__subst2,axiom,
% 0.17/0.38 ! [A: $tType,C: $tType] :
% 0.17/0.38 ( ( ( order @ C @ ( type2 @ C ) )
% 0.17/0.38 & ( order @ A @ ( type2 @ A ) ) )
% 0.17/0.38 => ! [A2: A,B4: A,F2: A > C,C2: C] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ B4 )
% 0.17/0.38 => ( ( ord_less @ C @ ( F2 @ B4 ) @ C2 )
% 0.17/0.38 => ( ! [X2: A,Y2: A] :
% 0.17/0.38 ( ( ord_less @ A @ X2 @ Y2 )
% 0.17/0.38 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.17/0.38 => ( ord_less @ C @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % order_less_subst2
% 0.17/0.38 thf(fact_117_lt__ex,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A] :
% 0.17/0.38 ? [Y2: A] : ( ord_less @ A @ Y2 @ X5 ) ) ).
% 0.17/0.38
% 0.17/0.38 % lt_ex
% 0.17/0.38 thf(fact_118_gt__ex,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( no_top @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A] :
% 0.17/0.38 ? [X1: A] : ( ord_less @ A @ X5 @ X1 ) ) ).
% 0.17/0.38
% 0.17/0.38 % gt_ex
% 0.17/0.38 thf(fact_119_neqE,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( X5 != Y )
% 0.17/0.38 => ( ~ ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ( ord_less @ A @ Y @ X5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % neqE
% 0.17/0.38 thf(fact_120_neq__iff,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( X5 != Y )
% 0.17/0.38 = ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 | ( ord_less @ A @ Y @ X5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % neq_iff
% 0.17/0.38 thf(fact_121_order_Oasym,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A,B4: A] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ B4 )
% 0.17/0.38 => ~ ( ord_less @ A @ B4 @ A2 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % order.asym
% 0.17/0.38 thf(fact_122_dense,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ? [Z: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Z )
% 0.17/0.38 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % dense
% 0.17/0.38 thf(fact_123_less__imp__neq,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ( X5 != Y ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_imp_neq
% 0.17/0.38 thf(fact_124_less__asym,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ~ ( ord_less @ A @ Y @ X5 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_asym
% 0.17/0.38 thf(fact_125_less__asym_H,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A,B4: A] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ B4 )
% 0.17/0.38 => ~ ( ord_less @ A @ B4 @ A2 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_asym'
% 0.17/0.38 thf(fact_126_less__trans,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A,Z3: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ( ( ord_less @ A @ Y @ Z3 )
% 0.17/0.38 => ( ord_less @ A @ X5 @ Z3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_trans
% 0.17/0.38 thf(fact_127_less__linear,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 | ( X5 = Y )
% 0.17/0.38 | ( ord_less @ A @ Y @ X5 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_linear
% 0.17/0.38 thf(fact_128_less__irrefl,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A] :
% 0.17/0.38 ~ ( ord_less @ A @ X5 @ X5 ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_irrefl
% 0.17/0.38 thf(fact_129_ord__eq__less__trans,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( ord @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A,B4: A,C2: A] :
% 0.17/0.38 ( ( A2 = B4 )
% 0.17/0.38 => ( ( ord_less @ A @ B4 @ C2 )
% 0.17/0.38 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ord_eq_less_trans
% 0.17/0.38 thf(fact_130_ord__less__eq__trans,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( ord @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A,B4: A,C2: A] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ B4 )
% 0.17/0.38 => ( ( B4 = C2 )
% 0.17/0.38 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ord_less_eq_trans
% 0.17/0.38 thf(fact_131_dual__order_Oasym,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [B4: A,A2: A] :
% 0.17/0.38 ( ( ord_less @ A @ B4 @ A2 )
% 0.17/0.38 => ~ ( ord_less @ A @ A2 @ B4 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % dual_order.asym
% 0.17/0.38 thf(fact_132_less__imp__not__eq,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ( X5 != Y ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_imp_not_eq
% 0.17/0.38 thf(fact_133_less__not__sym,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ~ ( ord_less @ A @ Y @ X5 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_not_sym
% 0.17/0.38 thf(fact_134_less__induct,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [P: A > $o,A2: A] :
% 0.17/0.38 ( ! [X2: A] :
% 0.17/0.38 ( ! [Y3: A] :
% 0.17/0.38 ( ( ord_less @ A @ Y3 @ X2 )
% 0.17/0.38 => ( P @ Y3 ) )
% 0.17/0.38 => ( P @ X2 ) )
% 0.17/0.38 => ( P @ A2 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_induct
% 0.17/0.38 thf(fact_135_antisym__conv3,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [Y: A,X5: A] :
% 0.17/0.38 ( ~ ( ord_less @ A @ Y @ X5 )
% 0.17/0.38 => ( ( ~ ( ord_less @ A @ X5 @ Y ) )
% 0.17/0.38 = ( X5 = Y ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % antisym_conv3
% 0.17/0.38 thf(fact_136_less__imp__not__eq2,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ( Y != X5 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_imp_not_eq2
% 0.17/0.38 thf(fact_137_less__imp__triv,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A,P: $o] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ( ( ord_less @ A @ Y @ X5 )
% 0.17/0.38 => P ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_imp_triv
% 0.17/0.38 thf(fact_138_linorder__cases,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ~ ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ( ( X5 != Y )
% 0.17/0.38 => ( ord_less @ A @ Y @ X5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % linorder_cases
% 0.17/0.38 thf(fact_139_dual__order_Oirrefl,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A] :
% 0.17/0.38 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.17/0.38
% 0.17/0.38 % dual_order.irrefl
% 0.17/0.38 thf(fact_140_order_Ostrict__trans,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A,B4: A,C2: A] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ B4 )
% 0.17/0.38 => ( ( ord_less @ A @ B4 @ C2 )
% 0.17/0.38 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % order.strict_trans
% 0.17/0.38 thf(fact_141_less__imp__not__less,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ord_less @ A @ X5 @ Y )
% 0.17/0.38 => ~ ( ord_less @ A @ Y @ X5 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % less_imp_not_less
% 0.17/0.38 thf(fact_142_dual__order_Ostrict__trans,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [B4: A,A2: A,C2: A] :
% 0.17/0.38 ( ( ord_less @ A @ B4 @ A2 )
% 0.17/0.38 => ( ( ord_less @ A @ C2 @ B4 )
% 0.17/0.38 => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % dual_order.strict_trans
% 0.17/0.38 thf(fact_143_not__less__iff__gr__or__eq,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X5: A,Y: A] :
% 0.17/0.38 ( ( ~ ( ord_less @ A @ X5 @ Y ) )
% 0.17/0.38 = ( ( ord_less @ A @ Y @ X5 )
% 0.17/0.38 | ( X5 = Y ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % not_less_iff_gr_or_eq
% 0.17/0.38 thf(fact_144_order_Ostrict__implies__not__eq,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [A2: A,B4: A] :
% 0.17/0.38 ( ( ord_less @ A @ A2 @ B4 )
% 0.17/0.38 => ( A2 != B4 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % order.strict_implies_not_eq
% 0.17/0.38 thf(fact_145_linordered__field__no__lb,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [X: A] :
% 0.17/0.38 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 0.17/0.38
% 0.17/0.38 % linordered_field_no_lb
% 0.17/0.38 thf(fact_146_iso__tuple__UNIV__I,axiom,
% 0.17/0.38 ! [A: $tType,X5: A] : ( member @ A @ X5 @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % iso_tuple_UNIV_I
% 0.17/0.38 thf(fact_147_UNIV__I,axiom,
% 0.17/0.38 ! [A: $tType,X5: A] : ( member @ A @ X5 @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % UNIV_I
% 0.17/0.38 thf(fact_148_poslsts__UNIV,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 = ( S
% 0.17/0.38 != ( coinductive_LNil @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % poslsts_UNIV
% 0.17/0.38 thf(fact_149_ltake__fin,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ltake_fin
% 0.17/0.38 thf(fact_150_ldrop__fin__iffT,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ldrop_fin_iffT
% 0.17/0.38 thf(fact_151_lstrict__prefix__lappend__conv,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coindu1478340336prefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.38 = ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lstrict_prefix_lappend_conv
% 0.17/0.38 thf(fact_152_lnull__lappend,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.38 = ( ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lnull_lappend
% 0.17/0.38 thf(fact_153_lappend_Odisc__iff_I2_J,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 0.17/0.38 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend.disc_iff(2)
% 0.17/0.38 thf(fact_154_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 0.17/0.38 ! [A: $tType,I: nat] :
% 0.17/0.38 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % LList2_Mirabelle_hamjzmohle.ldrop_LNil
% 0.17/0.38 thf(fact_155_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 0.17/0.38 ! [A: $tType,I: nat] :
% 0.17/0.38 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % LList2_Mirabelle_hamjzmohle.ltake_LNil
% 0.17/0.38 thf(fact_156_top__set__def,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( top_top @ ( set @ A ) )
% 0.17/0.38 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % top_set_def
% 0.17/0.38 thf(fact_157_ltake__ldrop__id,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,I: nat] :
% 0.17/0.38 ( ( coinductive_lappend @ A @ ( lList22119844313_ltake @ A @ X5 @ I ) @ ( lList2508575361_ldrop @ A @ X5 @ I ) )
% 0.17/0.38 = X5 ) ).
% 0.17/0.38
% 0.17/0.38 % ltake_ldrop_id
% 0.17/0.38 thf(fact_158_lappend_Oexhaust,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 => ~ ( coinductive_lnull @ A @ Ys ) )
% 0.17/0.38 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend.exhaust
% 0.17/0.38 thf(fact_159_lzip_Oexhaust,axiom,
% 0.17/0.38 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.17/0.38 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 | ( coinductive_lnull @ B @ Ys ) )
% 0.17/0.38 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 => ( coinductive_lnull @ B @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lzip.exhaust
% 0.17/0.38 thf(fact_160_llist_Odisc_I2_J,axiom,
% 0.17/0.38 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 0.17/0.38 ~ ( coinductive_lnull @ A @ ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist.disc(2)
% 0.17/0.38 thf(fact_161_llist_OdiscI_I2_J,axiom,
% 0.17/0.38 ! [A: $tType,Llist: coinductive_llist @ A,X212: A,X222: coinductive_llist @ A] :
% 0.17/0.38 ( ( Llist
% 0.17/0.38 = ( coinductive_LCons @ A @ X212 @ X222 ) )
% 0.17/0.38 => ~ ( coinductive_lnull @ A @ Llist ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist.discI(2)
% 0.17/0.38 thf(fact_162_not__lnull__conv,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( ~ ( coinductive_lnull @ A @ Xs ) )
% 0.17/0.38 = ( ? [X3: A,Xs2: coinductive_llist @ A] :
% 0.17/0.38 ( Xs
% 0.17/0.38 = ( coinductive_LCons @ A @ X3 @ Xs2 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % not_lnull_conv
% 0.17/0.38 thf(fact_163_lnull__def,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( coinductive_lnull @ A )
% 0.17/0.38 = ( ^ [Llist2: coinductive_llist @ A] :
% 0.17/0.38 ( Llist2
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lnull_def
% 0.17/0.38 thf(fact_164_llist_Ocollapse_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lnull @ A @ Llist )
% 0.17/0.38 => ( Llist
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist.collapse(1)
% 0.17/0.38 thf(fact_165_llist_OdiscI_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.17/0.38 ( ( Llist
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( coinductive_lnull @ A @ Llist ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist.discI(1)
% 0.17/0.38 thf(fact_166_llist_Odisc_I1_J,axiom,
% 0.17/0.38 ! [A: $tType] : ( coinductive_lnull @ A @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % llist.disc(1)
% 0.17/0.38 thf(fact_167_lappend__lnull2,axiom,
% 0.17/0.38 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lnull @ A @ Ys )
% 0.17/0.38 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.17/0.38 = Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_lnull2
% 0.17/0.38 thf(fact_168_lappend__lnull1,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.17/0.38 = Ys ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend_lnull1
% 0.17/0.38 thf(fact_169_lappend_Odisc_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_lnull @ A @ Ys )
% 0.17/0.38 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend.disc(1)
% 0.17/0.38 thf(fact_170_lappend_Odisc_I2_J,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 | ~ ( coinductive_lnull @ A @ Ys ) )
% 0.17/0.38 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend.disc(2)
% 0.17/0.38 thf(fact_171_lnull__imp__lfinite,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.17/0.38
% 0.17/0.38 % lnull_imp_lfinite
% 0.17/0.38 thf(fact_172_drop__nonLNil,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.17/0.38 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( T
% 0.17/0.38 != ( coinductive_LNil @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % drop_nonLNil
% 0.17/0.38 thf(fact_173_ldrop__finT,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ldrop_finT
% 0.17/0.38 thf(fact_174_lappend_Octr_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.38 ( ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_lnull @ A @ Ys )
% 0.17/0.38 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.17/0.38 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappend.ctr(1)
% 0.17/0.38 thf(fact_175_Coinductive__List_Ollast__LCons,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A,X5: A] :
% 0.17/0.38 ( ( ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X5 @ Xs ) )
% 0.17/0.38 = X5 ) )
% 0.17/0.38 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X5 @ Xs ) )
% 0.17/0.38 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % Coinductive_List.llast_LCons
% 0.17/0.38 thf(fact_176_UNIV__eq__I,axiom,
% 0.17/0.38 ! [A: $tType,A3: set @ A] :
% 0.17/0.38 ( ! [X2: A] : ( member @ A @ X2 @ A3 )
% 0.17/0.38 => ( ( top_top @ ( set @ A ) )
% 0.17/0.38 = A3 ) ) ).
% 0.17/0.38
% 0.17/0.38 % UNIV_eq_I
% 0.17/0.38 thf(fact_177_UNIV__witness,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ? [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % UNIV_witness
% 0.17/0.38 thf(fact_178_ltake__lappend__llength,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,S: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 0.17/0.38 = R ) ) ).
% 0.17/0.38
% 0.17/0.38 % ltake_lappend_llength
% 0.17/0.38 thf(fact_179_llength__drop__take,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.17/0.38 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 0.17/0.38 = I ) ) ).
% 0.17/0.38
% 0.17/0.38 % llength_drop_take
% 0.17/0.38 thf(fact_180_lapp__suff__llength,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,S: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( lList2508575361_ldrop @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 0.17/0.38 = S ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_suff_llength
% 0.17/0.38 thf(fact_181_top1I,axiom,
% 0.17/0.38 ! [A: $tType,X5: A] : ( top_top @ ( A > $o ) @ X5 ) ).
% 0.17/0.38
% 0.17/0.38 % top1I
% 0.17/0.38 thf(fact_182_top__empty__eq,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( top_top @ ( A > $o ) )
% 0.17/0.38 = ( ^ [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % top_empty_eq
% 0.17/0.38 thf(fact_183_top__conj_I1_J,axiom,
% 0.17/0.38 ! [A: $tType,X5: A,P: $o] :
% 0.17/0.38 ( ( ( top_top @ ( A > $o ) @ X5 )
% 0.17/0.38 & P )
% 0.17/0.38 = P ) ).
% 0.17/0.38
% 0.17/0.38 % top_conj(1)
% 0.17/0.38 thf(fact_184_top__conj_I2_J,axiom,
% 0.17/0.38 ! [A: $tType,P: $o,X5: A] :
% 0.17/0.38 ( ( P
% 0.17/0.38 & ( top_top @ ( A > $o ) @ X5 ) )
% 0.17/0.38 = P ) ).
% 0.17/0.38
% 0.17/0.38 % top_conj(2)
% 0.17/0.38 thf(fact_185_Coinductive__List_Ollast__lappend,axiom,
% 0.17/0.38 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ( ( coinductive_lnull @ A @ Ys )
% 0.17/0.38 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.38 = ( coinductive_llast @ A @ Xs ) ) )
% 0.17/0.38 & ( ~ ( coinductive_lnull @ A @ Ys )
% 0.17/0.38 => ( ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.38 = ( coinductive_llast @ A @ Ys ) ) )
% 0.17/0.38 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.38 = ( undefined @ A ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % Coinductive_List.llast_lappend
% 0.17/0.38 thf(fact_186_LList2__Mirabelle__hamjzmohle_Ollength__LCons,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,A2: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( lList21232602520length @ A @ ( coinductive_LCons @ A @ A2 @ R ) )
% 0.17/0.38 = ( suc @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % LList2_Mirabelle_hamjzmohle.llength_LCons
% 0.17/0.38 thf(fact_187_llength__take,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 0.17/0.38 = I ) ) ).
% 0.17/0.38
% 0.17/0.38 % llength_take
% 0.17/0.38 thf(fact_188_lapp__inf,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A,T: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( ( coinductive_lappend @ A @ S @ T )
% 0.17/0.38 = S ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_inf
% 0.17/0.38 thf(fact_189_notfin__inf,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A] :
% 0.17/0.38 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.17/0.38 = ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % notfin_inf
% 0.17/0.38 thf(fact_190_notinf__fin,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A] :
% 0.17/0.38 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.17/0.38 = ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % notinf_fin
% 0.17/0.38 thf(fact_191_ldrop__inf__iffT,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ldrop_inf_iffT
% 0.17/0.38 thf(fact_192_LList2__Mirabelle__hamjzmohle_Ollast__LNil,axiom,
% 0.17/0.38 ! [B: $tType] :
% 0.17/0.38 ( ( lList2170638824_llast @ B @ ( coinductive_LNil @ B ) )
% 0.17/0.38 = ( undefined @ B ) ) ).
% 0.17/0.38
% 0.17/0.38 % LList2_Mirabelle_hamjzmohle.llast_LNil
% 0.17/0.38 thf(fact_193_ldrop__infT,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ldrop_infT
% 0.17/0.38 thf(fact_194_inflstsI2,axiom,
% 0.17/0.38 ! [A: $tType,A2: A,A3: set @ A,T: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ A @ A2 @ A3 )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A2 @ T ) @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % inflstsI2
% 0.17/0.38 thf(fact_195_inflsts__cases,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ~ ! [A4: A,L2: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ A @ A4 @ A3 )
% 0.17/0.38 => ( S
% 0.17/0.38 != ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % inflsts_cases
% 0.17/0.38 thf(fact_196_infT__simp,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % infT_simp
% 0.17/0.38 thf(fact_197_Coinductive__List_Ollast__LNil,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 0.17/0.38 = ( undefined @ A ) ) ).
% 0.17/0.38
% 0.17/0.38 % Coinductive_List.llast_LNil
% 0.17/0.38 thf(fact_198_llast__linfinite,axiom,
% 0.17/0.38 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.38 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.17/0.38 => ( ( coinductive_llast @ A @ Xs )
% 0.17/0.38 = ( undefined @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % llast_linfinite
% 0.17/0.38 thf(fact_199_ltake__LCons__Suc,axiom,
% 0.17/0.38 ! [A: $tType,A2: A,L: coinductive_llist @ A,I: nat] :
% 0.17/0.38 ( ( lList22119844313_ltake @ A @ ( coinductive_LCons @ A @ A2 @ L ) @ ( suc @ I ) )
% 0.17/0.38 = ( coinductive_LCons @ A @ A2 @ ( lList22119844313_ltake @ A @ L @ I ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ltake_LCons_Suc
% 0.17/0.38 thf(fact_200_fin__inf__cases,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A] :
% 0.17/0.38 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % fin_inf_cases
% 0.17/0.38 thf(fact_201_app__invT,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,S: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % app_invT
% 0.17/0.38 thf(fact_202_lapp__infT,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) ) )
% 0.17/0.38 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_infT
% 0.17/0.38 thf(fact_203_lapp__inv2T,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) ) )
% 0.17/0.38 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_inv2T
% 0.17/0.38 thf(fact_204_lapp__fin__infT,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A,T: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_fin_infT
% 0.17/0.38 thf(fact_205_lift__Suc__mono__less__iff,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [F2: nat > A,N: nat,M: nat] :
% 0.17/0.38 ( ! [N2: nat] : ( ord_less @ A @ ( F2 @ N2 ) @ ( F2 @ ( suc @ N2 ) ) )
% 0.17/0.38 => ( ( ord_less @ A @ ( F2 @ N ) @ ( F2 @ M ) )
% 0.17/0.38 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lift_Suc_mono_less_iff
% 0.17/0.38 thf(fact_206_lift__Suc__mono__less,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.38 => ! [F2: nat > A,N: nat,N3: nat] :
% 0.17/0.38 ( ! [N2: nat] : ( ord_less @ A @ ( F2 @ N2 ) @ ( F2 @ ( suc @ N2 ) ) )
% 0.17/0.38 => ( ( ord_less @ nat @ N @ N3 )
% 0.17/0.38 => ( ord_less @ A @ ( F2 @ N ) @ ( F2 @ N3 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lift_Suc_mono_less
% 0.17/0.38 thf(fact_207_inflstsI,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( ~ ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % inflstsI
% 0.17/0.38 thf(fact_208_lapp__allT__iff,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A3 ) ) )
% 0.17/0.38 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_allT_iff
% 0.17/0.38 thf(fact_209_alllsts__UNIV,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllsts_UNIV
% 0.17/0.38 thf(fact_210_LConsE,axiom,
% 0.17/0.38 ! [A: $tType,X5: A,Xs: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X5 @ Xs ) @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 = ( ( member @ A @ X5 @ A3 )
% 0.17/0.38 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % LConsE
% 0.17/0.38 thf(fact_211_take__fin,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % take_fin
% 0.17/0.38 thf(fact_212_poslsts__iff,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A3 ) )
% 0.17/0.38 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 & ( S
% 0.17/0.38 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % poslsts_iff
% 0.17/0.38 thf(fact_213_alllsts_Ocoinduct,axiom,
% 0.17/0.38 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X5: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( X4 @ X5 )
% 0.17/0.38 => ( ! [X2: coinductive_llist @ A] :
% 0.17/0.38 ( ( X4 @ X2 )
% 0.17/0.38 => ( ( X2
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 | ? [L3: coinductive_llist @ A,A5: A] :
% 0.17/0.38 ( ( X2
% 0.17/0.38 = ( coinductive_LCons @ A @ A5 @ L3 ) )
% 0.17/0.38 & ( ( X4 @ L3 )
% 0.17/0.38 | ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A3 ) ) )
% 0.17/0.38 & ( member @ A @ A5 @ A3 ) ) ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllsts.coinduct
% 0.17/0.38 thf(fact_214_alllsts_Osimps,axiom,
% 0.17/0.38 ! [A: $tType,A2: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ A2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 = ( ( A2
% 0.17/0.38 = ( coinductive_LNil @ A ) )
% 0.17/0.38 | ? [L4: coinductive_llist @ A,A7: A] :
% 0.17/0.38 ( ( A2
% 0.17/0.38 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 0.17/0.38 & ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 & ( member @ A @ A7 @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllsts.simps
% 0.17/0.38 thf(fact_215_alllsts_Ocases,axiom,
% 0.17/0.38 ! [A: $tType,A2: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ A2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( ( A2
% 0.17/0.38 != ( coinductive_LNil @ A ) )
% 0.17/0.38 => ~ ! [L2: coinductive_llist @ A,A4: A] :
% 0.17/0.38 ( ( A2
% 0.17/0.38 = ( coinductive_LCons @ A @ A4 @ L2 ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ~ ( member @ A @ A4 @ A3 ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllsts.cases
% 0.17/0.38 thf(fact_216_ldropT,axiom,
% 0.17/0.38 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2435255213lllsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % ldropT
% 0.17/0.38 thf(fact_217_alllsts_OLCons__all,axiom,
% 0.17/0.38 ! [A: $tType,L: coinductive_llist @ A,A3: set @ A,A2: A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ A @ A2 @ A3 )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A2 @ L ) @ ( lList2435255213lllsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllsts.LCons_all
% 0.17/0.38 thf(fact_218_alllsts_OLNil__all,axiom,
% 0.17/0.38 ! [A: $tType,A3: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A3 ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllsts.LNil_all
% 0.17/0.38 thf(fact_219_lappT,axiom,
% 0.17/0.38 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A,T: coinductive_llist @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lappT
% 0.17/0.38 thf(fact_220_lapp__all__invT,axiom,
% 0.17/0.38 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % lapp_all_invT
% 0.17/0.38 thf(fact_221_finite__lemma,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A,B5: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ B5 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ B5 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finite_lemma
% 0.17/0.38 thf(fact_222_finsubsetall,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % finsubsetall
% 0.17/0.38 thf(fact_223_infsubsetall,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % infsubsetall
% 0.17/0.38 thf(fact_224_alllstsE,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( ~ ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % alllstsE
% 0.17/0.38 thf(fact_225_inflstsE,axiom,
% 0.17/0.38 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 0.17/0.38 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 => ~ ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) )
% 0.17/0.38 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % inflstsE
% 0.17/0.38 thf(fact_226_inflsts__def,axiom,
% 0.17/0.38 ! [A: $tType] :
% 0.17/0.38 ( ( lList21612149805nflsts @ A )
% 0.17/0.38 = ( ^ [A6: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A6 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % inflsts_def
% 0.17/0.38 thf(fact_227_fin__Un__inf,axiom,
% 0.17/0.38 ! [A: $tType,A3: set @ A] :
% 0.17/0.38 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A3 ) @ ( lList21612149805nflsts @ A @ A3 ) )
% 0.17/0.38 = ( lList2435255213lllsts @ A @ A3 ) ) ).
% 0.17/0.38
% 0.17/0.38 % fin_Un_inf
% 0.17/0.38 thf(fact_228_Un__iff,axiom,
% 0.17/0.38 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 0.17/0.38 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.38 = ( ( member @ A @ C2 @ A3 )
% 0.17/0.38 | ( member @ A @ C2 @ B5 ) ) ) ).
% 0.17/0.38
% 0.17/0.38 % Un_iff
% 0.17/0.38 thf(fact_229_UnCI,axiom,
% 0.17/0.38 ! [A: $tType,C2: A,B5: set @ A,A3: set @ A] :
% 0.17/0.39 ( ( ~ ( member @ A @ C2 @ B5 )
% 0.17/0.39 => ( member @ A @ C2 @ A3 ) )
% 0.17/0.39 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % UnCI
% 0.17/0.39 thf(fact_230_Diff__idemp,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) @ B5 )
% 0.17/0.39 = ( minus_minus @ ( set @ A ) @ A3 @ B5 ) ) ).
% 0.17/0.39
% 0.17/0.39 % Diff_idemp
% 0.17/0.39 thf(fact_231_Diff__iff,axiom,
% 0.17/0.39 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.39 = ( ( member @ A @ C2 @ A3 )
% 0.17/0.39 & ~ ( member @ A @ C2 @ B5 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % Diff_iff
% 0.17/0.39 thf(fact_232_DiffI,axiom,
% 0.17/0.39 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( member @ A @ C2 @ A3 )
% 0.17/0.39 => ( ~ ( member @ A @ C2 @ B5 )
% 0.17/0.39 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % DiffI
% 0.17/0.39 thf(fact_233_Un__Diff__cancel2,axiom,
% 0.17/0.39 ! [A: $tType,B5: set @ A,A3: set @ A] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B5 @ A3 ) @ A3 )
% 0.17/0.39 = ( sup_sup @ ( set @ A ) @ B5 @ A3 ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_Diff_cancel2
% 0.17/0.39 thf(fact_234_Un__Diff__cancel,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) @ A3 @ ( minus_minus @ ( set @ A ) @ B5 @ A3 ) )
% 0.17/0.39 = ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_Diff_cancel
% 0.17/0.39 thf(fact_235_Un__UNIV__right,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) @ A3 @ ( top_top @ ( set @ A ) ) )
% 0.17/0.39 = ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_UNIV_right
% 0.17/0.39 thf(fact_236_Un__UNIV__left,axiom,
% 0.17/0.39 ! [A: $tType,B5: set @ A] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B5 )
% 0.17/0.39 = ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_UNIV_left
% 0.17/0.39 thf(fact_237_Un__left__commute,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A,C3: set @ A] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) )
% 0.17/0.39 = ( sup_sup @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_left_commute
% 0.17/0.39 thf(fact_238_Un__left__absorb,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.39 = ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_left_absorb
% 0.17/0.39 thf(fact_239_Un__commute,axiom,
% 0.17/0.39 ! [A: $tType] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) )
% 0.17/0.39 = ( ^ [A6: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_commute
% 0.17/0.39 thf(fact_240_Un__absorb,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.17/0.39 = A3 ) ).
% 0.17/0.39
% 0.17/0.39 % Un_absorb
% 0.17/0.39 thf(fact_241_Un__assoc,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A,C3: set @ A] :
% 0.17/0.39 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) @ C3 )
% 0.17/0.39 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_assoc
% 0.17/0.39 thf(fact_242_ball__Un,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A,P: A > $o] :
% 0.17/0.39 ( ( ! [X3: A] :
% 0.17/0.39 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.39 => ( P @ X3 ) ) )
% 0.17/0.39 = ( ! [X3: A] :
% 0.17/0.39 ( ( member @ A @ X3 @ A3 )
% 0.17/0.39 => ( P @ X3 ) )
% 0.17/0.39 & ! [X3: A] :
% 0.17/0.39 ( ( member @ A @ X3 @ B5 )
% 0.17/0.39 => ( P @ X3 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % ball_Un
% 0.17/0.39 thf(fact_243_Un__Diff,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A,C3: set @ A] :
% 0.17/0.39 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) @ C3 )
% 0.17/0.39 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % Un_Diff
% 0.17/0.39 thf(fact_244_bex__Un,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A,P: A > $o] :
% 0.17/0.39 ( ( ? [X3: A] :
% 0.17/0.39 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.39 & ( P @ X3 ) ) )
% 0.17/0.39 = ( ? [X3: A] :
% 0.17/0.39 ( ( member @ A @ X3 @ A3 )
% 0.17/0.39 & ( P @ X3 ) )
% 0.17/0.39 | ? [X3: A] :
% 0.17/0.39 ( ( member @ A @ X3 @ B5 )
% 0.17/0.39 & ( P @ X3 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % bex_Un
% 0.17/0.39 thf(fact_245_DiffD2,axiom,
% 0.17/0.39 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.39 => ~ ( member @ A @ C2 @ B5 ) ) ).
% 0.17/0.39
% 0.17/0.39 % DiffD2
% 0.17/0.39 thf(fact_246_DiffD1,axiom,
% 0.17/0.39 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.39 => ( member @ A @ C2 @ A3 ) ) ).
% 0.17/0.39
% 0.17/0.39 % DiffD1
% 0.17/0.39 thf(fact_247_DiffE,axiom,
% 0.17/0.39 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.39 => ~ ( ( member @ A @ C2 @ A3 )
% 0.17/0.39 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % DiffE
% 0.17/0.39 thf(fact_248_UnI2,axiom,
% 0.17/0.39 ! [A: $tType,C2: A,B5: set @ A,A3: set @ A] :
% 0.17/0.39 ( ( member @ A @ C2 @ B5 )
% 0.17/0.39 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % UnI2
% 0.17/0.39 thf(fact_249_UnI1,axiom,
% 0.17/0.39 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( member @ A @ C2 @ A3 )
% 0.17/0.39 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % UnI1
% 0.17/0.39 thf(fact_250_UnE,axiom,
% 0.17/0.39 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 0.17/0.39 => ( ~ ( member @ A @ C2 @ A3 )
% 0.17/0.39 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % UnE
% 0.17/0.39 thf(fact_251_psubset__imp__ex__mem,axiom,
% 0.17/0.39 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.17/0.39 ( ( ord_less @ ( set @ A ) @ A3 @ B5 )
% 0.17/0.39 => ? [B3: A] : ( member @ A @ B3 @ ( minus_minus @ ( set @ A ) @ B5 @ A3 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % psubset_imp_ex_mem
% 0.17/0.39 thf(fact_252_sup__top__right,axiom,
% 0.17/0.39 ! [A: $tType] :
% 0.17/0.39 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.17/0.39 => ! [X5: A] :
% 0.17/0.39 ( ( sup_sup @ A @ X5 @ ( top_top @ A ) )
% 0.17/0.39 = ( top_top @ A ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % sup_top_right
% 0.17/0.39 thf(fact_253_sup__top__left,axiom,
% 0.17/0.39 ! [A: $tType] :
% 0.17/0.39 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.17/0.39 => ! [X5: A] :
% 0.17/0.39 ( ( sup_sup @ A @ ( top_top @ A ) @ X5 )
% 0.17/0.39 = ( top_top @ A ) ) ) ).
% 0.17/0.39
% 0.17/0.39 % sup_top_left
% 0.17/0.39
% 0.17/0.39 %----Type constructors (31)
% 0.17/0.39 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.17/0.39 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.17/0.39 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.17/0.39 ! [A8: $tType,A9: $tType] :
% 0.17/0.39 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.17/0.39 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.17/0.39 ! [A8: $tType,A9: $tType] :
% 0.17/0.39 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.17/0.39 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.17/0.39 ! [A8: $tType,A9: $tType] :
% 0.17/0.39 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 0.17/0.39 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.17/0.39 ! [A8: $tType,A9: $tType] :
% 0.17/0.39 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.17/0.39 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.17/0.39 ! [A8: $tType,A9: $tType] :
% 0.17/0.39 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.17/0.39 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_fun___Orderings_Otop,axiom,
% 0.17/0.39 ! [A8: $tType,A9: $tType] :
% 0.17/0.39 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.17/0.39 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_fun___Orderings_Oord,axiom,
% 0.17/0.39 ! [A8: $tType,A9: $tType] :
% 0.17/0.39 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.17/0.39 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.17/0.39 wellorder @ nat @ ( type2 @ nat ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Nat_Onat___Orderings_Opreorder_3,axiom,
% 0.17/0.39 preorder @ nat @ ( type2 @ nat ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.17/0.39 linorder @ nat @ ( type2 @ nat ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.17/0.39 no_top @ nat @ ( type2 @ nat ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 0.17/0.39 order @ nat @ ( type2 @ nat ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 0.17/0.39 ord @ nat @ ( type2 @ nat ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_6,axiom,
% 0.17/0.39 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Set_Oset___Orderings_Oorder__top_7,axiom,
% 0.17/0.39 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Set_Oset___Orderings_Opreorder_8,axiom,
% 0.17/0.39 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 0.17/0.39 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Set_Oset___Orderings_Otop_10,axiom,
% 0.17/0.39 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Set_Oset___Orderings_Oord_11,axiom,
% 0.17/0.39 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_12,axiom,
% 0.17/0.39 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_HOL_Obool___Orderings_Oorder__top_13,axiom,
% 0.17/0.39 order_top @ $o @ ( type2 @ $o ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_HOL_Obool___Orderings_Opreorder_14,axiom,
% 0.17/0.39 preorder @ $o @ ( type2 @ $o ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_HOL_Obool___Orderings_Olinorder_15,axiom,
% 0.17/0.39 linorder @ $o @ ( type2 @ $o ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_HOL_Obool___Orderings_Oorder_16,axiom,
% 0.17/0.39 order @ $o @ ( type2 @ $o ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_HOL_Obool___Orderings_Otop_17,axiom,
% 0.17/0.39 top @ $o @ ( type2 @ $o ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_HOL_Obool___Orderings_Oord_18,axiom,
% 0.17/0.39 ord @ $o @ ( type2 @ $o ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_19,axiom,
% 0.17/0.39 ! [A8: $tType] : ( preorder @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_20,axiom,
% 0.17/0.39 ! [A8: $tType] : ( order @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_21,axiom,
% 0.17/0.39 ! [A8: $tType] : ( ord @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %----Conjectures (1)
% 0.17/0.39 thf(conj_0,conjecture,
% 0.17/0.39 ~ ( ord_less @ ( coinductive_llist @ a ) @ r @ ( coinductive_LNil @ a ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 2.63/1.58 ---- Embedded in THF ---
% 2.63/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.63/1.58 %%% Generated on Tue Feb 24 06:10:52 EST 2026
% 2.63/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.63/1.58 %%% Logic specification used:
% 2.63/1.58 %%% thf(spec, logic, $$dhol).
% 2.63/1.58
% 2.63/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3Q38gBiG4C/DTF2DTF5656.p
% 2.63/1.58 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.63/1.58 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.63/1.58 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.63/1.58 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.63/1.58 thf(ty_tf_a, type, a: $tType).
% 2.63/1.58 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Ollist_Olnull, type, coinductive_lnull: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Olmember, type, coinductive_lmember: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > $o))))).
% 2.63/1.58 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.63/1.58 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.63/1.58 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts, type, lList2435255213lllsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp, type, lList21511617539llstsp: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > $o))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts, type, lList2236698231inlsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.63/1.58 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)))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp, type, lList2860480441nlstsp: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > $o))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts, type, lList22096119349pslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts, type, lList21612149805nflsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast, type, lList2370560421utlast: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop, type, lList2508575361_ldrop: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast, type, lList2170638824_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength, type, lList21232602520length: (!> [A:$tType]: (((coinductive_llist @ A) > nat)))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev, type, lList2281150353e_lrev: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake, type, lList22119844313_ltake: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 2.63/1.58 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts, type, lList21148268032oslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.63/1.58 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.63/1.58 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.63/1.58 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.63/1.58 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.63/1.58 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.63/1.58 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.63/1.58 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.63/1.58 thf(sy_v_r, type, r: (coinductive_llist @ a)).
% 2.63/1.58 thf(fact_0_lbutlast__LNil, axiom, (! [A:$tType]: ((((lList2370560421utlast @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_1_LNil__less__LCons, axiom, (! [A:$tType,A2:A,T:(coinductive_llist @ A)]: ((((ord_less @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (((coinductive_LCons @ A) @ A2) @ T))))).
% 2.63/1.58 thf(fact_2_minf_I11_J, axiom, (! [C:$tType,D:$tType]: ((((ord @ C) @ (type2 @ C)) => (! [F:D]: ((? [Z:C]: ((! [X:C]: (((((ord_less @ C) @ X) @ Z) => (F = F)))))))))))).
% 2.63/1.58 thf(fact_3_minf_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (~ ((((ord_less @ A) @ T) @ X)))))))))))))).
% 2.63/1.58 thf(fact_4_minf_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((ord_less @ A) @ X) @ T)))))))))))).
% 2.63/1.58 thf(fact_5_minf_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (X != T)))))))))))).
% 2.63/1.58 thf(fact_6_minf_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (X != T)))))))))))).
% 2.63/1.58 thf(fact_7_minf_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((P @ X) | (Q @ X)) = ((P2 @ X) | (Q2 @ X)))))))))))))))).
% 2.63/1.58 thf(fact_8_minf_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((P @ X) & (Q @ X)) = ((P2 @ X) & (Q2 @ X)))))))))))))))).
% 2.63/1.58 thf(fact_9_pinf_I11_J, axiom, (! [C:$tType,D:$tType]: ((((ord @ C) @ (type2 @ C)) => (! [F:D]: ((? [Z:C]: ((! [X:C]: (((((ord_less @ C) @ Z) @ X) => (F = F)))))))))))).
% 2.63/1.58 thf(fact_10_pinf_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((ord_less @ A) @ T) @ X)))))))))))).
% 2.63/1.58 thf(fact_11_pinf_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (~ ((((ord_less @ A) @ X) @ T)))))))))))))).
% 2.63/1.58 thf(fact_12_llistE, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X21:A,X22:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X21) @ X22)))))))))).
% 2.63/1.58 thf(fact_13_pinf_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((P @ X) & (Q @ X)) = ((P2 @ X) & (Q2 @ X)))))))))))))))).
% 2.63/1.58 thf(fact_14_pinf_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((P @ X) | (Q @ X)) = ((P2 @ X) | (Q2 @ X)))))))))))))))).
% 2.63/1.58 thf(fact_15_pinf_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (X != T)))))))))))).
% 2.63/1.58 thf(fact_16_pinf_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (X != T)))))))))))).
% 2.63/1.58 thf(fact_17_llist_Oinject, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X212) @ X222) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X212 = Y21) & (X222 = Y22)))))).
% 2.63/1.58 thf(fact_18_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X3:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X3) @ Xs2)))))))).
% 2.63/1.58 thf(fact_19_llist_Odistinct_I1_J, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X212) @ X222))))).
% 2.63/1.58 thf(fact_20_fps__induct, axiom, (! [A:$tType,L:(coinductive_llist @ A),A3:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList22096119349pslsts @ A) @ A3)) => ((! [A4:A]: (((((member @ A) @ A4) @ A3) => (P @ (((coinductive_LCons @ A) @ A4) @ (coinductive_LNil @ A)))))) => ((! [A4:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList22096119349pslsts @ A) @ A3)) => ((P @ L2) => ((((member @ A) @ A4) @ A3) => (P @ (((coinductive_LCons @ A) @ A4) @ L2))))))) => (P @ L))))))).
% 2.63/1.58 thf(fact_21_lbutlast__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A),A2:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => (((R = (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A2) @ R)) = (coinductive_LNil @ A))) & ((R != (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A2) @ R)) = (((coinductive_LCons @ A) @ A2) @ ((lList2370560421utlast @ A) @ R))))))))).
% 2.63/1.58 thf(fact_22_alllstsp_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X5:(coinductive_llist @ A),A3:(A > $o)]: (((X4 @ X5) => ((! [X2:(coinductive_llist @ A)]: (((X4 @ X2) => ((X2 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A5:A]: (((X2 = (((coinductive_LCons @ A) @ A5) @ L3)) & (((X4 @ L3) | (((lList21511617539llstsp @ A) @ A3) @ L3)) & (A3 @ A5))))))))) => (((lList21511617539llstsp @ A) @ A3) @ X5)))))).
% 2.63/1.58 thf(fact_23_finlstsp_Oinducts, axiom, (! [A:$tType,A3:(A > $o),X5:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((lList2860480441nlstsp @ A) @ A3) @ X5) => ((P @ (coinductive_LNil @ A)) => ((! [L2:(coinductive_llist @ A),A4:A]: (((((lList2860480441nlstsp @ A) @ A3) @ L2) => ((P @ L2) => ((A3 @ A4) => (P @ (((coinductive_LCons @ A) @ A4) @ L2))))))) => (P @ X5))))))).
% 2.63/1.58 thf(fact_24_finlstsp_Osimps, axiom, (! [A:$tType]: (((lList2860480441nlstsp @ A) = (^ [A6:(A > $o),A7:(coinductive_llist @ A)]: (((A7 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),B2:A]: (((A7 = (((coinductive_LCons @ A) @ B2) @ L4)) & ((((lList2860480441nlstsp @ A) @ A6) @ L4) & (A6 @ B2)))))))))))).
% 2.63/1.58 thf(fact_25_finlstsp_Ocases, axiom, (! [A:$tType,A3:(A > $o),A2:(coinductive_llist @ A)]: (((((lList2860480441nlstsp @ A) @ A3) @ A2) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A4:A]: (((A2 = (((coinductive_LCons @ A) @ A4) @ L2)) => ((((lList2860480441nlstsp @ A) @ A3) @ L2) => (~ ((A3 @ A4)))))))))))))).
% 2.63/1.58 thf(fact_26_alllstsp_Osimps, axiom, (! [A:$tType]: (((lList21511617539llstsp @ A) = (^ [A6:(A > $o),A7:(coinductive_llist @ A)]: (((A7 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),B2:A]: (((A7 = (((coinductive_LCons @ A) @ B2) @ L4)) & ((((lList21511617539llstsp @ A) @ A6) @ L4) & (A6 @ B2)))))))))))).
% 2.63/1.58 thf(fact_27_alllstsp_Ocases, axiom, (! [A:$tType,A3:(A > $o),A2:(coinductive_llist @ A)]: (((((lList21511617539llstsp @ A) @ A3) @ A2) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A4:A]: (((A2 = (((coinductive_LCons @ A) @ A4) @ L2)) => ((((lList21511617539llstsp @ A) @ A3) @ L2) => (~ ((A3 @ A4)))))))))))))).
% 2.63/1.58 thf(fact_28_llist__less__finT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A3:(set @ A)]: (((((ord_less @ (coinductive_llist @ A)) @ R) @ S) => ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_29_fpslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList22096119349pslsts @ A) @ A3)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A3)) & (S != (coinductive_LNil @ A))))))).
% 2.63/1.58 thf(fact_30_fpslsts__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList22096119349pslsts @ A) @ A3)) => (~ ((! [A4:A,Rs:(coinductive_llist @ A)]: (((R = (((coinductive_LCons @ A) @ A4) @ Rs)) => ((((member @ A) @ A4) @ A3) => (~ ((((member @ (coinductive_llist @ A)) @ Rs) @ ((lList2236698231inlsts @ A) @ A3)))))))))))))).
% 2.63/1.58 thf(fact_31_finlsts_OLCons__fin, axiom, (! [A:$tType,L:(coinductive_llist @ A),A3:(set @ A),A2:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A3)) => ((((member @ A) @ A2) @ A3) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A2) @ L)) @ ((lList2236698231inlsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_32_finlsts_OLNil__fin, axiom, (! [A:$tType,A3:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2236698231inlsts @ A) @ A3))))).
% 2.63/1.58 thf(fact_33_finlstsp_OLCons__fin, axiom, (! [A:$tType,A3:(A > $o),L:(coinductive_llist @ A),A2:A]: (((((lList2860480441nlstsp @ A) @ A3) @ L) => ((A3 @ A2) => (((lList2860480441nlstsp @ A) @ A3) @ (((coinductive_LCons @ A) @ A2) @ L))))))).
% 2.63/1.58 thf(fact_34_alllstsp_OLCons__all, axiom, (! [A:$tType,A3:(A > $o),L:(coinductive_llist @ A),A2:A]: (((((lList21511617539llstsp @ A) @ A3) @ L) => ((A3 @ A2) => (((lList21511617539llstsp @ A) @ A3) @ (((coinductive_LCons @ A) @ A2) @ L))))))).
% 2.63/1.58 thf(fact_35_alllstsp_OLNil__all, axiom, (! [A:$tType,A3:(A > $o)]: ((((lList21511617539llstsp @ A) @ A3) @ (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_36_finlstsp_OLNil__fin, axiom, (! [A:$tType,A3:(A > $o)]: ((((lList2860480441nlstsp @ A) @ A3) @ (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_37_finlsts_Ocases, axiom, (! [A:$tType,A2:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A2) @ ((lList2236698231inlsts @ A) @ A3)) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A4:A]: (((A2 = (((coinductive_LCons @ A) @ A4) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A3)) => (~ ((((member @ A) @ A4) @ A3)))))))))))))).
% 2.63/1.58 thf(fact_38_finlsts_Osimps, axiom, (! [A:$tType,A2:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A2) @ ((lList2236698231inlsts @ A) @ A3)) = ((A2 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A7:A]: (((A2 = (((coinductive_LCons @ A) @ A7) @ L4)) & ((((member @ (coinductive_llist @ A)) @ L4) @ ((lList2236698231inlsts @ A) @ A3)) & (((member @ A) @ A7) @ A3)))))))))).
% 2.63/1.58 thf(fact_39_finlsts__induct, axiom, (! [A:$tType,X5:(coinductive_llist @ A),A3:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ A3)) => ((! [L2:(coinductive_llist @ A)]: (((L2 = (coinductive_LNil @ A)) => (P @ L2)))) => ((! [A4:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A3)) => ((P @ L2) => ((((member @ A) @ A4) @ A3) => (P @ (((coinductive_LCons @ A) @ A4) @ L2))))))) => (P @ X5))))))).
% 2.63/1.58 thf(fact_40_finlsts_Oinducts, axiom, (! [A:$tType,X5:(coinductive_llist @ A),A3:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ A3)) => ((P @ (coinductive_LNil @ A)) => ((! [L2:(coinductive_llist @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A3)) => ((P @ L2) => ((((member @ A) @ A4) @ A3) => (P @ (((coinductive_LCons @ A) @ A4) @ L2))))))) => (P @ X5))))))).
% 2.63/1.58 thf(fact_41_LList2__Mirabelle__hamjzmohle_Ollast__LCons, axiom, (! [B:$tType,R:(coinductive_llist @ B),A3:(set @ B),A2:B]: (((((member @ (coinductive_llist @ B)) @ R) @ ((lList2236698231inlsts @ B) @ A3)) => (((R = (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A2) @ R)) = A2)) & ((R != (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A2) @ R)) = ((lList2170638824_llast @ B) @ R)))))))).
% 2.63/1.58 thf(fact_42_lbutlast__snoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A3:(set @ A),X5:A]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A3)) => (((lList2370560421utlast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ X5) @ (coinductive_LNil @ A)))) = Xs))))).
% 2.63/1.58 thf(fact_43_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Xs2)) & (((coindu328551480prefix @ A) @ Xs2) @ Ys))))))))).
% 2.63/1.58 thf(fact_44_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X5:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X5) @ Xs)) @ (coinductive_LNil @ B))))))).
% 2.63/1.58 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.63/1.58 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) = A3)))).
% 2.63/1.58 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.63/1.58 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G:(A > B)]: (((! [X2:A]: (((F2 @ X2) = (G @ X2)))) => (F2 = G))))).
% 2.63/1.58 thf(fact_49_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y) @ Ys))))).
% 2.63/1.58 thf(fact_50_finlsts__rec__LCons__def, axiom, (! [B:$tType,A:$tType,F2:((coinductive_llist @ A) > B),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B))),R:(coinductive_llist @ A),A3:(set @ A),A2:A]: (((F2 = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => ((F2 @ (((coinductive_LCons @ A) @ A2) @ R)) = (((D2 @ A2) @ R) @ (F2 @ R)))))))).
% 2.63/1.58 thf(fact_51_finlsts__rec__LCons, axiom, (! [B:$tType,A:$tType,R:(coinductive_llist @ A),A3:(set @ A),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B))),A2:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => ((((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2) @ (((coinductive_LCons @ A) @ A2) @ R)) = (((D2 @ A2) @ R) @ (((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2) @ R))))))).
% 2.63/1.58 thf(fact_52_llast__singleton, axiom, (! [A:$tType,X5:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X5) @ (coinductive_LNil @ A))) = X5)))).
% 2.63/1.58 thf(fact_53_lmember__code_I1_J, axiom, (! [A:$tType,X5:A]: ((~ ((((coinductive_lmember @ A) @ X5) @ (coinductive_LNil @ A))))))).
% 2.63/1.58 thf(fact_54_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X5:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_LCons @ A) @ Xa) @ X5)) @ Ys) = (((coinductive_LCons @ A) @ Xa) @ (((coinductive_lappend @ A) @ X5) @ Ys)))))).
% 2.63/1.58 thf(fact_55_lappend__is__LNil__conv, axiom, (! [A:$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))))))).
% 2.63/1.58 thf(fact_56_LNil__is__lappend__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ S) @ T)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.63/1.58 thf(fact_57_lappend__eq__LNil__iff, axiom, (! [A:$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))))))).
% 2.63/1.58 thf(fact_58_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.63/1.58 thf(fact_59_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 2.63/1.58 thf(fact_60_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.63/1.58 thf(fact_61_same__lappend__eq, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A),S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => (((((coinductive_lappend @ A) @ R) @ S) = (((coinductive_lappend @ A) @ R) @ T)) = (S = T)))))).
% 2.63/1.58 thf(fact_62_lapp__fin__fin__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A3)) = ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_63_llast__LCons2, axiom, (! [A:$tType,X5:A,Y:A,Xs:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X5) @ (((coinductive_LCons @ A) @ Y) @ Xs))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Xs)))))).
% 2.63/1.58 thf(fact_64_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X5:B,Xs:(coinductive_llist @ B),Y:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X5) @ Xs)) @ (((coinductive_LCons @ B) @ Y) @ Ys)) = ((X5 = Y) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 2.63/1.58 thf(fact_65_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.63/1.58 thf(fact_66_llast__snoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A3:(set @ A),X5:A]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A3)) => (((lList2170638824_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ X5) @ (coinductive_LNil @ A)))) = X5))))).
% 2.63/1.58 thf(fact_67_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs3:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs3) => (P @ Ys2)))) => (P @ Xs3)))) => (P @ Xs))))).
% 2.63/1.58 thf(fact_68_lappend__assoc, axiom, (! [A:$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)))))).
% 2.63/1.58 thf(fact_69_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_70_lappfin__finT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A3:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A3)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2236698231inlsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_71_lapp__fin__fin__lemma, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_72_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 2.63/1.58 thf(fact_73_finlsts__rec__LNil__def, axiom, (! [A:$tType,B:$tType,F2:((coinductive_llist @ A) > B),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B)))]: (((F2 = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2)) => ((F2 @ (coinductive_LNil @ A)) = C2))))).
% 2.63/1.58 thf(fact_74_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)))).
% 2.63/1.58 thf(fact_75_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 2.63/1.58 thf(fact_76_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.63/1.58 thf(fact_77_lrev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A3:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A3)) => ((P @ (coinductive_LNil @ A)) => ((! [X2:A,Xs3:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs3) @ ((lList2236698231inlsts @ A) @ A3)) => ((P @ Xs3) => ((((member @ A) @ X2) @ A3) => (P @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ X2) @ (coinductive_LNil @ A))))))))) => (P @ Xs))))))).
% 2.63/1.58 thf(fact_78_finlsts__rev__cases, axiom, (! [A:$tType,T:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A3)) => ((T != (coinductive_LNil @ A)) => (~ ((! [A4:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A3)) => ((((member @ A) @ A4) @ A3) => (T != (((coinductive_lappend @ A) @ L2) @ (((coinductive_LCons @ A) @ A4) @ (coinductive_LNil @ A))))))))))))))).
% 2.63/1.58 thf(fact_79_lbutlast__lapp__llast, axiom, (! [A:$tType,L:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList22096119349pslsts @ A) @ A3)) => (L = (((coinductive_lappend @ A) @ ((lList2370560421utlast @ A) @ L)) @ (((coinductive_LCons @ A) @ ((lList2170638824_llast @ A) @ L)) @ (coinductive_LNil @ A)))))))).
% 2.63/1.58 thf(fact_80_lmember__code_I2_J, axiom, (! [A:$tType,X5:A,Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lmember @ A) @ X5) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((X5 = Y) | (((coinductive_lmember @ A) @ X5) @ Ys)))))).
% 2.63/1.58 thf(fact_81_lrev__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A),A2:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => (((lList2281150353e_lrev @ A) @ (((coinductive_LCons @ A) @ A2) @ R)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ R)) @ (((coinductive_LCons @ A) @ A2) @ (coinductive_LNil @ A)))))))).
% 2.63/1.58 thf(fact_82_LList2__Mirabelle__hamjzmohle_Ollast__lappend, axiom, (! [A:$tType,X5:(coinductive_llist @ A),Y:(coinductive_llist @ A),A2:A]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Y) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2170638824_llast @ A) @ (((coinductive_lappend @ A) @ X5) @ (((coinductive_LCons @ A) @ A2) @ Y))) = ((lList2170638824_llast @ A) @ (((coinductive_LCons @ A) @ A2) @ Y)))))))).
% 2.63/1.58 thf(fact_83_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Ys))))))).
% 2.63/1.58 thf(fact_84_llimit__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((P @ (coinductive_LNil @ A)) => ((! [X2:A,Xs3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_LCons @ A) @ X2) @ Xs3)))))) => (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs) => (P @ Ys2)))) => (P @ Xs)) => (P @ Xs))))))).
% 2.63/1.58 thf(fact_85_ex__gt__or__lt, axiom, (! [A:$tType]: ((((condit1656338222tinuum @ A) @ (type2 @ A)) => (! [A2:A]: ((? [B3:A]: (((((ord_less @ A) @ A2) @ B3) | (((ord_less @ A) @ B3) @ A2)))))))))).
% 2.63/1.58 thf(fact_86_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((X5 != Y) => ((~ ((((ord_less @ A) @ X5) @ Y))) => (((ord_less @ A) @ Y) @ X5))))))))).
% 2.63/1.58 thf(fact_87_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B4:A,A2:A]: (((((ord_less @ A) @ B4) @ A2) => (A2 != B4)))))))).
% 2.63/1.58 thf(fact_88_linordered__field__no__ub, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [X:A]: ((? [X1:A]: ((((ord_less @ A) @ X) @ X1))))))))).
% 2.63/1.58 thf(fact_89_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X3:D]: ((top_top @ C)))))))).
% 2.63/1.58 thf(fact_90_lfinite__LCons, axiom, (! [A:$tType,X5:A,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X5) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 2.63/1.58 thf(fact_91_lfinite__code_I2_J, axiom, (! [B:$tType,X5:B,Xs:(coinductive_llist @ B)]: ((((coinductive_lfinite @ B) @ (((coinductive_LCons @ B) @ X5) @ Xs)) = ((coinductive_lfinite @ B) @ Xs))))).
% 2.63/1.58 thf(fact_92_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_93_lfinite__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & ((coinductive_lfinite @ A) @ Ys)))))).
% 2.63/1.58 thf(fact_94_lrev__LNil, axiom, (! [A:$tType]: ((((lList2281150353e_lrev @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_95_lrevT, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ ((lList2281150353e_lrev @ A) @ Xs)) @ ((lList2236698231inlsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_96_lrev__is__lrev__conv, axiom, (! [A:$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))))))).
% 2.63/1.58 thf(fact_97_lrev__lrev__ident, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ ((lList2281150353e_lrev @ A) @ Xs)) = Xs))))).
% 2.63/1.58 thf(fact_98_LNil__is__lrev__conv, axiom, (! [A:$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))))))).
% 2.63/1.58 thf(fact_99_lrev__is__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A))))))).
% 2.63/1.58 thf(fact_100_lrev__lappend, axiom, (! [A:$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)))))))).
% 2.63/1.58 thf(fact_101_top_Onot__eq__extremum, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A2:A]: (((A2 != (top_top @ A)) = (((ord_less @ A) @ A2) @ (top_top @ A))))))))).
% 2.63/1.58 thf(fact_102_top_Oextremum__strict, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A2:A]: ((~ ((((ord_less @ A) @ (top_top @ A)) @ A2))))))))).
% 2.63/1.58 thf(fact_103_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X5:A]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X5) @ Xs)))))).
% 2.63/1.58 thf(fact_104_lfinite__LNil, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_105_lappend__inf, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.63/1.58 thf(fact_106_fin__finite, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.63/1.58 thf(fact_107_finT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.63/1.58 thf(fact_108_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ Ys) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.63/1.58 thf(fact_109_lfinite_Oinducts, axiom, (! [A:$tType,X5:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ X5) => ((P @ (coinductive_LNil @ A)) => ((! [Xs3:(coinductive_llist @ A),X2:A]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_LCons @ A) @ X2) @ Xs3)))))) => (P @ X5))))))).
% 2.63/1.58 thf(fact_110_lfinite_Osimps, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) = (^ [A7:(coinductive_llist @ A)]: (((A7 = (coinductive_LNil @ A)) | (? [Xs4:(coinductive_llist @ A),X3:A]: (((A7 = (((coinductive_LCons @ A) @ X3) @ Xs4)) & ((coinductive_lfinite @ A) @ Xs4))))))))))).
% 2.63/1.58 thf(fact_111_lfinite_Ocases, axiom, (! [A:$tType,A2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ A2) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [Xs3:(coinductive_llist @ A)]: (((? [X2:A]: ((A2 = (((coinductive_LCons @ A) @ X2) @ Xs3)))) => (~ (((coinductive_lfinite @ A) @ Xs3))))))))))))).
% 2.63/1.58 thf(fact_112_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ Xs) => ((P @ (coinductive_LNil @ A)) => ((! [X2:A,Xs3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ X2) @ (coinductive_LNil @ A)))))))) => (P @ Xs))))))).
% 2.63/1.58 thf(fact_113_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F2:(B > A),B4:B,C2:B]: (((A2 = (F2 @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X2:B,Y2:B]: (((((ord_less @ B) @ X2) @ Y2) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y2))))) => (((ord_less @ A) @ A2) @ (F2 @ C2))))))))))).
% 2.63/1.58 thf(fact_114_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B4:A,F2:(A > B),C2:B]: (((((ord_less @ A) @ A2) @ B4) => (((F2 @ B4) = C2) => ((! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less @ B) @ (F2 @ X2)) @ (F2 @ Y2))))) => (((ord_less @ B) @ (F2 @ A2)) @ C2)))))))))).
% 2.63/1.58 thf(fact_115_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F2:(B > A),B4:B,C2:B]: (((((ord_less @ A) @ A2) @ (F2 @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X2:B,Y2:B]: (((((ord_less @ B) @ X2) @ Y2) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y2))))) => (((ord_less @ A) @ A2) @ (F2 @ C2))))))))))).
% 2.63/1.58 thf(fact_116_order__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B4:A,F2:(A > C),C2:C]: (((((ord_less @ A) @ A2) @ B4) => ((((ord_less @ C) @ (F2 @ B4)) @ C2) => ((! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less @ C) @ (F2 @ X2)) @ (F2 @ Y2))))) => (((ord_less @ C) @ (F2 @ A2)) @ C2)))))))))).
% 2.63/1.58 thf(fact_117_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X5:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X5))))))))).
% 2.63/1.58 thf(fact_118_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X5:A]: ((? [X1:A]: ((((ord_less @ A) @ X5) @ X1))))))))).
% 2.63/1.58 thf(fact_119_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((X5 != Y) => ((~ ((((ord_less @ A) @ X5) @ Y))) => (((ord_less @ A) @ Y) @ X5))))))))).
% 2.63/1.58 thf(fact_120_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((X5 != Y) = ((((ord_less @ A) @ X5) @ Y) | (((ord_less @ A) @ Y) @ X5))))))))).
% 2.63/1.58 thf(fact_121_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B4:A]: (((((ord_less @ A) @ A2) @ B4) => (~ ((((ord_less @ A) @ B4) @ A2)))))))))).
% 2.63/1.58 thf(fact_122_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((((ord_less @ A) @ X5) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X5) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 2.63/1.58 thf(fact_123_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((((ord_less @ A) @ X5) @ Y) => (X5 != Y)))))))).
% 2.63/1.58 thf(fact_124_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((((ord_less @ A) @ X5) @ Y) => (~ ((((ord_less @ A) @ Y) @ X5)))))))))).
% 2.63/1.58 thf(fact_125_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A2:A,B4:A]: (((((ord_less @ A) @ A2) @ B4) => (~ ((((ord_less @ A) @ B4) @ A2)))))))))).
% 2.63/1.58 thf(fact_126_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A,Z3:A]: (((((ord_less @ A) @ X5) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X5) @ Z3))))))))).
% 2.63/1.58 thf(fact_127_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((((ord_less @ A) @ X5) @ Y) | ((X5 = Y) | (((ord_less @ A) @ Y) @ X5))))))))).
% 2.63/1.58 thf(fact_128_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X5:A]: ((~ ((((ord_less @ A) @ X5) @ X5))))))))).
% 2.63/1.58 thf(fact_129_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B4:A,C2:A]: (((A2 = B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 2.63/1.58 thf(fact_130_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B4:A,C2:A]: (((((ord_less @ A) @ A2) @ B4) => ((B4 = C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 2.63/1.58 thf(fact_131_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B4:A,A2:A]: (((((ord_less @ A) @ B4) @ A2) => (~ ((((ord_less @ A) @ A2) @ B4)))))))))).
% 2.63/1.58 thf(fact_132_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((((ord_less @ A) @ X5) @ Y) => (X5 != Y)))))))).
% 2.63/1.58 thf(fact_133_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((((ord_less @ A) @ X5) @ Y) => (~ ((((ord_less @ A) @ Y) @ X5)))))))))).
% 2.63/1.58 thf(fact_134_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A2:A]: (((! [X2:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X2) => (P @ Y3)))) => (P @ X2)))) => (P @ A2)))))))).
% 2.63/1.58 thf(fact_135_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X5:A]: (((~ ((((ord_less @ A) @ Y) @ X5))) => ((~ ((((ord_less @ A) @ X5) @ Y))) = (X5 = Y))))))))).
% 2.63/1.58 thf(fact_136_less__imp__not__eq2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((((ord_less @ A) @ X5) @ Y) => (Y != X5)))))))).
% 2.63/1.58 thf(fact_137_less__imp__triv, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A,P:$o]: (((((ord_less @ A) @ X5) @ Y) => ((((ord_less @ A) @ Y) @ X5) => P)))))))).
% 2.63/1.58 thf(fact_138_linorder__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((~ ((((ord_less @ A) @ X5) @ Y))) => ((X5 != Y) => (((ord_less @ A) @ Y) @ X5))))))))).
% 2.63/1.58 thf(fact_139_dual__order_Oirrefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 2.63/1.58 thf(fact_140_order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B4:A,C2:A]: (((((ord_less @ A) @ A2) @ B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 2.63/1.58 thf(fact_141_less__imp__not__less, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((((ord_less @ A) @ X5) @ Y) => (~ ((((ord_less @ A) @ Y) @ X5)))))))))).
% 2.63/1.58 thf(fact_142_dual__order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B4:A,A2:A,C2:A]: (((((ord_less @ A) @ B4) @ A2) => ((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ A2))))))))).
% 2.63/1.58 thf(fact_143_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X5:A,Y:A]: (((~ ((((ord_less @ A) @ X5) @ Y))) = ((((ord_less @ A) @ Y) @ X5) | (X5 = Y))))))))).
% 2.63/1.58 thf(fact_144_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B4:A]: (((((ord_less @ A) @ A2) @ B4) => (A2 != B4)))))))).
% 2.63/1.58 thf(fact_145_linordered__field__no__lb, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [X:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X))))))))).
% 2.63/1.58 thf(fact_146_iso__tuple__UNIV__I, axiom, (! [A:$tType,X5:A]: ((((member @ A) @ X5) @ (top_top @ (set @ A)))))).
% 2.63/1.58 thf(fact_147_UNIV__I, axiom, (! [A:$tType,X5:A]: ((((member @ A) @ X5) @ (top_top @ (set @ A)))))).
% 2.63/1.58 thf(fact_148_poslsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ (top_top @ (set @ A)))) = (S != (coinductive_LNil @ A)))))).
% 2.63/1.58 thf(fact_149_ltake__fin, axiom, (! [A:$tType,R:(coinductive_llist @ A),I:nat]: ((((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ R) @ I)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))).
% 2.63/1.58 thf(fact_150_ldrop__fin__iffT, axiom, (! [A:$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)))))))).
% 2.63/1.58 thf(fact_151_lstrict__prefix__lappend__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.63/1.58 thf(fact_152_lnull__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lnull @ A) @ Xs) & ((coinductive_lnull @ A) @ Ys)))))).
% 2.63/1.58 thf(fact_153_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))) = ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.63/1.58 thf(fact_154_LList2__Mirabelle__hamjzmohle_Oldrop__LNil, axiom, (! [A:$tType,I:nat]: (((((lList2508575361_ldrop @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_155_LList2__Mirabelle__hamjzmohle_Oltake__LNil, axiom, (! [A:$tType,I:nat]: (((((lList22119844313_ltake @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_156_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.63/1.58 thf(fact_157_ltake__ldrop__id, axiom, (! [A:$tType,X5:(coinductive_llist @ A),I:nat]: (((((coinductive_lappend @ A) @ (((lList22119844313_ltake @ A) @ X5) @ I)) @ (((lList2508575361_ldrop @ A) @ X5) @ I)) = X5)))).
% 2.63/1.58 thf(fact_158_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (~ (((coinductive_lnull @ A) @ Ys)))) => ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.63/1.58 thf(fact_159_lzip_Oexhaust, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((~ ((((coinductive_lnull @ A) @ Xs) | ((coinductive_lnull @ B) @ Ys)))) => (~ (((~ (((coinductive_lnull @ A) @ Xs))) => ((coinductive_lnull @ B) @ Ys)))))))).
% 2.63/1.58 thf(fact_160_llist_Odisc_I2_J, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A)]: ((~ (((coinductive_lnull @ A) @ (((coinductive_LCons @ A) @ X212) @ X222))))))).
% 2.63/1.58 thf(fact_161_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A),X212:A,X222:(coinductive_llist @ A)]: (((Llist = (((coinductive_LCons @ A) @ X212) @ X222)) => (~ (((coinductive_lnull @ A) @ Llist))))))).
% 2.63/1.58 thf(fact_162_not__lnull__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ Xs))) = (? [X3:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X3) @ Xs2)))))))).
% 2.63/1.58 thf(fact_163_lnull__def, axiom, (! [A:$tType]: (((coinductive_lnull @ A) = (^ [Llist2:(coinductive_llist @ A)]: ((Llist2 = (coinductive_LNil @ A)))))))).
% 2.63/1.58 thf(fact_164_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Llist) => (Llist = (coinductive_LNil @ A)))))).
% 2.63/1.58 thf(fact_165_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: (((Llist = (coinductive_LNil @ A)) => ((coinductive_lnull @ A) @ Llist))))).
% 2.63/1.58 thf(fact_166_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coinductive_lnull @ A) @ (coinductive_LNil @ A))))).
% 2.63/1.58 thf(fact_167_lappend__lnull2, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.63/1.58 thf(fact_168_lappend__lnull1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Ys))))).
% 2.63/1.58 thf(fact_169_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))))).
% 2.63/1.58 thf(fact_170_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))) => (~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))))))).
% 2.63/1.58 thf(fact_171_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.63/1.58 thf(fact_172_drop__nonLNil, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: ((((((lList2508575361_ldrop @ A) @ T) @ I) != (coinductive_LNil @ A)) => (T != (coinductive_LNil @ A)))))).
% 2.63/1.58 thf(fact_173_ldrop__finT, axiom, (! [A:$tType,T:(coinductive_llist @ A),A3:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList2236698231inlsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_174_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A))))))).
% 2.63/1.58 thf(fact_175_Coinductive__List_Ollast__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X5:A]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X5) @ Xs)) = X5)) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X5) @ Xs)) = ((coinductive_llast @ A) @ Xs))))))).
% 2.63/1.58 thf(fact_176_UNIV__eq__I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X2:A]: ((((member @ A) @ X2) @ A3))) => ((top_top @ (set @ A)) = A3))))).
% 2.63/1.58 thf(fact_177_UNIV__witness, axiom, (! [A:$tType]: ((? [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A)))))))).
% 2.63/1.58 thf(fact_178_ltake__lappend__llength, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => ((((lList22119844313_ltake @ A) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21232602520length @ A) @ R)) = R))))).
% 2.63/1.58 thf(fact_179_llength__drop__take, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat]: ((((((lList2508575361_ldrop @ A) @ T) @ I) != (coinductive_LNil @ A)) => (((lList21232602520length @ A) @ (((lList22119844313_ltake @ A) @ T) @ I)) = I))))).
% 2.63/1.58 thf(fact_180_lapp__suff__llength, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => ((((lList2508575361_ldrop @ A) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21232602520length @ A) @ R)) = S))))).
% 2.63/1.58 thf(fact_181_top1I, axiom, (! [A:$tType,X5:A]: (((top_top @ (A > $o)) @ X5)))).
% 2.63/1.58 thf(fact_182_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A))))))))).
% 2.63/1.58 thf(fact_183_top__conj_I1_J, axiom, (! [A:$tType,X5:A,P:$o]: (((((top_top @ (A > $o)) @ X5) & P) = P)))).
% 2.63/1.58 thf(fact_184_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X5:A]: (((P & ((top_top @ (A > $o)) @ X5)) = P)))).
% 2.63/1.58 thf(fact_185_Coinductive__List_Ollast__lappend, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Ys) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Xs))) & ((~ (((coinductive_lnull @ A) @ Ys))) => ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Ys))) & ((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (undefined @ A))))))))).
% 2.63/1.58 thf(fact_186_LList2__Mirabelle__hamjzmohle_Ollength__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A),A2:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => (((lList21232602520length @ A) @ (((coinductive_LCons @ A) @ A2) @ R)) = (suc @ ((lList21232602520length @ A) @ R))))))).
% 2.63/1.58 thf(fact_187_llength__take, axiom, (! [A:$tType,T:(coinductive_llist @ A),A3:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A3)) => (((lList21232602520length @ A) @ (((lList22119844313_ltake @ A) @ T) @ I)) = I))))).
% 2.63/1.58 thf(fact_188_lapp__inf, axiom, (! [A:$tType,S:(coinductive_llist @ A),A3:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A3)) => ((((coinductive_lappend @ A) @ S) @ T) = S))))).
% 2.63/1.58 thf(fact_189_notfin__inf, axiom, (! [A:$tType,X5:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X5) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.63/1.58 thf(fact_190_notinf__fin, axiom, (! [A:$tType,X5:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X5) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.63/1.58 thf(fact_191_ldrop__inf__iffT, axiom, (! [A:$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)))))))).
% 2.63/1.58 thf(fact_192_LList2__Mirabelle__hamjzmohle_Ollast__LNil, axiom, (! [B:$tType]: ((((lList2170638824_llast @ B) @ (coinductive_LNil @ B)) = (undefined @ B))))).
% 2.63/1.58 thf(fact_193_ldrop__infT, axiom, (! [A:$tType,T:(coinductive_llist @ A),A3:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList21612149805nflsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_194_inflstsI2, axiom, (! [A:$tType,A2:A,A3:(set @ A),T:(coinductive_llist @ A)]: (((((member @ A) @ A2) @ A3) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A2) @ T)) @ ((lList21612149805nflsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_195_inflsts__cases, axiom, (! [A:$tType,S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A3)) => (~ ((! [A4:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList21612149805nflsts @ A) @ A3)) => ((((member @ A) @ A4) @ A3) => (S != (((coinductive_LCons @ A) @ A4) @ L2)))))))))))).
% 2.63/1.58 thf(fact_196_infT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.63/1.58 thf(fact_197_Coinductive__List_Ollast__LNil, axiom, (! [A:$tType]: ((((coinductive_llast @ A) @ (coinductive_LNil @ A)) = (undefined @ A))))).
% 2.63/1.58 thf(fact_198_llast__linfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ Xs) = (undefined @ A)))))).
% 2.63/1.58 thf(fact_199_ltake__LCons__Suc, axiom, (! [A:$tType,A2:A,L:(coinductive_llist @ A),I:nat]: (((((lList22119844313_ltake @ A) @ (((coinductive_LCons @ A) @ A2) @ L)) @ (suc @ I)) = (((coinductive_LCons @ A) @ A2) @ (((lList22119844313_ltake @ A) @ L) @ I)))))).
% 2.63/1.58 thf(fact_200_fin__inf__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.63/1.58 thf(fact_201_app__invT, axiom, (! [A:$tType,R:(coinductive_llist @ A),A3:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) => ((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_202_lapp__infT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A3)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A3))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_203_lapp__inv2T, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A3)) => (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A3))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_204_lapp__fin__infT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A3:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A3)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList21612149805nflsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_205_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [F2:(nat > A),N:nat,M:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F2 @ N2)) @ (F2 @ (suc @ N2))))) => ((((ord_less @ A) @ (F2 @ N)) @ (F2 @ M)) = (((ord_less @ nat) @ N) @ M))))))))).
% 2.63/1.58 thf(fact_206_lift__Suc__mono__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [F2:(nat > A),N:nat,N3:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F2 @ N2)) @ (F2 @ (suc @ N2))))) => ((((ord_less @ nat) @ N) @ N3) => (((ord_less @ A) @ (F2 @ N)) @ (F2 @ N3)))))))))).
% 2.63/1.58 thf(fact_207_inflstsI, axiom, (! [A:$tType,X5:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2435255213lllsts @ A) @ A3)) => ((~ ((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ X5) @ ((lList21612149805nflsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_208_lapp__allT__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A3)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A3)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A3))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_209_alllsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ (top_top @ (set @ A))))))).
% 2.63/1.58 thf(fact_210_LConsE, axiom, (! [A:$tType,X5:A,Xs:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X5) @ Xs)) @ ((lList2435255213lllsts @ A) @ A3)) = ((((member @ A) @ X5) @ A3) & (((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2435255213lllsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_211_take__fin, axiom, (! [A:$tType,T:(coinductive_llist @ A),A3:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ T) @ I)) @ ((lList2236698231inlsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_212_poslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ A3)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A3)) & (S != (coinductive_LNil @ A))))))).
% 2.63/1.58 thf(fact_213_alllsts_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X5:(coinductive_llist @ A),A3:(set @ A)]: (((X4 @ X5) => ((! [X2:(coinductive_llist @ A)]: (((X4 @ X2) => ((X2 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A5:A]: (((X2 = (((coinductive_LCons @ A) @ A5) @ L3)) & (((X4 @ L3) | (((member @ (coinductive_llist @ A)) @ L3) @ ((lList2435255213lllsts @ A) @ A3))) & (((member @ A) @ A5) @ A3))))))))) => (((member @ (coinductive_llist @ A)) @ X5) @ ((lList2435255213lllsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_214_alllsts_Osimps, axiom, (! [A:$tType,A2:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A2) @ ((lList2435255213lllsts @ A) @ A3)) = ((A2 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A7:A]: (((A2 = (((coinductive_LCons @ A) @ A7) @ L4)) & ((((member @ (coinductive_llist @ A)) @ L4) @ ((lList2435255213lllsts @ A) @ A3)) & (((member @ A) @ A7) @ A3)))))))))).
% 2.63/1.58 thf(fact_215_alllsts_Ocases, axiom, (! [A:$tType,A2:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A2) @ ((lList2435255213lllsts @ A) @ A3)) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A4:A]: (((A2 = (((coinductive_LCons @ A) @ A4) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2435255213lllsts @ A) @ A3)) => (~ ((((member @ A) @ A4) @ A3)))))))))))))).
% 2.63/1.58 thf(fact_216_ldropT, axiom, (! [A:$tType,T:(coinductive_llist @ A),A3:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList2435255213lllsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_217_alllsts_OLCons__all, axiom, (! [A:$tType,L:(coinductive_llist @ A),A3:(set @ A),A2:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2435255213lllsts @ A) @ A3)) => ((((member @ A) @ A2) @ A3) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A2) @ L)) @ ((lList2435255213lllsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_218_alllsts_OLNil__all, axiom, (! [A:$tType,A3:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2435255213lllsts @ A) @ A3))))).
% 2.63/1.58 thf(fact_219_lappT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A3:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A3)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2435255213lllsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_220_lapp__all__invT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2435255213lllsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_221_finite__lemma, axiom, (! [A:$tType,X5:(coinductive_llist @ A),A3:(set @ A),B5:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ A3)) => ((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2435255213lllsts @ A) @ B5)) => (((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ B5))))))).
% 2.63/1.58 thf(fact_222_finsubsetall, axiom, (! [A:$tType,X5:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ X5) @ ((lList2435255213lllsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_223_infsubsetall, axiom, (! [A:$tType,X5:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList21612149805nflsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ X5) @ ((lList2435255213lllsts @ A) @ A3)))))).
% 2.63/1.58 thf(fact_224_alllstsE, axiom, (! [A:$tType,X5:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2435255213lllsts @ A) @ A3)) => ((~ ((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ A3)))) => (((member @ (coinductive_llist @ A)) @ X5) @ ((lList21612149805nflsts @ A) @ A3))))))).
% 2.63/1.58 thf(fact_225_inflstsE, axiom, (! [A:$tType,X5:(coinductive_llist @ A),A3:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList21612149805nflsts @ A) @ A3)) => (~ (((((member @ (coinductive_llist @ A)) @ X5) @ ((lList2435255213lllsts @ A) @ A3)) => (((member @ (coinductive_llist @ A)) @ X5) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))))))).
% 2.63/1.58 thf(fact_226_inflsts__def, axiom, (! [A:$tType]: (((lList21612149805nflsts @ A) = (^ [A6:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A6)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))))).
% 2.63/1.58 thf(fact_227_fin__Un__inf, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A3)) @ ((lList21612149805nflsts @ A) @ A3)) = ((lList2435255213lllsts @ A) @ A3))))).
% 2.63/1.58 thf(fact_228_Un__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B5)) = ((((member @ A) @ C2) @ A3) | (((member @ A) @ C2) @ B5)))))).
% 2.63/1.58 thf(fact_229_UnCI, axiom, (! [A:$tType,C2:A,B5:(set @ A),A3:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B5))) => (((member @ A) @ C2) @ A3)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B5)))))).
% 2.63/1.58 thf(fact_230_Diff__idemp, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A3) @ B5)) @ B5) = (((minus_minus @ (set @ A)) @ A3) @ B5))))).
% 2.63/1.58 thf(fact_231_Diff__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A3) @ B5)) = ((((member @ A) @ C2) @ A3) & (~ ((((member @ A) @ C2) @ B5)))))))).
% 2.63/1.58 thf(fact_232_DiffI, axiom, (! [A:$tType,C2:A,A3:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ A3) => ((~ ((((member @ A) @ C2) @ B5))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A3) @ B5))))))).
% 2.63/1.58 thf(fact_233_Un__Diff__cancel2, axiom, (! [A:$tType,B5:(set @ A),A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ B5) @ A3)) @ A3) = (((sup_sup @ (set @ A)) @ B5) @ A3))))).
% 2.63/1.58 thf(fact_234_Un__Diff__cancel, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((minus_minus @ (set @ A)) @ B5) @ A3)) = (((sup_sup @ (set @ A)) @ A3) @ B5))))).
% 2.63/1.58 thf(fact_235_Un__UNIV__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.63/1.58 thf(fact_236_Un__UNIV__left, axiom, (! [A:$tType,B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ (top_top @ (set @ A))) @ B5) = (top_top @ (set @ A)))))).
% 2.63/1.58 thf(fact_237_Un__left__commute, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B5) @ C3)) = (((sup_sup @ (set @ A)) @ B5) @ (((sup_sup @ (set @ A)) @ A3) @ C3)))))).
% 2.63/1.58 thf(fact_238_Un__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B5)) = (((sup_sup @ (set @ A)) @ A3) @ B5))))).
% 2.63/1.58 thf(fact_239_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((sup_sup @ (set @ A)) @ B6) @ A6))))))).
% 2.63/1.58 thf(fact_240_Un__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ A3) = A3)))).
% 2.63/1.58 thf(fact_241_Un__assoc, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B5)) @ C3) = (((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B5) @ C3)))))).
% 2.63/1.58 thf(fact_242_ball__Un, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ (((sup_sup @ (set @ A)) @ A3) @ B5)) => (P @ X3)))) = ((! [X3:A]: (((((member @ A) @ X3) @ A3) => (P @ X3)))) & (! [X3:A]: (((((member @ A) @ X3) @ B5) => (P @ X3))))))))).
% 2.63/1.58 thf(fact_243_Un__Diff, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B5)) @ C3) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A3) @ C3)) @ (((minus_minus @ (set @ A)) @ B5) @ C3)))))).
% 2.63/1.58 thf(fact_244_bex__Un, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ (((sup_sup @ (set @ A)) @ A3) @ B5)) & (P @ X3)))) = ((? [X3:A]: (((((member @ A) @ X3) @ A3) & (P @ X3)))) | (? [X3:A]: (((((member @ A) @ X3) @ B5) & (P @ X3))))))))).
% 2.63/1.58 thf(fact_245_DiffD2, axiom, (! [A:$tType,C2:A,A3:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A3) @ B5)) => (~ ((((member @ A) @ C2) @ B5))))))).
% 2.63/1.58 thf(fact_246_DiffD1, axiom, (! [A:$tType,C2:A,A3:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A3) @ B5)) => (((member @ A) @ C2) @ A3))))).
% 2.63/1.58 thf(fact_247_DiffE, axiom, (! [A:$tType,C2:A,A3:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A3) @ B5)) => (~ (((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B5)))))))).
% 2.63/1.58 thf(fact_248_UnI2, axiom, (! [A:$tType,C2:A,B5:(set @ A),A3:(set @ A)]: (((((member @ A) @ C2) @ B5) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B5)))))).
% 2.63/1.58 thf(fact_249_UnI1, axiom, (! [A:$tType,C2:A,A3:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B5)))))).
% 2.63/1.58 thf(fact_250_UnE, axiom, (! [A:$tType,C2:A,A3:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B5)) => ((~ ((((member @ A) @ C2) @ A3))) => (((member @ A) @ C2) @ B5)))))).
% 2.63/1.58 thf(fact_251_psubset__imp__ex__mem, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((((ord_less @ (set @ A)) @ A3) @ B5) => (? [B3:A]: ((((member @ A) @ B3) @ (((minus_minus @ (set @ A)) @ B5) @ A3)))))))).
% 2.63/1.58 thf(fact_252_sup__top__right, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X5:A]: (((((sup_sup @ A) @ X5) @ (top_top @ A)) = (top_top @ A)))))))).
% 2.63/1.58 thf(fact_253_sup__top__left, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X5:A]: (((((sup_sup @ A) @ (top_top @ A)) @ X5) = (top_top @ A)))))))).
% 2.63/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.63/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: (((bounded_lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.63/1.58 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.63/1.58 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))))))).
% 2.63/1.58 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A8:$tType,A9:$tType]: ((((order_top @ A9) @ (type2 @ A9)) => ((order_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.63/1.58 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.63/1.58 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A9) @ (type2 @ A9)) => ((order @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.63/1.58 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.63/1.58 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.63/1.58 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, ((wellorder @ nat) @ (type2 @ nat))).
% 2.63/1.58 thf(tcon_Nat_Onat___Orderings_Opreorder_3, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.63/1.58 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.63/1.58 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, ((no_top @ nat) @ (type2 @ nat))).
% 2.63/1.58 thf(tcon_Nat_Onat___Orderings_Oorder_4, axiom, ((order @ nat) @ (type2 @ nat))).
% 2.63/1.58 thf(tcon_Nat_Onat___Orderings_Oord_5, axiom, ((ord @ nat) @ (type2 @ nat))).
% 2.63/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_6, axiom, (! [A8:$tType]: (((bounded_lattice_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.63/1.58 thf(tcon_Set_Oset___Orderings_Oorder__top_7, axiom, (! [A8:$tType]: (((order_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.63/1.58 thf(tcon_Set_Oset___Orderings_Opreorder_8, axiom, (! [A8:$tType]: (((preorder @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.63/1.58 thf(tcon_Set_Oset___Orderings_Oorder_9, axiom, (! [A8:$tType]: (((order @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.63/1.58 thf(tcon_Set_Oset___Orderings_Otop_10, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.63/1.58 thf(tcon_Set_Oset___Orderings_Oord_11, axiom, (! [A8:$tType]: (((ord @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.63/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_12, axiom, ((bounded_lattice_top @ $o) @ (type2 @ $o))).
% 2.63/1.58 thf(tcon_HOL_Obool___Orderings_Oorder__top_13, axiom, ((order_top @ $o) @ (type2 @ $o))).
% 2.63/1.58 thf(tcon_HOL_Obool___Orderings_Opreorder_14, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.63/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder_15, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.63/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_16, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.63/1.58 thf(tcon_HOL_Obool___Orderings_Otop_17, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.63/1.58 thf(tcon_HOL_Obool___Orderings_Oord_18, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.63/1.58 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_19, axiom, (! [A8:$tType]: (((preorder @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.63/1.58 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_20, axiom, (! [A8:$tType]: (((order @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.63/1.58 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_21, axiom, (! [A8:$tType]: (((ord @ (coinductive_llist @ A8)) @ (type2 @ (coinductive_llist @ A8)))))).
% 2.63/1.58 thf(conj_0, conjecture, (~ ((((ord_less @ (coinductive_llist @ a)) @ r) @ (coinductive_LNil @ a))))).
% 2.63/1.58 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.3Q38gBiG4C/DTF2DTF5656.p
% 2.63/1.58 ------------------------
% 2.82/1.63 ---- Cleaned THF ---
% 2.82/1.63 thf(ty_t_Coinductive__List_Ollist,type,
% 2.82/1.63 coinductive_llist: $tType > $tType ).
% 2.82/1.63
% 2.82/1.63 thf(ty_t_Set_Oset,type,
% 2.82/1.63 set: $tType > $tType ).
% 2.82/1.63
% 2.82/1.63 thf(ty_t_Nat_Onat,type,
% 2.82/1.63 nat: $tType ).
% 2.82/1.63
% 2.82/1.63 thf(ty_t_itself,type,
% 2.82/1.63 itself: $tType > $tType ).
% 2.82/1.63
% 2.82/1.63 thf(ty_tf_a,type,
% 2.82/1.63 a: $tType ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.82/1.63 bounded_lattice:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_HOL_Otype,type,
% 2.82/1.63 type:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Oord,type,
% 2.82/1.63 ord:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Otop,type,
% 2.82/1.63 top:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Oorder,type,
% 2.82/1.63 order:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Ono__bot,type,
% 2.82/1.63 no_bot:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Ono__top,type,
% 2.82/1.63 no_top:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Olinorder,type,
% 2.82/1.63 linorder:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Opreorder,type,
% 2.82/1.63 preorder:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Oorder__top,type,
% 2.82/1.63 order_top:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Owellorder,type,
% 2.82/1.63 wellorder:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Orderings_Odense__order,type,
% 2.82/1.63 dense_order:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.82/1.63 linordered_idom:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Fields_Olinordered__field,type,
% 2.82/1.63 linordered_field:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 2.82/1.63 bounded_lattice_top:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 2.82/1.63 condit1656338222tinuum:
% 2.82/1.63 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.82/1.63 coindu328551480prefix:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Olappend,type,
% 2.82/1.63 coinductive_lappend:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Olfinite,type,
% 2.82/1.63 coinductive_lfinite:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Ollast,type,
% 2.82/1.63 coinductive_llast:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.82/1.63 coinductive_LCons:
% 2.82/1.63 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.82/1.63 coinductive_LNil:
% 2.82/1.63 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 2.82/1.63 coinductive_lnull:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Olmember,type,
% 2.82/1.63 coinductive_lmember:
% 2.82/1.63 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.82/1.63 coindu1478340336prefix:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.82/1.63 minus_minus:
% 2.82/1.63 !>[A: $tType] : ( A > A > A ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_HOL_Oundefined,type,
% 2.82/1.63 undefined:
% 2.82/1.63 !>[A: $tType] : A ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 2.82/1.63 lList2435255213lllsts:
% 2.82/1.63 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp,type,
% 2.82/1.63 lList21511617539llstsp:
% 2.82/1.63 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 2.82/1.63 lList2236698231inlsts:
% 2.82/1.63 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 2.82/1.63 lList21916056377ts_rec:
% 2.82/1.63 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp,type,
% 2.82/1.63 lList2860480441nlstsp:
% 2.82/1.63 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 2.82/1.63 lList22096119349pslsts:
% 2.82/1.63 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 2.82/1.63 lList21612149805nflsts:
% 2.82/1.63 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 2.82/1.63 lList2370560421utlast:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 2.82/1.63 lList2508575361_ldrop:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 2.82/1.63 lList2170638824_llast:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 2.82/1.63 lList21232602520length:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 2.82/1.63 lList2281150353e_lrev:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 2.82/1.63 lList22119844313_ltake:
% 2.82/1.63 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 2.82/1.63 lList21148268032oslsts:
% 2.82/1.63 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.82/1.63 sup_sup:
% 2.82/1.63 !>[A: $tType] : ( A > A > A ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Nat_OSuc,type,
% 2.82/1.63 suc: nat > nat ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.82/1.63 ord_less:
% 2.82/1.63 !>[A: $tType] : ( A > A > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.82/1.63 top_top:
% 2.82/1.63 !>[A: $tType] : A ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Pure_Otype,type,
% 2.82/1.63 type2:
% 2.82/1.63 !>[A: $tType] : ( itself @ A ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_Set_OCollect,type,
% 2.82/1.63 collect:
% 2.82/1.63 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_c_member,type,
% 2.82/1.63 member:
% 2.82/1.63 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(sy_v_r,type,
% 2.82/1.63 r: coinductive_llist @ a ).
% 2.82/1.63
% 2.82/1.63 thf(fact_0_lbutlast__LNil,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_1_LNil__less__LCons,axiom,
% 2.82/1.63 ! [A: $tType,A2: A,T: coinductive_llist @ A] : ( ord_less @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ A @ A2 @ T ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_2_minf_I11_J,axiom,
% 2.82/1.63 ! [C: $tType,D: $tType] :
% 2.82/1.63 ( ( ord @ C @ ( type2 @ C ) )
% 2.82/1.63 => ! [F: D] :
% 2.82/1.63 ? [Z: C] :
% 2.82/1.63 ! [X: C] :
% 2.82/1.63 ( ( ord_less @ C @ X @ Z )
% 2.82/1.63 => ( F = F ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_3_minf_I7_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [T: A] :
% 2.82/1.63 ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ X @ Z )
% 2.82/1.63 => ~ ( ord_less @ A @ T @ X ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_4_minf_I5_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [T: A] :
% 2.82/1.63 ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ X @ Z )
% 2.82/1.63 => ( ord_less @ A @ X @ T ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_5_minf_I4_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [T: A] :
% 2.82/1.63 ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ X @ Z )
% 2.82/1.63 => ( X != T ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_6_minf_I3_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [T: A] :
% 2.82/1.63 ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ X @ Z )
% 2.82/1.63 => ( X != T ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_7_minf_I2_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.82/1.63 ( ? [Z2: A] :
% 2.82/1.63 ! [X2: A] :
% 2.82/1.63 ( ( ord_less @ A @ X2 @ Z2 )
% 2.82/1.63 => ( ( P @ X2 )
% 2.82/1.63 = ( P2 @ X2 ) ) )
% 2.82/1.63 => ( ? [Z2: A] :
% 2.82/1.63 ! [X2: A] :
% 2.82/1.63 ( ( ord_less @ A @ X2 @ Z2 )
% 2.82/1.63 => ( ( Q @ X2 )
% 2.82/1.63 = ( Q2 @ X2 ) ) )
% 2.82/1.63 => ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ X @ Z )
% 2.82/1.63 => ( ( ( P @ X )
% 2.82/1.63 | ( Q @ X ) )
% 2.82/1.63 = ( ( P2 @ X )
% 2.82/1.63 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_8_minf_I1_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.82/1.63 ( ? [Z2: A] :
% 2.82/1.63 ! [X2: A] :
% 2.82/1.63 ( ( ord_less @ A @ X2 @ Z2 )
% 2.82/1.63 => ( ( P @ X2 )
% 2.82/1.63 = ( P2 @ X2 ) ) )
% 2.82/1.63 => ( ? [Z2: A] :
% 2.82/1.63 ! [X2: A] :
% 2.82/1.63 ( ( ord_less @ A @ X2 @ Z2 )
% 2.82/1.63 => ( ( Q @ X2 )
% 2.82/1.63 = ( Q2 @ X2 ) ) )
% 2.82/1.63 => ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ X @ Z )
% 2.82/1.63 => ( ( ( P @ X )
% 2.82/1.63 & ( Q @ X ) )
% 2.82/1.63 = ( ( P2 @ X )
% 2.82/1.63 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_9_pinf_I11_J,axiom,
% 2.82/1.63 ! [C: $tType,D: $tType] :
% 2.82/1.63 ( ( ord @ C @ ( type2 @ C ) )
% 2.82/1.63 => ! [F: D] :
% 2.82/1.63 ? [Z: C] :
% 2.82/1.63 ! [X: C] :
% 2.82/1.63 ( ( ord_less @ C @ Z @ X )
% 2.82/1.63 => ( F = F ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_10_pinf_I7_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [T: A] :
% 2.82/1.63 ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z @ X )
% 2.82/1.63 => ( ord_less @ A @ T @ X ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_11_pinf_I5_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [T: A] :
% 2.82/1.63 ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z @ X )
% 2.82/1.63 => ~ ( ord_less @ A @ X @ T ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_12_llistE,axiom,
% 2.82/1.63 ! [A: $tType,Y: coinductive_llist @ A] :
% 2.82/1.63 ( ( Y
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ~ ! [X21: A,X22: coinductive_llist @ A] :
% 2.82/1.63 ( Y
% 2.82/1.63 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_13_pinf_I1_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.82/1.63 ( ? [Z2: A] :
% 2.82/1.63 ! [X2: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z2 @ X2 )
% 2.82/1.63 => ( ( P @ X2 )
% 2.82/1.63 = ( P2 @ X2 ) ) )
% 2.82/1.63 => ( ? [Z2: A] :
% 2.82/1.63 ! [X2: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z2 @ X2 )
% 2.82/1.63 => ( ( Q @ X2 )
% 2.82/1.63 = ( Q2 @ X2 ) ) )
% 2.82/1.63 => ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z @ X )
% 2.82/1.63 => ( ( ( P @ X )
% 2.82/1.63 & ( Q @ X ) )
% 2.82/1.63 = ( ( P2 @ X )
% 2.82/1.63 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_14_pinf_I2_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.82/1.63 ( ? [Z2: A] :
% 2.82/1.63 ! [X2: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z2 @ X2 )
% 2.82/1.63 => ( ( P @ X2 )
% 2.82/1.63 = ( P2 @ X2 ) ) )
% 2.82/1.63 => ( ? [Z2: A] :
% 2.82/1.63 ! [X2: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z2 @ X2 )
% 2.82/1.63 => ( ( Q @ X2 )
% 2.82/1.63 = ( Q2 @ X2 ) ) )
% 2.82/1.63 => ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z @ X )
% 2.82/1.63 => ( ( ( P @ X )
% 2.82/1.63 | ( Q @ X ) )
% 2.82/1.63 = ( ( P2 @ X )
% 2.82/1.63 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_15_pinf_I3_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [T: A] :
% 2.82/1.63 ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z @ X )
% 2.82/1.63 => ( X != T ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_16_pinf_I4_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [T: A] :
% 2.82/1.63 ? [Z: A] :
% 2.82/1.63 ! [X: A] :
% 2.82/1.63 ( ( ord_less @ A @ Z @ X )
% 2.82/1.63 => ( X != T ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_17_llist_Oinject,axiom,
% 2.82/1.63 ! [A: $tType,X212: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.82/1.63 ( ( ( coinductive_LCons @ A @ X212 @ X222 )
% 2.82/1.63 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.82/1.63 = ( ( X212 = Y21 )
% 2.82/1.63 & ( X222 = Y22 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_18_neq__LNil__conv,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( Xs
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( ? [X3: A,Xs2: coinductive_llist @ A] :
% 2.82/1.63 ( Xs
% 2.82/1.63 = ( coinductive_LCons @ A @ X3 @ Xs2 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_19_llist_Odistinct_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_LNil @ A )
% 2.82/1.63 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_20_fps__induct,axiom,
% 2.82/1.63 ! [A: $tType,L: coinductive_llist @ A,A3: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A3 ) )
% 2.82/1.63 => ( ! [A4: A] :
% 2.82/1.63 ( ( member @ A @ A4 @ A3 )
% 2.82/1.63 => ( P @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) )
% 2.82/1.63 => ( ! [A4: A,L2: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList22096119349pslsts @ A @ A3 ) )
% 2.82/1.63 => ( ( P @ L2 )
% 2.82/1.63 => ( ( member @ A @ A4 @ A3 )
% 2.82/1.63 => ( P @ ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) )
% 2.82/1.63 => ( P @ L ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_21_lbutlast__LCons,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,A2: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( ( R
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A2 @ R ) )
% 2.82/1.63 = ( coinductive_LNil @ A ) ) )
% 2.82/1.63 & ( ( R
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A2 @ R ) )
% 2.82/1.63 = ( coinductive_LCons @ A @ A2 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_22_alllstsp_Ocoinduct,axiom,
% 2.82/1.63 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X5: coinductive_llist @ A,A3: A > $o] :
% 2.82/1.63 ( ( X4 @ X5 )
% 2.82/1.63 => ( ! [X2: coinductive_llist @ A] :
% 2.82/1.63 ( ( X4 @ X2 )
% 2.82/1.63 => ( ( X2
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 | ? [L3: coinductive_llist @ A,A5: A] :
% 2.82/1.63 ( ( X2
% 2.82/1.63 = ( coinductive_LCons @ A @ A5 @ L3 ) )
% 2.82/1.63 & ( ( X4 @ L3 )
% 2.82/1.63 | ( lList21511617539llstsp @ A @ A3 @ L3 ) )
% 2.82/1.63 & ( A3 @ A5 ) ) ) )
% 2.82/1.63 => ( lList21511617539llstsp @ A @ A3 @ X5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_23_finlstsp_Oinducts,axiom,
% 2.82/1.63 ! [A: $tType,A3: A > $o,X5: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.82/1.63 ( ( lList2860480441nlstsp @ A @ A3 @ X5 )
% 2.82/1.63 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ! [L2: coinductive_llist @ A,A4: A] :
% 2.82/1.63 ( ( lList2860480441nlstsp @ A @ A3 @ L2 )
% 2.82/1.63 => ( ( P @ L2 )
% 2.82/1.63 => ( ( A3 @ A4 )
% 2.82/1.63 => ( P @ ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) )
% 2.82/1.63 => ( P @ X5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_24_finlstsp_Osimps,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( lList2860480441nlstsp @ A )
% 2.82/1.63 = ( ^ [A6: A > $o,A7: coinductive_llist @ A] :
% 2.82/1.63 ( ( A7
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 | ? [L4: coinductive_llist @ A,B2: A] :
% 2.82/1.63 ( ( A7
% 2.82/1.63 = ( coinductive_LCons @ A @ B2 @ L4 ) )
% 2.82/1.63 & ( lList2860480441nlstsp @ A @ A6 @ L4 )
% 2.82/1.63 & ( A6 @ B2 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_25_finlstsp_Ocases,axiom,
% 2.82/1.63 ! [A: $tType,A3: A > $o,A2: coinductive_llist @ A] :
% 2.82/1.63 ( ( lList2860480441nlstsp @ A @ A3 @ A2 )
% 2.82/1.63 => ( ( A2
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ~ ! [L2: coinductive_llist @ A,A4: A] :
% 2.82/1.63 ( ( A2
% 2.82/1.63 = ( coinductive_LCons @ A @ A4 @ L2 ) )
% 2.82/1.63 => ( ( lList2860480441nlstsp @ A @ A3 @ L2 )
% 2.82/1.63 => ~ ( A3 @ A4 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_26_alllstsp_Osimps,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( lList21511617539llstsp @ A )
% 2.82/1.63 = ( ^ [A6: A > $o,A7: coinductive_llist @ A] :
% 2.82/1.63 ( ( A7
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 | ? [L4: coinductive_llist @ A,B2: A] :
% 2.82/1.63 ( ( A7
% 2.82/1.63 = ( coinductive_LCons @ A @ B2 @ L4 ) )
% 2.82/1.63 & ( lList21511617539llstsp @ A @ A6 @ L4 )
% 2.82/1.63 & ( A6 @ B2 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_27_alllstsp_Ocases,axiom,
% 2.82/1.63 ! [A: $tType,A3: A > $o,A2: coinductive_llist @ A] :
% 2.82/1.63 ( ( lList21511617539llstsp @ A @ A3 @ A2 )
% 2.82/1.63 => ( ( A2
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ~ ! [L2: coinductive_llist @ A,A4: A] :
% 2.82/1.63 ( ( A2
% 2.82/1.63 = ( coinductive_LCons @ A @ A4 @ L2 ) )
% 2.82/1.63 => ( ( lList21511617539llstsp @ A @ A3 @ L2 )
% 2.82/1.63 => ~ ( A3 @ A4 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_28_llist__less__finT,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( ord_less @ ( coinductive_llist @ A ) @ R @ S )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_29_fpslsts__iff,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A3 ) )
% 2.82/1.63 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 & ( S
% 2.82/1.63 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_30_fpslsts__cases,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A3 ) )
% 2.82/1.63 => ~ ! [A4: A,Rs: coinductive_llist @ A] :
% 2.82/1.63 ( ( R
% 2.82/1.63 = ( coinductive_LCons @ A @ A4 @ Rs ) )
% 2.82/1.63 => ( ( member @ A @ A4 @ A3 )
% 2.82/1.63 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_31_finlsts_OLCons__fin,axiom,
% 2.82/1.63 ! [A: $tType,L: coinductive_llist @ A,A3: set @ A,A2: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ A @ A2 @ A3 )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A2 @ L ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_32_finlsts_OLNil__fin,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A3 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_33_finlstsp_OLCons__fin,axiom,
% 2.82/1.63 ! [A: $tType,A3: A > $o,L: coinductive_llist @ A,A2: A] :
% 2.82/1.63 ( ( lList2860480441nlstsp @ A @ A3 @ L )
% 2.82/1.63 => ( ( A3 @ A2 )
% 2.82/1.63 => ( lList2860480441nlstsp @ A @ A3 @ ( coinductive_LCons @ A @ A2 @ L ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_34_alllstsp_OLCons__all,axiom,
% 2.82/1.63 ! [A: $tType,A3: A > $o,L: coinductive_llist @ A,A2: A] :
% 2.82/1.63 ( ( lList21511617539llstsp @ A @ A3 @ L )
% 2.82/1.63 => ( ( A3 @ A2 )
% 2.82/1.63 => ( lList21511617539llstsp @ A @ A3 @ ( coinductive_LCons @ A @ A2 @ L ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_35_alllstsp_OLNil__all,axiom,
% 2.82/1.63 ! [A: $tType,A3: A > $o] : ( lList21511617539llstsp @ A @ A3 @ ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_36_finlstsp_OLNil__fin,axiom,
% 2.82/1.63 ! [A: $tType,A3: A > $o] : ( lList2860480441nlstsp @ A @ A3 @ ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_37_finlsts_Ocases,axiom,
% 2.82/1.63 ! [A: $tType,A2: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ A2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( A2
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ~ ! [L2: coinductive_llist @ A,A4: A] :
% 2.82/1.63 ( ( A2
% 2.82/1.63 = ( coinductive_LCons @ A @ A4 @ L2 ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ~ ( member @ A @ A4 @ A3 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_38_finlsts_Osimps,axiom,
% 2.82/1.63 ! [A: $tType,A2: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ A2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 = ( ( A2
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 | ? [L4: coinductive_llist @ A,A7: A] :
% 2.82/1.63 ( ( A2
% 2.82/1.63 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 2.82/1.63 & ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 & ( member @ A @ A7 @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_39_finlsts__induct,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ! [L2: coinductive_llist @ A] :
% 2.82/1.63 ( ( L2
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( P @ L2 ) )
% 2.82/1.63 => ( ! [A4: A,L2: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( P @ L2 )
% 2.82/1.63 => ( ( member @ A @ A4 @ A3 )
% 2.82/1.63 => ( P @ ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) )
% 2.82/1.63 => ( P @ X5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_40_finlsts_Oinducts,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ! [L2: coinductive_llist @ A,A4: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( P @ L2 )
% 2.82/1.63 => ( ( member @ A @ A4 @ A3 )
% 2.82/1.63 => ( P @ ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) )
% 2.82/1.63 => ( P @ X5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_41_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 2.82/1.63 ! [B: $tType,R: coinductive_llist @ B,A3: set @ B,A2: B] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A3 ) )
% 2.82/1.63 => ( ( ( R
% 2.82/1.63 = ( coinductive_LNil @ B ) )
% 2.82/1.63 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A2 @ R ) )
% 2.82/1.63 = A2 ) )
% 2.82/1.63 & ( ( R
% 2.82/1.63 != ( coinductive_LNil @ B ) )
% 2.82/1.63 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A2 @ R ) )
% 2.82/1.63 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_42_lbutlast__snoc,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,A3: set @ A,X5: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( lList2370560421utlast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X5 @ ( coinductive_LNil @ A ) ) ) )
% 2.82/1.63 = Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_43_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.82/1.63 = ( ( Xs
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 | ? [Xs2: coinductive_llist @ A] :
% 2.82/1.63 ( ( Xs
% 2.82/1.63 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 2.82/1.63 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_44_lstrict__prefix__code_I3_J,axiom,
% 2.82/1.63 ! [B: $tType,X5: B,Xs: coinductive_llist @ B] :
% 2.82/1.63 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X5 @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_45_mem__Collect__eq,axiom,
% 2.82/1.63 ! [A: $tType,A2: A,P: A > $o] :
% 2.82/1.63 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.82/1.63 = ( P @ A2 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_46_Collect__mem__eq,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A] :
% 2.82/1.63 ( ( collect @ A
% 2.82/1.63 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 2.82/1.63 = A3 ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_47_Collect__cong,axiom,
% 2.82/1.63 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.82/1.63 ( ! [X2: A] :
% 2.82/1.63 ( ( P @ X2 )
% 2.82/1.63 = ( Q @ X2 ) )
% 2.82/1.63 => ( ( collect @ A @ P )
% 2.82/1.63 = ( collect @ A @ Q ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_48_ext,axiom,
% 2.82/1.63 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 2.82/1.63 ( ! [X2: A] :
% 2.82/1.63 ( ( F2 @ X2 )
% 2.82/1.63 = ( G @ X2 ) )
% 2.82/1.63 => ( F2 = G ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_49_lstrict__prefix__code_I2_J,axiom,
% 2.82/1.63 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_50_finlsts__rec__LCons__def,axiom,
% 2.82/1.63 ! [B: $tType,A: $tType,F2: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A3: set @ A,A2: A] :
% 2.82/1.63 ( ( F2
% 2.82/1.63 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( F2 @ ( coinductive_LCons @ A @ A2 @ R ) )
% 2.82/1.63 = ( D2 @ A2 @ R @ ( F2 @ R ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_51_finlsts__rec__LCons,axiom,
% 2.82/1.63 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A3: set @ A,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,A2: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ ( coinductive_LCons @ A @ A2 @ R ) )
% 2.82/1.63 = ( D2 @ A2 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ R ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_52_llast__singleton,axiom,
% 2.82/1.63 ! [A: $tType,X5: A] :
% 2.82/1.63 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X5 @ ( coinductive_LNil @ A ) ) )
% 2.82/1.63 = X5 ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_53_lmember__code_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,X5: A] :
% 2.82/1.63 ~ ( coinductive_lmember @ A @ X5 @ ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_54_lappend__code_I2_J,axiom,
% 2.82/1.63 ! [A: $tType,Xa: A,X5: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X5 ) @ Ys )
% 2.82/1.63 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X5 @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_55_lappend__is__LNil__conv,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.82/1.63 ( ( ( coinductive_lappend @ A @ S @ T )
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( ( S
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 & ( T
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_56_LNil__is__lappend__conv,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.82/1.63 ( ( ( coinductive_LNil @ A )
% 2.82/1.63 = ( coinductive_lappend @ A @ S @ T ) )
% 2.82/1.63 = ( ( S
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 & ( T
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_57_lappend__eq__LNil__iff,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( ( Xs
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 & ( Ys
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_58_LNil__eq__lappend__iff,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( ( coinductive_LNil @ A )
% 2.82/1.63 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.82/1.63 = ( ( Xs
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 & ( Ys
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_59_lappend__LNil2,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.82/1.63 = Xs ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_60_lappend__code_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.82/1.63 = Ys ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_61_same__lappend__eq,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( ( coinductive_lappend @ A @ R @ S )
% 2.82/1.63 = ( coinductive_lappend @ A @ R @ T ) )
% 2.82/1.63 = ( S = T ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_62_lapp__fin__fin__iff,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_63_llast__LCons2,axiom,
% 2.82/1.63 ! [A: $tType,X5: A,Y: A,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X5 @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 2.82/1.63 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_64_lstrict__prefix__code_I4_J,axiom,
% 2.82/1.63 ! [B: $tType,X5: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 2.82/1.63 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X5 @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 2.82/1.63 = ( ( X5 = Y )
% 2.82/1.63 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_65_lstrict__prefix__code_I1_J,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_66_llast__snoc,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,A3: set @ A,X5: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X5 @ ( coinductive_LNil @ A ) ) ) )
% 2.82/1.63 = X5 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_67_llist__less__induct,axiom,
% 2.82/1.63 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ! [Xs3: coinductive_llist @ A] :
% 2.82/1.63 ( ! [Ys2: coinductive_llist @ A] :
% 2.82/1.63 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 2.82/1.63 => ( P @ Ys2 ) )
% 2.82/1.63 => ( P @ Xs3 ) )
% 2.82/1.63 => ( P @ Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_68_lappend__assoc,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 2.82/1.63 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_69_lappend__LNil__LNil,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_70_lappfin__finT,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A,T: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_71_lapp__fin__fin__lemma,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_72_lappend__snocL1__conv__LCons2,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.82/1.63 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_73_finlsts__rec__LNil__def,axiom,
% 2.82/1.63 ! [A: $tType,B: $tType,F2: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 2.82/1.63 ( ( F2
% 2.82/1.63 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 2.82/1.63 => ( ( F2 @ ( coinductive_LNil @ A ) )
% 2.82/1.63 = C2 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_74_finlsts__rec__LNil,axiom,
% 2.82/1.63 ! [B: $tType,A: $tType,C2: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 2.82/1.63 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D2 @ ( coinductive_LNil @ B ) )
% 2.82/1.63 = C2 ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_75_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( Xs
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_76_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_77_lrev__induct,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,A3: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ! [X2: A,Xs3: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( P @ Xs3 )
% 2.82/1.63 => ( ( member @ A @ X2 @ A3 )
% 2.82/1.63 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 2.82/1.63 => ( P @ Xs ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_78_finlsts__rev__cases,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( T
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ~ ! [A4: A,L2: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ A @ A4 @ A3 )
% 2.82/1.63 => ( T
% 2.82/1.63 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_79_lbutlast__lapp__llast,axiom,
% 2.82/1.63 ! [A: $tType,L: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A3 ) )
% 2.82/1.63 => ( L
% 2.82/1.63 = ( coinductive_lappend @ A @ ( lList2370560421utlast @ A @ L ) @ ( coinductive_LCons @ A @ ( lList2170638824_llast @ A @ L ) @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_80_lmember__code_I2_J,axiom,
% 2.82/1.63 ! [A: $tType,X5: A,Y: A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lmember @ A @ X5 @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.82/1.63 = ( ( X5 = Y )
% 2.82/1.63 | ( coinductive_lmember @ A @ X5 @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_81_lrev__LCons,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,A2: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A2 @ R ) )
% 2.82/1.63 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A2 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_82_LList2__Mirabelle__hamjzmohle_Ollast__lappend,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,Y: coinductive_llist @ A,A2: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ X5 @ ( coinductive_LCons @ A @ A2 @ Y ) ) )
% 2.82/1.63 = ( lList2170638824_llast @ A @ ( coinductive_LCons @ A @ A2 @ Y ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_83_llast__lappend__LCons,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 2.82/1.63 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_84_llimit__induct,axiom,
% 2.82/1.63 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( P @ ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ! [X2: A,Xs3: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.82/1.63 => ( ( P @ Xs3 )
% 2.82/1.63 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs3 ) ) ) )
% 2.82/1.63 => ( ( ! [Ys2: coinductive_llist @ A] :
% 2.82/1.63 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs )
% 2.82/1.63 => ( P @ Ys2 ) )
% 2.82/1.63 => ( P @ Xs ) )
% 2.82/1.63 => ( P @ Xs ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_85_ex__gt__or__lt,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A] :
% 2.82/1.63 ? [B3: A] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ B3 )
% 2.82/1.63 | ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_86_linorder__neqE__linordered__idom,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( X5 != Y )
% 2.82/1.63 => ( ~ ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ( ord_less @ A @ Y @ X5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_87_dual__order_Ostrict__implies__not__eq,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [B4: A,A2: A] :
% 2.82/1.63 ( ( ord_less @ A @ B4 @ A2 )
% 2.82/1.63 => ( A2 != B4 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_88_linordered__field__no__ub,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X: A] :
% 2.82/1.63 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_89_top__apply,axiom,
% 2.82/1.63 ! [C: $tType,D: $tType] :
% 2.82/1.63 ( ( top @ C @ ( type2 @ C ) )
% 2.82/1.63 => ( ( top_top @ ( D > C ) )
% 2.82/1.63 = ( ^ [X3: D] : ( top_top @ C ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_90_lfinite__LCons,axiom,
% 2.82/1.63 ! [A: $tType,X5: A,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X5 @ Xs ) )
% 2.82/1.63 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_91_lfinite__code_I2_J,axiom,
% 2.82/1.63 ! [B: $tType,X5: B,Xs: coinductive_llist @ B] :
% 2.82/1.63 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X5 @ Xs ) )
% 2.82/1.63 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_92_lfinite__code_I1_J,axiom,
% 2.82/1.63 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_93_lfinite__lappend,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.82/1.63 = ( ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_94_lrev__LNil,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_95_lrevT,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_96_lrev__is__lrev__conv,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.82/1.63 = ( lList2281150353e_lrev @ A @ Ys ) )
% 2.82/1.63 = ( Xs = Ys ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_97_lrev__lrev__ident,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 2.82/1.63 = Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_98_LNil__is__lrev__conv,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( ( coinductive_LNil @ A )
% 2.82/1.63 = ( lList2281150353e_lrev @ A @ Xs ) )
% 2.82/1.63 = ( Xs
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_99_lrev__is__LNil__conv,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( Xs
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_100_lrev__lappend,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.82/1.63 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_101_top_Onot__eq__extremum,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order_top @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A] :
% 2.82/1.63 ( ( A2
% 2.82/1.63 != ( top_top @ A ) )
% 2.82/1.63 = ( ord_less @ A @ A2 @ ( top_top @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_102_top_Oextremum__strict,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order_top @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A] :
% 2.82/1.63 ~ ( ord_less @ A @ ( top_top @ A ) @ A2 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_103_lfinite__LConsI,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,X5: A] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X5 @ Xs ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_104_lfinite__LNil,axiom,
% 2.82/1.63 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_105_lappend__inf,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.82/1.63 = Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_106_fin__finite,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_107_finT__simp,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_108_lstrict__prefix__lfinite1,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 2.82/1.63 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_109_lfinite_Oinducts,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ X5 )
% 2.82/1.63 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ! [Xs3: coinductive_llist @ A,X2: A] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.82/1.63 => ( ( P @ Xs3 )
% 2.82/1.63 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs3 ) ) ) )
% 2.82/1.63 => ( P @ X5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_110_lfinite_Osimps,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( coinductive_lfinite @ A )
% 2.82/1.63 = ( ^ [A7: coinductive_llist @ A] :
% 2.82/1.63 ( ( A7
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 | ? [Xs4: coinductive_llist @ A,X3: A] :
% 2.82/1.63 ( ( A7
% 2.82/1.63 = ( coinductive_LCons @ A @ X3 @ Xs4 ) )
% 2.82/1.63 & ( coinductive_lfinite @ A @ Xs4 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_111_lfinite_Ocases,axiom,
% 2.82/1.63 ! [A: $tType,A2: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ A2 )
% 2.82/1.63 => ( ( A2
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ~ ! [Xs3: coinductive_llist @ A] :
% 2.82/1.63 ( ? [X2: A] :
% 2.82/1.63 ( A2
% 2.82/1.63 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 2.82/1.63 => ~ ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_112_lfinite__rev__induct,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ! [X2: A,Xs3: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.82/1.63 => ( ( P @ Xs3 )
% 2.82/1.63 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 2.82/1.63 => ( P @ Xs ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_113_ord__eq__less__subst,axiom,
% 2.82/1.63 ! [A: $tType,B: $tType] :
% 2.82/1.63 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.82/1.63 & ( ord @ A @ ( type2 @ A ) ) )
% 2.82/1.63 => ! [A2: A,F2: B > A,B4: B,C2: B] :
% 2.82/1.63 ( ( A2
% 2.82/1.63 = ( F2 @ B4 ) )
% 2.82/1.63 => ( ( ord_less @ B @ B4 @ C2 )
% 2.82/1.63 => ( ! [X2: B,Y2: B] :
% 2.82/1.63 ( ( ord_less @ B @ X2 @ Y2 )
% 2.82/1.63 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 2.82/1.63 => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_114_ord__less__eq__subst,axiom,
% 2.82/1.63 ! [A: $tType,B: $tType] :
% 2.82/1.63 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.82/1.63 & ( ord @ A @ ( type2 @ A ) ) )
% 2.82/1.63 => ! [A2: A,B4: A,F2: A > B,C2: B] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ B4 )
% 2.82/1.63 => ( ( ( F2 @ B4 )
% 2.82/1.63 = C2 )
% 2.82/1.63 => ( ! [X2: A,Y2: A] :
% 2.82/1.63 ( ( ord_less @ A @ X2 @ Y2 )
% 2.82/1.63 => ( ord_less @ B @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 2.82/1.63 => ( ord_less @ B @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_115_order__less__subst1,axiom,
% 2.82/1.63 ! [A: $tType,B: $tType] :
% 2.82/1.63 ( ( ( order @ B @ ( type2 @ B ) )
% 2.82/1.63 & ( order @ A @ ( type2 @ A ) ) )
% 2.82/1.63 => ! [A2: A,F2: B > A,B4: B,C2: B] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ ( F2 @ B4 ) )
% 2.82/1.63 => ( ( ord_less @ B @ B4 @ C2 )
% 2.82/1.63 => ( ! [X2: B,Y2: B] :
% 2.82/1.63 ( ( ord_less @ B @ X2 @ Y2 )
% 2.82/1.63 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 2.82/1.63 => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_116_order__less__subst2,axiom,
% 2.82/1.63 ! [A: $tType,C: $tType] :
% 2.82/1.63 ( ( ( order @ C @ ( type2 @ C ) )
% 2.82/1.63 & ( order @ A @ ( type2 @ A ) ) )
% 2.82/1.63 => ! [A2: A,B4: A,F2: A > C,C2: C] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ B4 )
% 2.82/1.63 => ( ( ord_less @ C @ ( F2 @ B4 ) @ C2 )
% 2.82/1.63 => ( ! [X2: A,Y2: A] :
% 2.82/1.63 ( ( ord_less @ A @ X2 @ Y2 )
% 2.82/1.63 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 2.82/1.63 => ( ord_less @ C @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_117_lt__ex,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( no_bot @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A] :
% 2.82/1.63 ? [Y2: A] : ( ord_less @ A @ Y2 @ X5 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_118_gt__ex,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( no_top @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A] :
% 2.82/1.63 ? [X1: A] : ( ord_less @ A @ X5 @ X1 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_119_neqE,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( X5 != Y )
% 2.82/1.63 => ( ~ ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ( ord_less @ A @ Y @ X5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_120_neq__iff,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( X5 != Y )
% 2.82/1.63 = ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 | ( ord_less @ A @ Y @ X5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_121_order_Oasym,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A,B4: A] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ B4 )
% 2.82/1.63 => ~ ( ord_less @ A @ B4 @ A2 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_122_dense,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( dense_order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ? [Z: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Z )
% 2.82/1.63 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_123_less__imp__neq,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ( X5 != Y ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_124_less__asym,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( preorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ~ ( ord_less @ A @ Y @ X5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_125_less__asym_H,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( preorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A,B4: A] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ B4 )
% 2.82/1.63 => ~ ( ord_less @ A @ B4 @ A2 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_126_less__trans,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( preorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A,Z3: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ( ( ord_less @ A @ Y @ Z3 )
% 2.82/1.63 => ( ord_less @ A @ X5 @ Z3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_127_less__linear,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 | ( X5 = Y )
% 2.82/1.63 | ( ord_less @ A @ Y @ X5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_128_less__irrefl,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( preorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A] :
% 2.82/1.63 ~ ( ord_less @ A @ X5 @ X5 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_129_ord__eq__less__trans,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( ord @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A,B4: A,C2: A] :
% 2.82/1.63 ( ( A2 = B4 )
% 2.82/1.63 => ( ( ord_less @ A @ B4 @ C2 )
% 2.82/1.63 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_130_ord__less__eq__trans,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( ord @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A,B4: A,C2: A] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ B4 )
% 2.82/1.63 => ( ( B4 = C2 )
% 2.82/1.63 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_131_dual__order_Oasym,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [B4: A,A2: A] :
% 2.82/1.63 ( ( ord_less @ A @ B4 @ A2 )
% 2.82/1.63 => ~ ( ord_less @ A @ A2 @ B4 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_132_less__imp__not__eq,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ( X5 != Y ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_133_less__not__sym,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( preorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ~ ( ord_less @ A @ Y @ X5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_134_less__induct,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [P: A > $o,A2: A] :
% 2.82/1.63 ( ! [X2: A] :
% 2.82/1.63 ( ! [Y3: A] :
% 2.82/1.63 ( ( ord_less @ A @ Y3 @ X2 )
% 2.82/1.63 => ( P @ Y3 ) )
% 2.82/1.63 => ( P @ X2 ) )
% 2.82/1.63 => ( P @ A2 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_135_antisym__conv3,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [Y: A,X5: A] :
% 2.82/1.63 ( ~ ( ord_less @ A @ Y @ X5 )
% 2.82/1.63 => ( ( ~ ( ord_less @ A @ X5 @ Y ) )
% 2.82/1.63 = ( X5 = Y ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_136_less__imp__not__eq2,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ( Y != X5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_137_less__imp__triv,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( preorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A,P: $o] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ( ( ord_less @ A @ Y @ X5 )
% 2.82/1.63 => P ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_138_linorder__cases,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ~ ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ( ( X5 != Y )
% 2.82/1.63 => ( ord_less @ A @ Y @ X5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_139_dual__order_Oirrefl,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A] :
% 2.82/1.63 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_140_order_Ostrict__trans,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A,B4: A,C2: A] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ B4 )
% 2.82/1.63 => ( ( ord_less @ A @ B4 @ C2 )
% 2.82/1.63 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_141_less__imp__not__less,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( preorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ord_less @ A @ X5 @ Y )
% 2.82/1.63 => ~ ( ord_less @ A @ Y @ X5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_142_dual__order_Ostrict__trans,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [B4: A,A2: A,C2: A] :
% 2.82/1.63 ( ( ord_less @ A @ B4 @ A2 )
% 2.82/1.63 => ( ( ord_less @ A @ C2 @ B4 )
% 2.82/1.63 => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_143_not__less__iff__gr__or__eq,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linorder @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A,Y: A] :
% 2.82/1.63 ( ( ~ ( ord_less @ A @ X5 @ Y ) )
% 2.82/1.63 = ( ( ord_less @ A @ Y @ X5 )
% 2.82/1.63 | ( X5 = Y ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_144_order_Ostrict__implies__not__eq,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [A2: A,B4: A] :
% 2.82/1.63 ( ( ord_less @ A @ A2 @ B4 )
% 2.82/1.63 => ( A2 != B4 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_145_linordered__field__no__lb,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X: A] :
% 2.82/1.63 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_146_iso__tuple__UNIV__I,axiom,
% 2.82/1.63 ! [A: $tType,X5: A] : ( member @ A @ X5 @ ( top_top @ ( set @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_147_UNIV__I,axiom,
% 2.82/1.63 ! [A: $tType,X5: A] : ( member @ A @ X5 @ ( top_top @ ( set @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_148_poslsts__UNIV,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 = ( S
% 2.82/1.63 != ( coinductive_LNil @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_149_ltake__fin,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_150_ldrop__fin__iffT,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_151_lstrict__prefix__lappend__conv,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coindu1478340336prefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.82/1.63 = ( ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_152_lnull__lappend,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.82/1.63 = ( ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_153_lappend_Odisc__iff_I2_J,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 2.82/1.63 = ( ~ ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_154_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 2.82/1.63 ! [A: $tType,I: nat] :
% 2.82/1.63 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_155_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 2.82/1.63 ! [A: $tType,I: nat] :
% 2.82/1.63 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_156_top__set__def,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( top_top @ ( set @ A ) )
% 2.82/1.63 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_157_ltake__ldrop__id,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,I: nat] :
% 2.82/1.63 ( ( coinductive_lappend @ A @ ( lList22119844313_ltake @ A @ X5 @ I ) @ ( lList2508575361_ldrop @ A @ X5 @ I ) )
% 2.82/1.63 = X5 ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_158_lappend_Oexhaust,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 => ~ ( coinductive_lnull @ A @ Ys ) )
% 2.82/1.63 => ( ~ ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_159_lzip_Oexhaust,axiom,
% 2.82/1.63 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 2.82/1.63 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 | ( coinductive_lnull @ B @ Ys ) )
% 2.82/1.63 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 => ( coinductive_lnull @ B @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_160_llist_Odisc_I2_J,axiom,
% 2.82/1.63 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 2.82/1.63 ~ ( coinductive_lnull @ A @ ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_161_llist_OdiscI_I2_J,axiom,
% 2.82/1.63 ! [A: $tType,Llist: coinductive_llist @ A,X212: A,X222: coinductive_llist @ A] :
% 2.82/1.63 ( ( Llist
% 2.82/1.63 = ( coinductive_LCons @ A @ X212 @ X222 ) )
% 2.82/1.63 => ~ ( coinductive_lnull @ A @ Llist ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_162_not__lnull__conv,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( ~ ( coinductive_lnull @ A @ Xs ) )
% 2.82/1.63 = ( ? [X3: A,Xs2: coinductive_llist @ A] :
% 2.82/1.63 ( Xs
% 2.82/1.63 = ( coinductive_LCons @ A @ X3 @ Xs2 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_163_lnull__def,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( coinductive_lnull @ A )
% 2.82/1.63 = ( ^ [Llist2: coinductive_llist @ A] :
% 2.82/1.63 ( Llist2
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_164_llist_Ocollapse_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,Llist: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lnull @ A @ Llist )
% 2.82/1.63 => ( Llist
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_165_llist_OdiscI_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,Llist: coinductive_llist @ A] :
% 2.82/1.63 ( ( Llist
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( coinductive_lnull @ A @ Llist ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_166_llist_Odisc_I1_J,axiom,
% 2.82/1.63 ! [A: $tType] : ( coinductive_lnull @ A @ ( coinductive_LNil @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_167_lappend__lnull2,axiom,
% 2.82/1.63 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lnull @ A @ Ys )
% 2.82/1.63 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.82/1.63 = Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_168_lappend__lnull1,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.82/1.63 = Ys ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_169_lappend_Odisc_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_lnull @ A @ Ys )
% 2.82/1.63 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_170_lappend_Odisc_I2_J,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 | ~ ( coinductive_lnull @ A @ Ys ) )
% 2.82/1.63 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_171_lnull__imp__lfinite,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_172_drop__nonLNil,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.82/1.63 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( T
% 2.82/1.63 != ( coinductive_LNil @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_173_ldrop__finT,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_174_lappend_Octr_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.82/1.63 ( ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_lnull @ A @ Ys )
% 2.82/1.63 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.82/1.63 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_175_Coinductive__List_Ollast__LCons,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A,X5: A] :
% 2.82/1.63 ( ( ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X5 @ Xs ) )
% 2.82/1.63 = X5 ) )
% 2.82/1.63 & ( ~ ( coinductive_lnull @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X5 @ Xs ) )
% 2.82/1.63 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_176_UNIV__eq__I,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A] :
% 2.82/1.63 ( ! [X2: A] : ( member @ A @ X2 @ A3 )
% 2.82/1.63 => ( ( top_top @ ( set @ A ) )
% 2.82/1.63 = A3 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_177_UNIV__witness,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ? [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_178_ltake__lappend__llength,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,S: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 2.82/1.63 = R ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_179_llength__drop__take,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.82/1.63 ( ( ( lList2508575361_ldrop @ A @ T @ I )
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 2.82/1.63 = I ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_180_lapp__suff__llength,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,S: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( lList2508575361_ldrop @ A @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21232602520length @ A @ R ) )
% 2.82/1.63 = S ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_181_top1I,axiom,
% 2.82/1.63 ! [A: $tType,X5: A] : ( top_top @ ( A > $o ) @ X5 ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_182_top__empty__eq,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( top_top @ ( A > $o ) )
% 2.82/1.63 = ( ^ [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_183_top__conj_I1_J,axiom,
% 2.82/1.63 ! [A: $tType,X5: A,P: $o] :
% 2.82/1.63 ( ( ( top_top @ ( A > $o ) @ X5 )
% 2.82/1.63 & P )
% 2.82/1.63 = P ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_184_top__conj_I2_J,axiom,
% 2.82/1.63 ! [A: $tType,P: $o,X5: A] :
% 2.82/1.63 ( ( P
% 2.82/1.63 & ( top_top @ ( A > $o ) @ X5 ) )
% 2.82/1.63 = P ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_185_Coinductive__List_Ollast__lappend,axiom,
% 2.82/1.63 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ( ( coinductive_lnull @ A @ Ys )
% 2.82/1.63 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.82/1.63 = ( coinductive_llast @ A @ Xs ) ) )
% 2.82/1.63 & ( ~ ( coinductive_lnull @ A @ Ys )
% 2.82/1.63 => ( ( ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.82/1.63 = ( coinductive_llast @ A @ Ys ) ) )
% 2.82/1.63 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.82/1.63 = ( undefined @ A ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_186_LList2__Mirabelle__hamjzmohle_Ollength__LCons,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,A2: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( lList21232602520length @ A @ ( coinductive_LCons @ A @ A2 @ R ) )
% 2.82/1.63 = ( suc @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_187_llength__take,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 2.82/1.63 = I ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_188_lapp__inf,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A,T: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( ( coinductive_lappend @ A @ S @ T )
% 2.82/1.63 = S ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_189_notfin__inf,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A] :
% 2.82/1.63 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.82/1.63 = ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_190_notinf__fin,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A] :
% 2.82/1.63 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.82/1.63 = ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_191_ldrop__inf__iffT,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,I: nat] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 = ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_192_LList2__Mirabelle__hamjzmohle_Ollast__LNil,axiom,
% 2.82/1.63 ! [B: $tType] :
% 2.82/1.63 ( ( lList2170638824_llast @ B @ ( coinductive_LNil @ B ) )
% 2.82/1.63 = ( undefined @ B ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_193_ldrop__infT,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList21612149805nflsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_194_inflstsI2,axiom,
% 2.82/1.63 ! [A: $tType,A2: A,A3: set @ A,T: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ A @ A2 @ A3 )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A2 @ T ) @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_195_inflsts__cases,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ~ ! [A4: A,L2: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ A @ A4 @ A3 )
% 2.82/1.63 => ( S
% 2.82/1.63 != ( coinductive_LCons @ A @ A4 @ L2 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_196_infT__simp,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_197_Coinductive__List_Ollast__LNil,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 2.82/1.63 = ( undefined @ A ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_198_llast__linfinite,axiom,
% 2.82/1.63 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.82/1.63 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.82/1.63 => ( ( coinductive_llast @ A @ Xs )
% 2.82/1.63 = ( undefined @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_199_ltake__LCons__Suc,axiom,
% 2.82/1.63 ! [A: $tType,A2: A,L: coinductive_llist @ A,I: nat] :
% 2.82/1.63 ( ( lList22119844313_ltake @ A @ ( coinductive_LCons @ A @ A2 @ L ) @ ( suc @ I ) )
% 2.82/1.63 = ( coinductive_LCons @ A @ A2 @ ( lList22119844313_ltake @ A @ L @ I ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_200_fin__inf__cases,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A] :
% 2.82/1.63 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_201_app__invT,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,A3: set @ A,S: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_202_lapp__infT,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) ) )
% 2.82/1.63 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_203_lapp__inv2T,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A3 ) ) )
% 2.82/1.63 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_204_lapp__fin__infT,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A,T: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_205_lift__Suc__mono__less__iff,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [F2: nat > A,N: nat,M: nat] :
% 2.82/1.63 ( ! [N2: nat] : ( ord_less @ A @ ( F2 @ N2 ) @ ( F2 @ ( suc @ N2 ) ) )
% 2.82/1.63 => ( ( ord_less @ A @ ( F2 @ N ) @ ( F2 @ M ) )
% 2.82/1.63 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_206_lift__Suc__mono__less,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( order @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [F2: nat > A,N: nat,N3: nat] :
% 2.82/1.63 ( ! [N2: nat] : ( ord_less @ A @ ( F2 @ N2 ) @ ( F2 @ ( suc @ N2 ) ) )
% 2.82/1.63 => ( ( ord_less @ nat @ N @ N3 )
% 2.82/1.63 => ( ord_less @ A @ ( F2 @ N ) @ ( F2 @ N3 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_207_inflstsI,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( ~ ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_208_lapp__allT__iff,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A3 ) ) )
% 2.82/1.63 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_209_alllsts__UNIV,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_210_LConsE,axiom,
% 2.82/1.63 ! [A: $tType,X5: A,Xs: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X5 @ Xs ) @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 = ( ( member @ A @ X5 @ A3 )
% 2.82/1.63 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_211_take__fin,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_212_poslsts__iff,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A3 ) )
% 2.82/1.63 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 & ( S
% 2.82/1.63 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_213_alllsts_Ocoinduct,axiom,
% 2.82/1.63 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X5: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( X4 @ X5 )
% 2.82/1.63 => ( ! [X2: coinductive_llist @ A] :
% 2.82/1.63 ( ( X4 @ X2 )
% 2.82/1.63 => ( ( X2
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 | ? [L3: coinductive_llist @ A,A5: A] :
% 2.82/1.63 ( ( X2
% 2.82/1.63 = ( coinductive_LCons @ A @ A5 @ L3 ) )
% 2.82/1.63 & ( ( X4 @ L3 )
% 2.82/1.63 | ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A3 ) ) )
% 2.82/1.63 & ( member @ A @ A5 @ A3 ) ) ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_214_alllsts_Osimps,axiom,
% 2.82/1.63 ! [A: $tType,A2: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ A2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 = ( ( A2
% 2.82/1.63 = ( coinductive_LNil @ A ) )
% 2.82/1.63 | ? [L4: coinductive_llist @ A,A7: A] :
% 2.82/1.63 ( ( A2
% 2.82/1.63 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 2.82/1.63 & ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 & ( member @ A @ A7 @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_215_alllsts_Ocases,axiom,
% 2.82/1.63 ! [A: $tType,A2: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ A2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( ( A2
% 2.82/1.63 != ( coinductive_LNil @ A ) )
% 2.82/1.63 => ~ ! [L2: coinductive_llist @ A,A4: A] :
% 2.82/1.63 ( ( A2
% 2.82/1.63 = ( coinductive_LCons @ A @ A4 @ L2 ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ~ ( member @ A @ A4 @ A3 ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_216_ldropT,axiom,
% 2.82/1.63 ! [A: $tType,T: coinductive_llist @ A,A3: set @ A,I: nat] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2435255213lllsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_217_alllsts_OLCons__all,axiom,
% 2.82/1.63 ! [A: $tType,L: coinductive_llist @ A,A3: set @ A,A2: A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ A @ A2 @ A3 )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A2 @ L ) @ ( lList2435255213lllsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_218_alllsts_OLNil__all,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A3 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_219_lappT,axiom,
% 2.82/1.63 ! [A: $tType,S: coinductive_llist @ A,A3: set @ A,T: coinductive_llist @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_220_lapp__all__invT,axiom,
% 2.82/1.63 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_221_finite__lemma,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ B5 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ B5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_222_finsubsetall,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_223_infsubsetall,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_224_alllstsE,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( ~ ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ A3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_225_inflstsE,axiom,
% 2.82/1.63 ! [A: $tType,X5: coinductive_llist @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 => ~ ( ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2435255213lllsts @ A @ A3 ) )
% 2.82/1.63 => ( member @ ( coinductive_llist @ A ) @ X5 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_226_inflsts__def,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( lList21612149805nflsts @ A )
% 2.82/1.63 = ( ^ [A6: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A6 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_227_fin__Un__inf,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A3 ) @ ( lList21612149805nflsts @ A @ A3 ) )
% 2.82/1.63 = ( lList2435255213lllsts @ A @ A3 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_228_Un__iff,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 = ( ( member @ A @ C2 @ A3 )
% 2.82/1.63 | ( member @ A @ C2 @ B5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_229_UnCI,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,B5: set @ A,A3: set @ A] :
% 2.82/1.63 ( ( ~ ( member @ A @ C2 @ B5 )
% 2.82/1.63 => ( member @ A @ C2 @ A3 ) )
% 2.82/1.63 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_230_Diff__idemp,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) @ B5 )
% 2.82/1.63 = ( minus_minus @ ( set @ A ) @ A3 @ B5 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_231_Diff__iff,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 = ( ( member @ A @ C2 @ A3 )
% 2.82/1.63 & ~ ( member @ A @ C2 @ B5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_232_DiffI,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ A3 )
% 2.82/1.63 => ( ~ ( member @ A @ C2 @ B5 )
% 2.82/1.63 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_233_Un__Diff__cancel2,axiom,
% 2.82/1.63 ! [A: $tType,B5: set @ A,A3: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B5 @ A3 ) @ A3 )
% 2.82/1.63 = ( sup_sup @ ( set @ A ) @ B5 @ A3 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_234_Un__Diff__cancel,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) @ A3 @ ( minus_minus @ ( set @ A ) @ B5 @ A3 ) )
% 2.82/1.63 = ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_235_Un__UNIV__right,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) @ A3 @ ( top_top @ ( set @ A ) ) )
% 2.82/1.63 = ( top_top @ ( set @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_236_Un__UNIV__left,axiom,
% 2.82/1.63 ! [A: $tType,B5: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B5 )
% 2.82/1.63 = ( top_top @ ( set @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_237_Un__left__commute,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A,C3: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) )
% 2.82/1.63 = ( sup_sup @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_238_Un__left__absorb,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 = ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_239_Un__commute,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) )
% 2.82/1.63 = ( ^ [A6: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_240_Un__absorb,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 2.82/1.63 = A3 ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_241_Un__assoc,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A,C3: set @ A] :
% 2.82/1.63 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) @ C3 )
% 2.82/1.63 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_242_ball__Un,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A,P: A > $o] :
% 2.82/1.63 ( ( ! [X3: A] :
% 2.82/1.63 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 => ( P @ X3 ) ) )
% 2.82/1.63 = ( ! [X3: A] :
% 2.82/1.63 ( ( member @ A @ X3 @ A3 )
% 2.82/1.63 => ( P @ X3 ) )
% 2.82/1.63 & ! [X3: A] :
% 2.82/1.63 ( ( member @ A @ X3 @ B5 )
% 2.82/1.63 => ( P @ X3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_243_Un__Diff,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A,C3: set @ A] :
% 2.82/1.63 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) @ C3 )
% 2.82/1.63 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A3 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_244_bex__Un,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A,P: A > $o] :
% 2.82/1.63 ( ( ? [X3: A] :
% 2.82/1.63 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 & ( P @ X3 ) ) )
% 2.82/1.63 = ( ? [X3: A] :
% 2.82/1.63 ( ( member @ A @ X3 @ A3 )
% 2.82/1.63 & ( P @ X3 ) )
% 2.82/1.63 | ? [X3: A] :
% 2.82/1.63 ( ( member @ A @ X3 @ B5 )
% 2.82/1.63 & ( P @ X3 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_245_DiffD2,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 => ~ ( member @ A @ C2 @ B5 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_246_DiffD1,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 => ( member @ A @ C2 @ A3 ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_247_DiffE,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 => ~ ( ( member @ A @ C2 @ A3 )
% 2.82/1.63 => ( member @ A @ C2 @ B5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_248_UnI2,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,B5: set @ A,A3: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ B5 )
% 2.82/1.63 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_249_UnI1,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ A3 )
% 2.82/1.63 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_250_UnE,axiom,
% 2.82/1.63 ! [A: $tType,C2: A,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B5 ) )
% 2.82/1.63 => ( ~ ( member @ A @ C2 @ A3 )
% 2.82/1.63 => ( member @ A @ C2 @ B5 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_251_psubset__imp__ex__mem,axiom,
% 2.82/1.63 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.82/1.63 ( ( ord_less @ ( set @ A ) @ A3 @ B5 )
% 2.82/1.63 => ? [B3: A] : ( member @ A @ B3 @ ( minus_minus @ ( set @ A ) @ B5 @ A3 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_252_sup__top__right,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A] :
% 2.82/1.63 ( ( sup_sup @ A @ X5 @ ( top_top @ A ) )
% 2.82/1.63 = ( top_top @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(fact_253_sup__top__left,axiom,
% 2.82/1.63 ! [A: $tType] :
% 2.82/1.63 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.82/1.63 => ! [X5: A] :
% 2.82/1.63 ( ( sup_sup @ A @ ( top_top @ A ) @ X5 )
% 2.82/1.63 = ( top_top @ A ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.82/1.63 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.82/1.63 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.82/1.63 ! [A8: $tType,A9: $tType] :
% 2.82/1.63 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.82/1.63 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 2.82/1.63 ! [A8: $tType,A9: $tType] :
% 2.82/1.63 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.82/1.63 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 2.82/1.63 ! [A8: $tType,A9: $tType] :
% 2.82/1.63 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 2.82/1.63 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.82/1.63 ! [A8: $tType,A9: $tType] :
% 2.82/1.63 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 2.82/1.63 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.82/1.63 ! [A8: $tType,A9: $tType] :
% 2.82/1.63 ( ( order @ A9 @ ( type2 @ A9 ) )
% 2.82/1.63 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_fun___Orderings_Otop,axiom,
% 2.82/1.63 ! [A8: $tType,A9: $tType] :
% 2.82/1.63 ( ( top @ A9 @ ( type2 @ A9 ) )
% 2.82/1.63 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_fun___Orderings_Oord,axiom,
% 2.82/1.63 ! [A8: $tType,A9: $tType] :
% 2.82/1.63 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 2.82/1.63 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.82/1.63 wellorder @ nat @ ( type2 @ nat ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Nat_Onat___Orderings_Opreorder_3,axiom,
% 2.82/1.63 preorder @ nat @ ( type2 @ nat ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.82/1.63 linorder @ nat @ ( type2 @ nat ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 2.82/1.63 no_top @ nat @ ( type2 @ nat ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 2.82/1.63 order @ nat @ ( type2 @ nat ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 2.82/1.63 ord @ nat @ ( type2 @ nat ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_6,axiom,
% 2.82/1.63 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Set_Oset___Orderings_Oorder__top_7,axiom,
% 2.82/1.63 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Set_Oset___Orderings_Opreorder_8,axiom,
% 2.82/1.63 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 2.82/1.63 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Set_Oset___Orderings_Otop_10,axiom,
% 2.82/1.63 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Set_Oset___Orderings_Oord_11,axiom,
% 2.82/1.63 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_12,axiom,
% 2.82/1.63 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_HOL_Obool___Orderings_Oorder__top_13,axiom,
% 2.82/1.63 order_top @ $o @ ( type2 @ $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_HOL_Obool___Orderings_Opreorder_14,axiom,
% 2.82/1.63 preorder @ $o @ ( type2 @ $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_HOL_Obool___Orderings_Olinorder_15,axiom,
% 2.82/1.63 linorder @ $o @ ( type2 @ $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_HOL_Obool___Orderings_Oorder_16,axiom,
% 2.82/1.63 order @ $o @ ( type2 @ $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_HOL_Obool___Orderings_Otop_17,axiom,
% 2.82/1.63 top @ $o @ ( type2 @ $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_HOL_Obool___Orderings_Oord_18,axiom,
% 2.82/1.63 ord @ $o @ ( type2 @ $o ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Coinductive__List_Ollist___Orderings_Opreorder_19,axiom,
% 2.82/1.63 ! [A8: $tType] : ( preorder @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Coinductive__List_Ollist___Orderings_Oorder_20,axiom,
% 2.82/1.63 ! [A8: $tType] : ( order @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(tcon_Coinductive__List_Ollist___Orderings_Oord_21,axiom,
% 2.82/1.63 ! [A8: $tType] : ( ord @ ( coinductive_llist @ A8 ) @ ( type2 @ ( coinductive_llist @ A8 ) ) ) ).
% 2.82/1.63
% 2.82/1.63 thf(conj_0,conjecture,
% 2.82/1.63 ~ ( ord_less @ ( coinductive_llist @ a ) @ r @ ( coinductive_LNil @ a ) ) ).
% 2.82/1.63 ------------------------
% 2.82/1.67 % (5758)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_5656 for (2999ds/27Mi)
% 2.82/1.67 % (5760)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_5656 for (2999ds/2Mi)
% 2.82/1.67 % (5759)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/2Mi)
% 2.82/1.67 % (5757)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_5656 for (2999ds/4Mi)
% 2.82/1.67 % (5756)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/183Mi)
% 2.82/1.67 % (5761)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_5656 for (2999ds/275Mi)
% 2.82/1.67 % (5762)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/18Mi)
% 2.82/1.67 % (5759)Instruction limit reached!
% 2.82/1.67 % (5759)------------------------------
% 2.82/1.67 % (5759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.67 % (5759)Termination reason: Unknown
% 2.82/1.67 % (5759)Termination phase: shuffling
% 2.82/1.67
% 2.82/1.67 % (5760)Instruction limit reached!
% 2.82/1.67 % (5760)------------------------------
% 2.82/1.67 % (5760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.67 % (5760)Termination reason: Unknown
% 2.82/1.67 % (5760)Termination phase: shuffling
% 2.82/1.67
% 2.82/1.67 % (5760)Memory used [KB]: 1407
% 2.82/1.67 % (5760)Time elapsed: 0.003 s
% 2.82/1.67 % (5760)Instructions burned: 3 (million)
% 2.82/1.67 % (5760)------------------------------
% 2.82/1.67 % (5760)------------------------------
% 2.82/1.67 % (5759)Memory used [KB]: 1279
% 2.82/1.67 % (5759)Time elapsed: 0.003 s
% 2.82/1.67 % (5759)Instructions burned: 2 (million)
% 2.82/1.67 % (5759)------------------------------
% 2.82/1.67 % (5759)------------------------------
% 2.82/1.67 % (5757)Instruction limit reached!
% 2.82/1.67 % (5757)------------------------------
% 2.82/1.67 % (5757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.67 % (5757)Termination reason: Unknown
% 2.82/1.67 % (5757)Termination phase: shuffling
% 2.82/1.67
% 2.82/1.67 % (5757)Memory used [KB]: 1407
% 2.82/1.67 % (5757)Time elapsed: 0.004 s
% 2.82/1.67 % (5757)Instructions burned: 4 (million)
% 2.82/1.67 % (5757)------------------------------
% 2.82/1.67 % (5757)------------------------------
% 2.82/1.68 % (5762)Instruction limit reached!
% 2.82/1.68 % (5762)------------------------------
% 2.82/1.68 % (5762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.68 % (5762)Termination reason: Unknown
% 2.82/1.68 % (5762)Termination phase: shuffling
% 2.82/1.68
% 2.82/1.68 % (5762)Memory used [KB]: 1663
% 2.82/1.68 % (5762)Time elapsed: 0.011 s
% 2.82/1.68 % (5762)Instructions burned: 18 (million)
% 2.82/1.68 % (5762)------------------------------
% 2.82/1.68 % (5762)------------------------------
% 2.82/1.68 % (5758)Instruction limit reached!
% 2.82/1.68 % (5758)------------------------------
% 2.82/1.68 % (5758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.68 % (5758)Termination reason: Unknown
% 2.82/1.68 % (5758)Termination phase: Property scanning
% 2.82/1.68
% 2.82/1.68 % (5758)Memory used [KB]: 1791
% 2.82/1.68 % (5758)Time elapsed: 0.015 s
% 2.82/1.68 % (5758)Instructions burned: 27 (million)
% 2.82/1.68 % (5758)------------------------------
% 2.82/1.68 % (5758)------------------------------
% 2.82/1.69 % (5763)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/3Mi)
% 2.82/1.69 % (5764)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_5656 for (2999ds/37Mi)
% 2.82/1.69 % (5765)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_5656 for (2999ds/15Mi)
% 2.82/1.69 % (5761)Refutation not found, incomplete strategy
% 2.82/1.69 % (5761)------------------------------
% 2.82/1.69 % (5761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.69 % (5761)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.69
% 2.82/1.69
% 2.82/1.69 % (5761)Memory used [KB]: 6268
% 2.82/1.69 % (5761)Time elapsed: 0.020 s
% 2.82/1.69 % (5761)Instructions burned: 35 (million)
% 2.82/1.69 % (5761)------------------------------
% 2.82/1.69 % (5761)------------------------------
% 2.82/1.69 % (5763)Instruction limit reached!
% 2.82/1.69 % (5763)------------------------------
% 2.82/1.69 % (5763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.69 % (5763)Termination reason: Unknown
% 2.82/1.69 % (5763)Termination phase: shuffling
% 2.82/1.69
% 2.82/1.69 % (5763)Memory used [KB]: 1407
% 2.82/1.69 % (5763)Time elapsed: 0.003 s
% 2.82/1.69 % (5763)Instructions burned: 3 (million)
% 2.82/1.69 % (5763)------------------------------
% 2.82/1.69 % (5763)------------------------------
% 2.82/1.69 % (5766)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_5656 for (2999ds/3Mi)
% 2.82/1.69 % (5765)Instruction limit reached!
% 2.82/1.69 % (5765)------------------------------
% 2.82/1.69 % (5765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.69 % (5765)Termination reason: Unknown
% 2.82/1.69 % (5765)Termination phase: shuffling
% 2.82/1.69
% 2.82/1.69 % (5765)Memory used [KB]: 1663
% 2.82/1.69 % (5765)Time elapsed: 0.009 s
% 2.82/1.69 % (5765)Instructions burned: 15 (million)
% 2.82/1.69 % (5765)------------------------------
% 2.82/1.69 % (5765)------------------------------
% 2.82/1.69 % (5766)Instruction limit reached!
% 2.82/1.69 % (5766)------------------------------
% 2.82/1.69 % (5766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.69 % (5766)Termination reason: Unknown
% 2.82/1.69 % (5766)Termination phase: shuffling
% 2.82/1.69
% 2.82/1.69 % (5766)Memory used [KB]: 1407
% 2.82/1.69 % (5766)Time elapsed: 0.003 s
% 2.82/1.69 % (5766)Instructions burned: 3 (million)
% 2.82/1.69 % (5766)------------------------------
% 2.82/1.69 % (5766)------------------------------
% 2.87/1.70 % (5767)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_5656 for (2999ds/1041Mi)
% 2.87/1.70 % (5764)Instruction limit reached!
% 2.87/1.70 % (5764)------------------------------
% 2.87/1.70 % (5764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.70 % (5764)Termination reason: Unknown
% 2.87/1.70 % (5764)Termination phase: Property scanning
% 2.87/1.70
% 2.87/1.70 % (5764)Memory used [KB]: 2046
% 2.87/1.70 % (5764)Time elapsed: 0.019 s
% 2.87/1.70 % (5764)Instructions burned: 39 (million)
% 2.87/1.70 % (5764)------------------------------
% 2.87/1.70 % (5764)------------------------------
% 2.87/1.70 % (5768)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/7Mi)
% 2.87/1.70 % (5769)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/16Mi)
% 2.87/1.71 % (5768)Instruction limit reached!
% 2.87/1.71 % (5768)------------------------------
% 2.87/1.71 % (5768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.71 % (5768)Termination reason: Unknown
% 2.87/1.71 % (5768)Termination phase: shuffling
% 2.87/1.71
% 2.87/1.71 % (5768)Memory used [KB]: 1407
% 2.87/1.71 % (5768)Time elapsed: 0.005 s
% 2.87/1.71 % (5768)Instructions burned: 7 (million)
% 2.87/1.71 % (5768)------------------------------
% 2.87/1.71 % (5768)------------------------------
% 2.87/1.71 % (5770)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/3Mi)
% 2.87/1.71 % (5771)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/3Mi)
% 2.87/1.71 % (5770)Instruction limit reached!
% 2.87/1.71 % (5770)------------------------------
% 2.87/1.71 % (5770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.71 % (5770)Termination reason: Unknown
% 2.87/1.71 % (5770)Termination phase: shuffling
% 2.87/1.71
% 2.87/1.71 % (5770)Memory used [KB]: 1407
% 2.87/1.71 % (5770)Time elapsed: 0.003 s
% 2.87/1.71 % (5770)Instructions burned: 3 (million)
% 2.87/1.71 % (5770)------------------------------
% 2.87/1.71 % (5770)------------------------------
% 2.87/1.71 % (5769)Instruction limit reached!
% 2.87/1.71 % (5769)------------------------------
% 2.87/1.71 % (5769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.71 % (5769)Termination reason: Unknown
% 2.87/1.71 % (5769)Termination phase: shuffling
% 2.87/1.71
% 2.87/1.71 % (5769)Memory used [KB]: 1663
% 2.87/1.71 % (5769)Time elapsed: 0.010 s
% 2.87/1.71 % (5769)Instructions burned: 16 (million)
% 2.87/1.71 % (5769)------------------------------
% 2.87/1.71 % (5769)------------------------------
% 2.87/1.71 % (5771)Instruction limit reached!
% 2.87/1.71 % (5771)------------------------------
% 2.87/1.71 % (5771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.71 % (5771)Termination reason: Unknown
% 2.87/1.71 % (5771)Termination phase: shuffling
% 2.87/1.71
% 2.87/1.71 % (5771)Memory used [KB]: 1407
% 2.87/1.71 % (5771)Time elapsed: 0.003 s
% 2.87/1.71 % (5771)Instructions burned: 3 (million)
% 2.87/1.71 % (5771)------------------------------
% 2.87/1.71 % (5771)------------------------------
% 2.87/1.72 % (5772)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/7Mi)
% 2.87/1.72 % (5773)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/3Mi)
% 2.87/1.72 % (5772)Instruction limit reached!
% 2.87/1.72 % (5772)------------------------------
% 2.87/1.72 % (5772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.72 % (5772)Termination reason: Unknown
% 2.87/1.72 % (5772)Termination phase: shuffling
% 2.87/1.72
% 2.87/1.72 % (5772)Memory used [KB]: 1407
% 2.87/1.72 % (5772)Time elapsed: 0.005 s
% 2.87/1.72 % (5772)Instructions burned: 7 (million)
% 2.87/1.72 % (5772)------------------------------
% 2.87/1.72 % (5772)------------------------------
% 2.87/1.72 % (5773)Instruction limit reached!
% 2.87/1.72 % (5773)------------------------------
% 2.87/1.72 % (5773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.72 % (5773)Termination reason: Unknown
% 2.87/1.72 % (5773)Termination phase: shuffling
% 2.87/1.72
% 2.87/1.72 % (5773)Memory used [KB]: 1407
% 2.87/1.72 % (5773)Time elapsed: 0.003 s
% 2.87/1.72 % (5773)Instructions burned: 4 (million)
% 2.87/1.72 % (5773)------------------------------
% 2.87/1.72 % (5773)------------------------------
% 2.87/1.73 % (5774)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/4Mi)
% 2.87/1.73 % (5775)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/18Mi)
% 2.87/1.73 % (5776)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/710Mi)
% 2.87/1.73 % (5774)Instruction limit reached!
% 2.87/1.73 % (5774)------------------------------
% 2.87/1.73 % (5774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.73 % (5774)Termination reason: Unknown
% 2.87/1.73 % (5774)Termination phase: shuffling
% 2.87/1.73
% 2.87/1.73 % (5774)Memory used [KB]: 1407
% 2.87/1.73 % (5774)Time elapsed: 0.004 s
% 2.87/1.73 % (5774)Instructions burned: 5 (million)
% 2.87/1.73 % (5774)------------------------------
% 2.87/1.73 % (5774)------------------------------
% 2.87/1.74 % (5775)Instruction limit reached!
% 2.87/1.74 % (5775)------------------------------
% 2.87/1.74 % (5775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.74 % (5775)Termination reason: Unknown
% 2.87/1.74 % (5775)Termination phase: shuffling
% 2.87/1.74
% 2.87/1.74 % (5775)Memory used [KB]: 1663
% 2.87/1.74 % (5775)Time elapsed: 0.011 s
% 2.87/1.74 % (5775)Instructions burned: 19 (million)
% 2.87/1.74 % (5775)------------------------------
% 2.87/1.74 % (5775)------------------------------
% 2.87/1.74 % (5777)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/6Mi)
% 2.87/1.74 % (5778)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/902Mi)
% 2.87/1.74 % (5777)Instruction limit reached!
% 2.87/1.74 % (5777)------------------------------
% 2.87/1.74 % (5777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.74 % (5777)Termination reason: Unknown
% 2.87/1.74 % (5777)Termination phase: shuffling
% 2.87/1.74
% 2.87/1.74 % (5777)Memory used [KB]: 1407
% 2.87/1.74 % (5777)Time elapsed: 0.005 s
% 2.87/1.74 % (5777)Instructions burned: 7 (million)
% 2.87/1.74 % (5777)------------------------------
% 2.87/1.74 % (5777)------------------------------
% 2.87/1.75 % (5779)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/21Mi)
% 2.87/1.75 % (5780)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/5Mi)
% 2.87/1.75 % (5756)Instruction limit reached!
% 2.87/1.75 % (5756)------------------------------
% 2.87/1.75 % (5756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.75 % (5756)Termination reason: Unknown
% 2.87/1.75 % (5756)Termination phase: Saturation
% 2.87/1.75
% 2.87/1.75 % (5756)Memory used [KB]: 7036
% 2.87/1.75 % (5756)Time elapsed: 0.089 s
% 2.87/1.75 % (5756)Instructions burned: 183 (million)
% 2.87/1.75 % (5756)------------------------------
% 2.87/1.75 % (5756)------------------------------
% 2.87/1.76 % (5780)Instruction limit reached!
% 2.87/1.76 % (5780)------------------------------
% 2.87/1.76 % (5780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.76 % (5780)Termination reason: Unknown
% 2.87/1.76 % (5780)Termination phase: shuffling
% 2.87/1.76
% 2.87/1.76 % (5780)Memory used [KB]: 1407
% 2.87/1.76 % (5780)Time elapsed: 0.004 s
% 2.87/1.76 % (5780)Instructions burned: 6 (million)
% 2.87/1.76 % (5780)------------------------------
% 2.87/1.76 % (5780)------------------------------
% 2.87/1.76 % (5779)Instruction limit reached!
% 2.87/1.76 % (5779)------------------------------
% 2.87/1.76 % (5779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.76 % (5779)Termination reason: Unknown
% 2.87/1.76 % (5779)Termination phase: shuffling
% 2.87/1.76
% 2.87/1.76 % (5779)Memory used [KB]: 1663
% 2.87/1.76 % (5779)Time elapsed: 0.012 s
% 2.87/1.76 % (5779)Instructions burned: 21 (million)
% 2.87/1.76 % (5779)------------------------------
% 2.87/1.76 % (5779)------------------------------
% 2.87/1.76 % (5781)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_5656 for (2999ds/6Mi)
% 2.87/1.76 % (5781)Instruction limit reached!
% 2.87/1.76 % (5781)------------------------------
% 2.87/1.76 % (5781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.76 % (5781)Termination reason: Unknown
% 2.87/1.76 % (5781)Termination phase: shuffling
% 2.87/1.76
% 2.87/1.76 % (5781)Memory used [KB]: 1407
% 2.87/1.76 % (5781)Time elapsed: 0.004 s
% 2.87/1.76 % (5781)Instructions burned: 6 (million)
% 2.87/1.76 % (5781)------------------------------
% 2.87/1.76 % (5781)------------------------------
% 2.87/1.77 % (5782)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5656 for (2998ds/377Mi)
% 2.87/1.77 % (5783)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_5656 for (2998ds/779Mi)
% 2.87/1.77 % (5784)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_5656 for (2998ds/19Mi)
% 2.87/1.78 % (5785)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5656 for (2998ds/879Mi)
% 2.87/1.78 % (5784)Instruction limit reached!
% 2.87/1.78 % (5784)------------------------------
% 2.87/1.78 % (5784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.78 % (5784)Termination reason: Unknown
% 2.87/1.78 % (5784)Termination phase: shuffling
% 2.87/1.78
% 2.87/1.78 % (5784)Memory used [KB]: 1663
% 2.87/1.78 % (5784)Time elapsed: 0.010 s
% 2.87/1.78 % (5784)Instructions burned: 19 (million)
% 2.87/1.78 % (5784)------------------------------
% 2.87/1.78 % (5784)------------------------------
% 2.87/1.80 % (5786)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5656 for (2998ds/17Mi)
% 2.87/1.80 % (5786)Instruction limit reached!
% 2.87/1.80 % (5786)------------------------------
% 2.87/1.80 % (5786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.80 % (5786)Termination reason: Unknown
% 2.87/1.80 % (5786)Termination phase: shuffling
% 2.87/1.80
% 2.87/1.80 % (5786)Memory used [KB]: 1663
% 2.87/1.80 % (5786)Time elapsed: 0.010 s
% 2.87/1.80 % (5786)Instructions burned: 17 (million)
% 2.87/1.80 % (5786)------------------------------
% 2.87/1.80 % (5786)------------------------------
% 2.87/1.82 % (5787)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5656 for (2998ds/3Mi)
% 2.87/1.82 % (5787)Instruction limit reached!
% 2.87/1.82 % (5787)------------------------------
% 2.87/1.82 % (5787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.82 % (5787)Termination reason: Unknown
% 2.87/1.82 % (5787)Termination phase: shuffling
% 2.87/1.82
% 2.87/1.82 % (5787)Memory used [KB]: 1279
% 2.87/1.82 % (5787)Time elapsed: 0.003 s
% 2.87/1.82 % (5787)Instructions burned: 3 (million)
% 2.87/1.82 % (5787)------------------------------
% 2.87/1.82 % (5787)------------------------------
% 2.87/1.84 % (5788)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5656 for (2998ds/30Mi)
% 2.87/1.85 % (5788)Instruction limit reached!
% 2.87/1.85 % (5788)------------------------------
% 2.87/1.85 % (5788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.85 % (5788)Termination reason: Unknown
% 2.87/1.85 % (5788)Termination phase: Property scanning
% 2.87/1.85
% 2.87/1.85 % (5788)Memory used [KB]: 1791
% 2.87/1.85 % (5788)Time elapsed: 0.016 s
% 2.87/1.85 % (5788)Instructions burned: 30 (million)
% 2.87/1.85 % (5788)------------------------------
% 2.87/1.85 % (5788)------------------------------
% 2.87/1.87 % (5789)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5656 for (2997ds/127Mi)
% 2.87/1.90 % (5783)First to succeed.
% 2.87/1.90 % (5783)Refutation found. Thanks to Tanya!
% 2.87/1.90 % SZS status Theorem for DTF2THF_5656
% 2.87/1.90 % SZS output start Proof for DTF2THF_5656
% 2.87/1.90 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.87/1.90 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 2.87/1.90 thf(type_def_8, type, set: ($tType) > $tType).
% 2.87/1.90 thf(type_def_9, type, nat: $tType).
% 2.87/1.90 thf(type_def_10, type, a: $tType).
% 2.87/1.90 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 2.87/1.90 thf(func_def_1, type, set: ($tType) > $tType).
% 2.87/1.90 thf(func_def_2, type, nat: $tType).
% 2.87/1.90 thf(func_def_3, type, itself: ($tType) > $tType).
% 2.87/1.90 thf(func_def_4, type, a: $tType).
% 2.87/1.90 thf(func_def_5, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_7, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_8, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_9, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_10, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_11, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_12, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_13, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_14, type, order_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_15, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_16, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_17, type, linordered_idom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_18, type, linordered_field: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_19, type, bounded_lattice_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_20, type, condit1656338222tinuum: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.87/1.90 thf(func_def_21, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.87/1.90 thf(func_def_22, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_23, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 2.87/1.90 thf(func_def_24, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_25, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_26, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_27, type, coinductive_lnull: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 2.87/1.90 thf(func_def_28, type, coinductive_lmember: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > $o)).
% 2.87/1.90 thf(func_def_29, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.87/1.90 thf(func_def_30, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.87/1.90 thf(func_def_31, type, undefined: !>[X0: $tType]:(X0)).
% 2.87/1.90 thf(func_def_32, type, lList2435255213lllsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_33, type, lList21511617539llstsp: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > $o)).
% 2.87/1.90 thf(func_def_34, type, lList2236698231inlsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_35, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0)).
% 2.87/1.90 thf(func_def_36, type, lList2860480441nlstsp: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > $o)).
% 2.87/1.90 thf(func_def_37, type, lList22096119349pslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_38, type, lList21612149805nflsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_39, type, lList2370560421utlast: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_40, type, lList2508575361_ldrop: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_41, type, lList2170638824_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_42, type, lList21232602520length: !>[X0: $tType]:(coinductive_llist @ X0 > nat)).
% 2.87/1.90 thf(func_def_43, type, lList2281150353e_lrev: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_44, type, lList22119844313_ltake: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_45, type, lList21148268032oslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_46, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.87/1.90 thf(func_def_47, type, suc: nat > nat).
% 2.87/1.90 thf(func_def_48, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.87/1.90 thf(func_def_49, type, top_top: !>[X0: $tType]:(X0)).
% 2.87/1.90 thf(func_def_50, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.87/1.90 thf(func_def_51, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.87/1.90 thf(func_def_52, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.87/1.90 thf(func_def_53, type, r: coinductive_llist @ a).
% 2.87/1.90 thf(func_def_72, type, sK1: !>[X0: $tType]:((X0 > $o) > set @ X0 > set @ X0 > X0)).
% 2.87/1.90 thf(func_def_73, type, sK2: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.87/1.90 thf(func_def_74, type, sK3: !>[X0: $tType]:(X0 > X0)).
% 2.87/1.90 thf(func_def_75, type, sK4: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_76, type, sK5: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_77, type, sK6: !>[X0: $tType]:(X0 > X0)).
% 2.87/1.90 thf(func_def_78, type, sK7: !>[X0: $tType]:(X0)).
% 2.87/1.90 thf(func_def_79, type, sK8: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.87/1.90 thf(func_def_80, type, sK9: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_81, type, sK10: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0)).
% 2.87/1.90 thf(func_def_82, type, sK11: !>[X0: $tType]:(set @ X0 > X0)).
% 2.87/1.90 thf(func_def_83, type, sK12: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0)).
% 2.87/1.90 thf(func_def_84, type, sK13: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_85, type, sK14: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.87/1.90 thf(func_def_86, type, sK15: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.87/1.90 thf(func_def_87, type, sK16: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_88, type, sK17: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_89, type, sK18: !>[X0: $tType]:(X0)).
% 2.87/1.90 thf(func_def_90, type, sK19: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.87/1.90 thf(func_def_91, type, sK20: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_92, type, sK21: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_93, type, sK22: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_94, type, sK23: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_95, type, sK24: !>[X0: $tType]:(X0 > X0)).
% 2.87/1.90 thf(func_def_96, type, sK25: !>[X0: $tType]:(X0 > X0)).
% 2.87/1.90 thf(func_def_97, type, sK26: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_98, type, sK27: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_99, type, sK28: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.87/1.90 thf(func_def_100, type, sK29: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_101, type, sK30: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_102, type, sK31: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_103, type, sK32: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_104, type, sK33: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_105, type, sK34: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_106, type, sK35: !>[X0: $tType]:(X0 > X0)).
% 2.87/1.90 thf(func_def_107, type, sK36: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_108, type, sK37: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_109, type, sK38: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_110, type, sK39: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.87/1.90 thf(func_def_111, type, sK40: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_112, type, sK41: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.87/1.90 thf(func_def_113, type, sK42: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 2.87/1.90 thf(func_def_114, type, sK43: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 2.87/1.90 thf(func_def_115, type, sK44: !>[X0: $tType]:(X0 > X0)).
% 2.87/1.90 thf(func_def_116, type, ph45: !>[X0: $tType]:(X0)).
% 2.87/1.90 thf(f2758,plain,(
% 2.87/1.90 $false),
% 2.87/1.90 inference(trivial_inequality_removal,[status(thm)],[f2755])).
% 2.87/1.90 thf(f2755,plain,(
% 2.87/1.90 ($true = $false)),
% 2.87/1.90 inference(superposition,[status(thm)],[f2718,f1018])).
% 2.87/1.90 thf(f1018,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (((order @ coinductive_llist @ X0 @ type2 @ coinductive_llist @ X0) = $true)) )),
% 2.87/1.90 inference(cnf_transformation,[status(thm)],[f979])).
% 2.87/1.90 thf(f979,plain,(
% 2.87/1.90 ! [X0 : $tType] : ((order @ coinductive_llist @ X0 @ type2 @ coinductive_llist @ X0) = $true)),
% 2.87/1.90 inference(closure,[status(thm)],[f747])).
% 2.87/1.90 thf(f747,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (((order @ coinductive_llist @ X0 @ type2 @ coinductive_llist @ X0) = $true)) )),
% 2.87/1.90 inference(fool_elimination,[status(thm)],[f746])).
% 2.87/1.90 thf(f746,plain,(
% 2.87/1.90 ! [X0 : $tType] : (order @ coinductive_llist @ X0 @ type2 @ coinductive_llist @ X0)),
% 2.87/1.90 inference(rectify,[status(thm)],[f284])).
% 2.87/1.90 thf(f284,axiom,(
% 2.87/1.90 ! [X66 : $tType] : (order @ coinductive_llist @ X66 @ type2 @ coinductive_llist @ X66)),
% 2.87/1.90 file('/export/starexec/sandbox/tmp/tmp.3Q38gBiG4C/DTF2THF_5656.p',tcon_Coinductive__List_Ollist___Orderings_Oorder_20)).
% 2.87/1.90 thf(f2718,plain,(
% 2.87/1.90 ((order @ coinductive_llist @ a @ type2 @ coinductive_llist @ a) = $false)),
% 2.87/1.90 inference(trivial_inequality_removal,[status(thm)],[f2702])).
% 2.87/1.90 thf(f2702,plain,(
% 2.87/1.90 ((order @ coinductive_llist @ a @ type2 @ coinductive_llist @ a) = $false) | (r != r)),
% 2.87/1.90 inference(backward_demodulation,[status(thm)],[f2570,f2698])).
% 2.87/1.90 thf(f2698,plain,(
% 2.87/1.90 (r = coinductive_LNil @ a)),
% 2.87/1.90 inference(trivial_inequality_removal,[status(thm)],[f2695])).
% 2.87/1.90 thf(f2695,plain,(
% 2.87/1.90 (r = coinductive_LNil @ a) | ($true = $false)),
% 2.87/1.90 inference(superposition,[status(thm)],[f2691,f2643])).
% 2.87/1.90 thf(f2643,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ X1)) | (coinductive_LNil @ X0 = X1)) )),
% 2.87/1.90 inference(superposition,[status(thm)],[f1261,f2316])).
% 2.87/1.90 thf(f2316,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ (sK37 @ X0 @ X1) @ (sK36 @ X0 @ X1)) = X1) | (coinductive_LNil @ X0 = X1)) )),
% 2.87/1.90 inference(equality_proxy_clausification,[status(thm)],[f2315])).
% 2.87/1.90 thf(f2315,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 = X1) | ($true = ((coinductive_LCons @ X0 @ (sK37 @ X0 @ X1) @ (sK36 @ X0 @ X1)) = X1))) )),
% 2.87/1.90 inference(not_proxy_clausification,[status(thm)],[f2314])).
% 2.87/1.90 thf(f2314,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($false = (~ ((coinductive_LCons @ X0 @ (sK37 @ X0 @ X1) @ (sK36 @ X0 @ X1)) = X1))) | (coinductive_LNil @ X0 = X1)) )),
% 2.87/1.90 inference(equality_proxy_clausification,[status(thm)],[f2313])).
% 2.87/1.90 thf(f2313,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (coinductive_LNil @ X0 = X1)) | ($false = (~ ((coinductive_LCons @ X0 @ (sK37 @ X0 @ X1) @ (sK36 @ X0 @ X1)) = X1)))) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f2312])).
% 2.87/1.90 thf(f2312,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($false = ((^[Y0 : X0]: (~ ((coinductive_LCons @ X0 @ Y0 @ (sK36 @ X0 @ X1)) = X1))) @ (sK37 @ X0 @ X1))) | ($true = (coinductive_LNil @ X0 = X1))) )),
% 2.87/1.90 inference(sigma_clausification,[status(thm)],[f2311])).
% 2.87/1.90 thf(f2311,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((!! @ X0 @ (^[Y0 : X0]: (~ ((coinductive_LCons @ X0 @ Y0 @ (sK36 @ X0 @ X1)) = X1)))) = $false) | ($true = (coinductive_LNil @ X0 = X1))) )),
% 2.87/1.90 inference(not_proxy_clausification,[status(thm)],[f2310])).
% 2.87/1.90 thf(f2310,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($false = (~ (coinductive_LNil @ X0 = X1))) | ((!! @ X0 @ (^[Y0 : X0]: (~ ((coinductive_LCons @ X0 @ Y0 @ (sK36 @ X0 @ X1)) = X1)))) = $false)) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f2309])).
% 2.87/1.90 thf(f2309,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($false = ((^[Y0 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: (~ ((coinductive_LCons @ X0 @ Y1 @ Y0) = X1))))) @ (sK36 @ X0 @ X1))) | ($false = (~ (coinductive_LNil @ X0 = X1)))) )),
% 2.87/1.90 inference(sigma_clausification,[status(thm)],[f2308])).
% 2.87/1.90 thf(f2308,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($false = (!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: (~ ((coinductive_LCons @ X0 @ Y1 @ Y0) = X1))))))) | ($false = (~ (coinductive_LNil @ X0 = X1)))) )),
% 2.87/1.90 inference(not_proxy_clausification,[status(thm)],[f2307])).
% 2.87/1.90 thf(f2307,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (~ (!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: (~ ((coinductive_LCons @ X0 @ Y1 @ Y0) = X1)))))))) | ($false = (~ (coinductive_LNil @ X0 = X1)))) )),
% 2.87/1.90 inference(binary_proxy_clausification,[status(thm)],[f2306])).
% 2.87/1.90 thf(f2306,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = ((~ (coinductive_LNil @ X0 = X1)) => (~ (!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: (~ ((coinductive_LCons @ X0 @ Y1 @ Y0) = X1)))))))))) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f2305])).
% 2.87/1.90 thf(f2305,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = ((^[Y0 : coinductive_llist @ X0]: ((~ (coinductive_LNil @ X0 = Y0)) => (~ (!! @ coinductive_llist @ X0 @ (^[Y1 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y2 : X0]: (~ ((coinductive_LCons @ X0 @ Y2 @ Y1) = Y0))))))))) @ X1))) )),
% 2.87/1.90 inference(pi_clausification,[status(thm)],[f1141])).
% 2.87/1.90 thf(f1141,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (($true = (!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: ((~ (coinductive_LNil @ X0 = Y0)) => (~ (!! @ coinductive_llist @ X0 @ (^[Y1 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y2 : X0]: (~ ((coinductive_LCons @ X0 @ Y2 @ Y1) = Y0)))))))))))) )),
% 2.87/1.90 inference(cnf_transformation,[status(thm)],[f856])).
% 2.87/1.90 thf(f856,plain,(
% 2.87/1.90 ! [X0 : $tType] : ($true = (!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: ((~ (coinductive_LNil @ X0 = Y0)) => (~ (!! @ coinductive_llist @ X0 @ (^[Y1 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y2 : X0]: (~ ((coinductive_LCons @ X0 @ Y2 @ Y1) = Y0)))))))))))),
% 2.87/1.90 inference(closure,[status(thm)],[f765])).
% 2.87/1.90 thf(f765,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (($true = (!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: ((~ (coinductive_LNil @ X0 = Y0)) => (~ (!! @ coinductive_llist @ X0 @ (^[Y1 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y2 : X0]: (~ ((coinductive_LCons @ X0 @ Y2 @ Y1) = Y0)))))))))))) )),
% 2.87/1.90 inference(fool_elimination,[status(thm)],[f764])).
% 2.87/1.90 thf(f764,plain,(
% 2.87/1.90 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 != X1) => ~! [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) != X1))),
% 2.87/1.90 inference(rectify,[status(thm)],[f13])).
% 2.87/1.90 thf(f13,axiom,(
% 2.87/1.90 ! [X0 : $tType,X15 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 != X15) => ~! [X16 : X0,X17 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X16 @ X17) != X15))),
% 2.87/1.90 file('/export/starexec/sandbox/tmp/tmp.3Q38gBiG4C/DTF2THF_5656.p',fact_12_llistE)).
% 2.87/1.90 thf(f1261,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : coinductive_llist @ X0] : (($true = (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ X2 @ X1)))) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f1260])).
% 2.87/1.90 thf(f1260,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : coinductive_llist @ X0] : (($true = ((^[Y0 : X0]: (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ Y0 @ X1))) @ X2))) )),
% 2.87/1.90 inference(pi_clausification,[status(thm)],[f1259])).
% 2.87/1.90 thf(f1259,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (!! @ X0 @ (^[Y0 : X0]: (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ Y0 @ X1)))))) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f1258])).
% 2.87/1.90 thf(f1258,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = ((^[Y0 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ Y1 @ Y0))))) @ X1))) )),
% 2.87/1.90 inference(pi_clausification,[status(thm)],[f1086])).
% 2.87/1.90 thf(f1086,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (((!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ Y1 @ Y0)))))) = $true)) )),
% 2.87/1.90 inference(cnf_transformation,[status(thm)],[f858])).
% 2.87/1.90 thf(f858,plain,(
% 2.87/1.90 ! [X0 : $tType] : ((!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ Y1 @ Y0)))))) = $true)),
% 2.87/1.90 inference(closure,[status(thm)],[f398])).
% 2.87/1.90 thf(f398,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (((!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ Y1 @ Y0)))))) = $true)) )),
% 2.87/1.90 inference(fool_elimination,[status(thm)],[f397])).
% 2.87/1.90 thf(f397,plain,(
% 2.87/1.90 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0] : (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2))),
% 2.87/1.90 inference(rectify,[status(thm)],[f2])).
% 2.87/1.90 thf(f2,axiom,(
% 2.87/1.90 ! [X0 : $tType,X2 : X0,X3 : coinductive_llist @ X0] : (ord_less @ coinductive_llist @ X0 @ coinductive_LNil @ X0 @ (coinductive_LCons @ X0 @ X2 @ X3))),
% 2.87/1.90 file('/export/starexec/sandbox/tmp/tmp.3Q38gBiG4C/DTF2THF_5656.p',fact_1_LNil__less__LCons)).
% 2.87/1.90 thf(f2691,plain,(
% 2.87/1.90 ((ord_less @ coinductive_llist @ a @ coinductive_LNil @ a @ r) = $false)),
% 2.87/1.90 inference(trivial_inequality_removal,[status(thm)],[f2690])).
% 2.87/1.90 thf(f2690,plain,(
% 2.87/1.90 ($true = $false) | ((ord_less @ coinductive_llist @ a @ coinductive_LNil @ a @ r) = $false)),
% 2.87/1.90 inference(forward_demodulation,[status(thm)],[f2673,f1018])).
% 2.87/1.90 thf(f2673,plain,(
% 2.87/1.90 ((ord_less @ coinductive_llist @ a @ coinductive_LNil @ a @ r) = $false) | ((order @ coinductive_llist @ a @ type2 @ coinductive_llist @ a) = $false)),
% 2.87/1.90 inference(trivial_inequality_removal,[status(thm)],[f2665])).
% 2.87/1.90 thf(f2665,plain,(
% 2.87/1.90 ((ord_less @ coinductive_llist @ a @ coinductive_LNil @ a @ r) = $false) | ((order @ coinductive_llist @ a @ type2 @ coinductive_llist @ a) = $false) | ($true = $false)),
% 2.87/1.90 inference(superposition,[status(thm)],[f1808,f1177])).
% 2.87/1.90 thf(f1177,plain,(
% 2.87/1.90 ((ord_less @ coinductive_llist @ a @ r @ coinductive_LNil @ a) = $true)),
% 2.87/1.90 inference(boolean_simplification,[status(thm)],[f1105])).
% 2.87/1.90 thf(f1105,plain,(
% 2.87/1.90 ($true = (~ (~ (ord_less @ coinductive_llist @ a @ r @ coinductive_LNil @ a))))),
% 2.87/1.90 inference(cnf_transformation,[status(thm)],[f767])).
% 2.87/1.90 thf(f767,plain,(
% 2.87/1.90 ($true = (~ (~ (ord_less @ coinductive_llist @ a @ r @ coinductive_LNil @ a))))),
% 2.87/1.90 inference(fool_elimination,[status(thm)],[f766])).
% 2.87/1.90 thf(f766,plain,(
% 2.87/1.90 ~~(ord_less @ coinductive_llist @ a @ r @ coinductive_LNil @ a)),
% 2.87/1.90 inference(rectify,[status(thm)],[f287])).
% 2.87/1.90 thf(f287,negated_conjecture,(
% 2.87/1.90 ~~(ord_less @ coinductive_llist @ a @ r @ coinductive_LNil @ a)),
% 2.87/1.90 inference(negated_conjecture,[status(cth)],[f286])).
% 2.87/1.90 thf(f286,conjecture,(
% 2.87/1.90 ~(ord_less @ coinductive_llist @ a @ r @ coinductive_LNil @ a)),
% 2.87/1.90 file('/export/starexec/sandbox/tmp/tmp.3Q38gBiG4C/DTF2THF_5656.p',conj_0)).
% 2.87/1.90 thf(f1808,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($false = (ord_less @ X0 @ X1 @ X2)) | ((order @ X0 @ type2 @ X0) = $false) | ((ord_less @ X0 @ X2 @ X1) = $false)) )),
% 2.87/1.90 inference(not_proxy_clausification,[status(thm)],[f1807])).
% 2.87/1.90 thf(f1807,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = (~ (ord_less @ X0 @ X1 @ X2))) | ((order @ X0 @ type2 @ X0) = $false) | ((ord_less @ X0 @ X2 @ X1) = $false)) )),
% 2.87/1.90 inference(binary_proxy_clausification,[status(thm)],[f1806])).
% 2.87/1.90 thf(f1806,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((order @ X0 @ type2 @ X0) = $false) | ($true = ((ord_less @ X0 @ X2 @ X1) => (~ (ord_less @ X0 @ X1 @ X2))))) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f1805])).
% 2.87/1.90 thf(f1805,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((order @ X0 @ type2 @ X0) = $false) | ($true = ((^[Y0 : X0]: ((ord_less @ X0 @ Y0 @ X1) => (~ (ord_less @ X0 @ X1 @ Y0)))) @ X2))) )),
% 2.87/1.90 inference(pi_clausification,[status(thm)],[f1804])).
% 2.87/1.90 thf(f1804,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : X0] : (($true = (!! @ X0 @ (^[Y0 : X0]: ((ord_less @ X0 @ Y0 @ X1) => (~ (ord_less @ X0 @ X1 @ Y0)))))) | ((order @ X0 @ type2 @ X0) = $false)) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f1803])).
% 2.87/1.90 thf(f1803,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : X0] : (($true = ((^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (ord_less @ X0 @ Y0 @ Y1)))))) @ X1)) | ((order @ X0 @ type2 @ X0) = $false)) )),
% 2.87/1.90 inference(pi_clausification,[status(thm)],[f1802])).
% 2.87/1.90 thf(f1802,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (($true = (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (ord_less @ X0 @ Y0 @ Y1)))))))) | ((order @ X0 @ type2 @ X0) = $false)) )),
% 2.87/1.90 inference(binary_proxy_clausification,[status(thm)],[f1061])).
% 2.87/1.90 thf(f1061,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (($true = ((order @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (ord_less @ X0 @ Y0 @ Y1)))))))))) )),
% 2.87/1.90 inference(cnf_transformation,[status(thm)],[f980])).
% 2.87/1.90 thf(f980,plain,(
% 2.87/1.90 ! [X0 : $tType] : ($true = ((order @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (ord_less @ X0 @ Y0 @ Y1)))))))))),
% 2.87/1.90 inference(closure,[status(thm)],[f679])).
% 2.87/1.90 thf(f679,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (($true = ((order @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (ord_less @ X0 @ Y0 @ Y1)))))))))) )),
% 2.87/1.90 inference(fool_elimination,[status(thm)],[f678])).
% 2.87/1.90 thf(f678,plain,(
% 2.87/1.90 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : ((ord_less @ X0 @ X1 @ X2) => ~(ord_less @ X0 @ X2 @ X1)))),
% 2.87/1.90 inference(rectify,[status(thm)],[f122])).
% 2.87/1.90 thf(f122,axiom,(
% 2.87/1.90 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X2 : X0,X50 : X0] : ((ord_less @ X0 @ X2 @ X50) => ~(ord_less @ X0 @ X50 @ X2)))),
% 2.87/1.90 file('/export/starexec/sandbox/tmp/tmp.3Q38gBiG4C/DTF2THF_5656.p',fact_121_order_Oasym)).
% 2.87/1.90 thf(f2570,plain,(
% 2.87/1.90 (r != coinductive_LNil @ a) | ((order @ coinductive_llist @ a @ type2 @ coinductive_llist @ a) = $false)),
% 2.87/1.90 inference(trivial_inequality_removal,[status(thm)],[f2569])).
% 2.87/1.90 thf(f2569,plain,(
% 2.87/1.90 ((order @ coinductive_llist @ a @ type2 @ coinductive_llist @ a) = $false) | ($true = $false) | (r != coinductive_LNil @ a)),
% 2.87/1.90 inference(superposition,[status(thm)],[f1177,f1199])).
% 2.87/1.90 thf(f1199,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((ord_less @ X0 @ X2 @ X1) = $false) | ((order @ X0 @ type2 @ X0) = $false) | (X1 != X2)) )),
% 2.87/1.90 inference(equality_proxy_clausification,[status(thm)],[f1198])).
% 2.87/1.90 thf(f1198,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((X2 = X1) = $false) | ((ord_less @ X0 @ X2 @ X1) = $false) | ((order @ X0 @ type2 @ X0) = $false)) )),
% 2.87/1.90 inference(not_proxy_clausification,[status(thm)],[f1197])).
% 2.87/1.90 thf(f1197,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = (~ (X2 = X1))) | ((order @ X0 @ type2 @ X0) = $false) | ((ord_less @ X0 @ X2 @ X1) = $false)) )),
% 2.87/1.90 inference(binary_proxy_clausification,[status(thm)],[f1196])).
% 2.87/1.90 thf(f1196,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = ((ord_less @ X0 @ X2 @ X1) => (~ (X2 = X1)))) | ((order @ X0 @ type2 @ X0) = $false)) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f1195])).
% 2.87/1.90 thf(f1195,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = ((^[Y0 : X0]: ((ord_less @ X0 @ Y0 @ X1) => (~ (Y0 = X1)))) @ X2)) | ((order @ X0 @ type2 @ X0) = $false)) )),
% 2.87/1.90 inference(pi_clausification,[status(thm)],[f1194])).
% 2.87/1.90 thf(f1194,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : X0] : (((order @ X0 @ type2 @ X0) = $false) | ($true = (!! @ X0 @ (^[Y0 : X0]: ((ord_less @ X0 @ Y0 @ X1) => (~ (Y0 = X1))))))) )),
% 2.87/1.90 inference(beta_eta_normalization,[status(thm)],[f1193])).
% 2.87/1.90 thf(f1193,plain,(
% 2.87/1.90 ( ! [X0 : $tType,X1 : X0] : (($true = ((^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))) @ X1)) | ((order @ X0 @ type2 @ X0) = $false)) )),
% 2.87/1.90 inference(pi_clausification,[status(thm)],[f1192])).
% 2.87/1.90 thf(f1192,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (($true = (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))))) | ((order @ X0 @ type2 @ X0) = $false)) )),
% 2.87/1.90 inference(binary_proxy_clausification,[status(thm)],[f1092])).
% 2.87/1.90 thf(f1092,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (($true = ((order @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))))))) )),
% 2.87/1.90 inference(cnf_transformation,[status(thm)],[f983])).
% 2.87/1.90 thf(f983,plain,(
% 2.87/1.90 ! [X0 : $tType] : ($true = ((order @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))))))),
% 2.87/1.90 inference(closure,[status(thm)],[f612])).
% 2.87/1.90 thf(f612,plain,(
% 2.87/1.90 ( ! [X0 : $tType] : (($true = ((order @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))))))) )),
% 2.87/1.90 inference(fool_elimination,[status(thm)],[f611])).
% 2.87/1.90 thf(f611,plain,(
% 2.87/1.90 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : ((ord_less @ X0 @ X1 @ X2) => (X1 != X2)))),
% 2.87/1.90 inference(rectify,[status(thm)],[f133])).
% 2.87/1.90 thf(f133,axiom,(
% 2.87/1.90 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X31 : X0,X15 : X0] : ((ord_less @ X0 @ X31 @ X15) => (X15 != X31)))),
% 2.87/1.90 file('/export/starexec/sandbox/tmp/tmp.3Q38gBiG4C/DTF2THF_5656.p',fact_132_less__imp__not__eq)).
% 2.87/1.90 % SZS output end Proof for DTF2THF_5656
% 2.87/1.90 % (5783)------------------------------
% 2.87/1.90 % (5783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.90 % (5783)Termination reason: Refutation
% 2.87/1.90
% 2.87/1.90 % (5783)Memory used [KB]: 7547
% 2.87/1.90 % (5783)Time elapsed: 0.149 s
% 2.87/1.90 % (5783)Instructions burned: 258 (million)
% 2.87/1.90 % (5783)------------------------------
% 2.87/1.90 % (5783)------------------------------
% 2.87/1.90 % (5755)Success in time 0.249 s
%------------------------------------------------------------------------------